JP3627066B2 - Panorama projection method and panorama projection apparatus - Google Patents

Description

（１０）式のようになる。
【００８８】
ここで以下のような置き換えを導入する。
ｃ_１ａ_２−ｃ_２ａ_１＝ｔ_１
ｃ_１ｂ_２−ｃ_２ｂ_１＝ｔ_２
ｃ_１ ^２＋ａ_１ ^２＝ｔ_３
ａ_１ ^２＋ｂ_１ ^２＝ｔ_４
そうすると、（１０）式は次のようになる。
（ｔ_１ｕ＋ｔ_２）^２＝ｋ（ｔ_３ｕ^２＋２ａ_１ｂ_１ｕ＋ｔ^２）
これを整理すると、以下のようになる。
（ｔ_１ ^２−ｋｔ_３）ｕ_２ ^２＋２（ｔ_１ｔ_２−ａ_１ｂ_１ｋ）ｕ＋（ｔ_２ ^２−ｋｔ_４）＝０
この式から、ｕは以下のようにして求められる。

（１１）式のｕを用いると、（９）式のｖが求められる。さらに、（４），（５），（６）を用いて、Ｓ’（ｘ，ｙ，ｚ）が得られる。
【００８９】
複数の断層像２３についてはｄ_０が異なり、複数のｄ_０に対してＳ’が得られる。異なる視点ｅ（ｘ１，ｙ１，ｚ）についても、同様に、異なる（ｘ，ｙ，ｚ）が得られる。
【００９０】
一方、θが与えられると、（４），（５），（６）式から各断層像上の通過点の座標が得られ、その近傍の輪郭点の投影データが得られる。断層像が複数あるので、輪郭点が複数存在することもある。θが与えられると、これら複数の輪郭点は同じ位置として円柱投影面２１に投影されるが、視点の遠いところから表示メモリに書き込むと、視点に一番近い投影像が見える。
【００９１】
このようにして、視点ｅを視直線Ｖ軸上で表示する長さの部分だけ動かし、各視点ｅにおいて角度θを０から±９０度変えると、三次元投影像が円柱投影面２１上に得られる。この投影像をパノラマ変換により２次投影平面４に変換し、対応する画像表示メモリ５３に書き込み、ＣＲＴモニタ５４に表示する。
【００９２】
陰影変換は、２次投影平面４上で実行する。この陰影変換には、視直線Ｖからの距離に応じて濃淡を着ける方法、視直線に直交する各個別平面内での投影直線とのなす角度に応じて輝度変換する方法、視直線Ｖからの距離に応じて等高線のように輝度を変換する方法等が考えられる。
【００９３】
本実施例の直線パノラマ投影方法によれば、血管壁，腸壁などの管状の投影対象を投影する際に、直線または曲線に沿って切り開かれたパノラマ写真のように、ゆがみが少なくパノラマ状の広い視野が得られる。
【００９４】
《曲線パノラマ投影方法》
図１２は、本発明による曲線パノラマ投影方法の一実施例の手順を示すフローチャートである。本実施例の曲線パノラマ投影方法を適用すべきハードウエアの構成は、上記直線パノラマ投影方法を適用すべきハードウエアの構成と変わらないので、その説明を省略する。
【００９５】
ステップ２０１：本発明による曲線パノラマ投影方法においては、マウス，トラックボール等のポインティングデバイスを用いて、曲がった管状の投影対象に対して、管を通るように適当な任意の視曲線を引く。この視曲線には、視点が分布する。
ステップ２０２：視曲線の任意の点を決め、その点に接線を引き、その接線を中心軸とした短かい円柱投影面を仮定する。
ステップ２０３：上記短円柱投影面を投影曲面として曲線パノラマ投影方法により、短い範囲の物体を投影する。この投影方法は、まず直線投影（平行投影と中心投影を組み合わせた投影方法）方法により円柱投影面からなる投影面（円柱投影面：後述パノラマ変換による補正前の投影平面）へ投影するものである。
ステップ２０４：その投影後に、前記複数の投影曲面の結果を、２次投影平面に後述のパノラマ変換により展開し、それらを直線上に並べ、前記投影対象の投影像を得るものである。
【００９６】
ここでパノラマ変換とは、投影対象を円柱状の投影曲面に投影し、円柱投影面を平面に展開し、投影対象を２次投影平面に投影する処理をいう。
【００９７】
すなわち本発明では、前記円柱投影面を投影面として曲線投影したあと、その投影画像を投影平面に展開する。この場合、投影面である半円柱投影面上に分布した各点と、ＣＲＴの表示画素のアドレスとを対応させ、パノラマ画像表示の効果を投影平面（ＣＲＴ画面）上で得る。
【００９８】
次に、図１３〜図１７を参照して上記発明方法のパノラマ変換の原理について説明する。
【００９９】
図１３は、曲線パノラマ投影方法において、視曲線の接線が中心軸と一致する円柱投影面の投影像を曲線パノラマ変換により平面に展開し、ゆがみを少なくしながら広視野化する原理を説明する図である。図１３において、短円柱投影面２１は、視曲線Ｃ上の視点ｅに中心を持ち、視点ｅを通る接線Ｖを中心軸とする円柱投影面である。ここでは、接線Ｖの方向をｘ軸に平行に設定してある。また、平面４は、座標（ｘ，ｙ，ｚ）の原点Ｏに接し、原点Ｏおいてｚ軸に垂直な２次投影平面であり、パノラマ変換による補正後の投影平面としての２次投影平面である。この投影平面４は、ＣＲＴの表示画面に相当する。
【０１００】
図１３において、ｘ，ｙ，ｚは三次元座標系の各軸、Ｏは三次元座標系の原点、ｅは曲線Ｃ上の視点、Ｃは視点ｅが連続的に分布する空間曲線すなわち視曲線、Ｖは視点ｅにおける曲線Ｃの接線、Ｒは円柱投影面２１の半径である。半径Ｒは、また、視曲線Ｃと投影平面４との距離でもある。ＱはＣから発した光線による円柱投影面上の点（ｘ_１，θ）、Ｐは２次投影平面４上の点（η_１，ξ_１）、Θは視点ｅから円弧全体を見込む角度、θはＱ点とＶ軸を結んだ線とＺ軸のなす角、ｄθは１８０度をＮ等分した単位角度、Ｌは円柱投影面２１上の円弧ＯＱ、Ｌ’はＬと同じ長さを持ったｙ軸上の直線ＯＰ、η_１はＰ点に対応するＣＲＴ上のＸ座標、ξ_１はＰ点に対応するＣＲＴ上のＹ座標である。
【０１０１】
図１４は、図１３の原理において、円柱投影面の中心角が１８０度である場合の曲線パノラマ変換を説明する図である。
【０１０２】
図１３において、ｘ＝０におけるｙ−ｚ平面に着目すると、図１４となる。
【０１０３】
図１４において、視曲線Ｃに直交する平面（任意のｙ−ｚ平面）間は独立であり、各々の面内で投影計算を行えばよい。このため、ｘ＝０におけるｙ−ｚ平面に着目すると、図１４となる。図１４で、半円弧Ιの１８０度の角度を等角度で分割し、それを横軸（ｙ軸）方向表示画素に対応させる。半円弧Ιの円周を等間隔に分割し、表示画素に対応させると考えてもよい。
【０１０４】
図１５は、図１３の原理において、円柱投影面の中心角が１８０度よりも大きい場合の曲線パノラマ変換を説明する図である。図１５は円弧Ι全体を視点ｅから見込む角度Θが１８０度より大きい場合の分割の例であるが、この場合でも式は変わらない。
【０１０５】
図１４で、角度ＱｅＯをθ，１画素あたりの角度をｄθ，ＮをＣＲＴ上の横
（Ｘ軸）方向表示画素数（例：５１２），ｎを任意位置を表す画素数とすると、次の式が成り立つ。
ｄθ＝Θ／Ｎ＝π／Ｎ
Ｌ’＝Ｌ
ξ_１＝ＯＱ_１＝Ｌ＝Ｒ・ｎｄθ＝π・ｎ・Ｒ／Ｎ
η_１＝ｘ_１（紙面に垂直）
ただし、図１３で、Θは視曲線Ｃから半円弧全体を見込む角度、ｄθ、θはラジアン単位で表現する。Ｑは投影平面４上のＰ点に対応する円柱投影面２１上の点、θはＱ点とＶ軸を結んだ線とｚ軸とのなす角、Ｌは円柱投影面２１上の円弧の長さ、Ｌ’はＬと同じ長さを持った線分であり、ｙ軸上の直線ＯＰである。
【０１０６】
ここでＯＡ＝π・Ｒ／２、ＯＡの２倍の長さの範囲をＣＲＴ画面の横（Ｘ軸）の表示の長さに対応させる。縦（Ｙ軸：紙面に垂直な方向）はＣＲＴ画面の画素数により決める。
【０１０７】
図１６は、曲線パノラマ投影方法において、視曲線が外側にある円柱投影面の投影像を曲線パノラマ変換により平面に展開し、ゆがみを少なくしながら広視野化する原理を説明する図である。図１６は、視曲線Ｃと円柱投影面２１との距離が円柱の半径よりも大きい場合である。
【０１０８】
図１７は、図１６の原理において、円柱投影面の中心角が１８０度である場合の曲線パノラマ変換を説明する図である。すなわち、図１６で、ｘ＝０におけるｙ−ｚ平面に着目すると、図１７となる。図１７で直線Ｐｅと円柱投影面との交点Ｑのｙ−ｚ平面上での座標は、ｙ軸上の点Ｐとｅを結ぶ直線とｚ軸上の原点から距離Ｒの点Ｏ’を中心とする半径Ｒの円周との交点Ｑとなる。
【０１０９】
図１６および図１７において、ｘ，ｙ，ｚは三次元座標系の各軸、Ｏは三次元座標系の原点、ｅは視点、Ｃは視点ｅが連続的に分布する視曲線、ｈは視点ｅと投影平面４との距離、Ｒは円柱投影面２１の半径、Ｐは投影平面４上の点（Ｘ_１，Ｙ_１）、Θは視点ｅから円弧全体を見込む角度、Ｐ_１は円柱投影面２１上の点Ｑ_１に対応する２次投影平面４上の点、θはＱ点とＶ軸を結んだ線とｚ軸のなす角、ｄθは角度ΘをＮ等分した単位角度、Ｌは円柱投影面２１上の円弧ＯＱ_１の長さ、Ｌ’はＬと同じ長さを持った線分でｙ軸上の直線の長さＯＰ_１である。
【０１１０】
図１７において、角度ＱＯ’Ｏをφ，角度ｅＱＯ’をωとすると、次の式が成り立つ。
φ＝ω＋θ
Ｒ／ｓｉｎθ＝（ｈ−Ｒ）／ｓｉｎω
これら２つの式から以下のようにして、η_１，ξ_１が求められる。
ω＝ｓｉｎ￣ ^１［｛（ｈ−Ｒ）ｓｉｎθ｝／Ｒ］
ｄθ＝Θ／Ｎ
θ＝ｎ・ｄθ ＝ｎ・Θ／Ｎ
Ｌ’＝Ｌ
ゆえに
ξ_１＝Ｒ・φ＝Ｒ（ω＋θ）
η_１＝Ｌ
この、η_１，ξ_１が表示メモリ上の画素アドレスとなる。すなわち、２次投影平面４の点Ｐは、ＣＲＴ画面上では点（η_１，ξ_１）に表示され、パノラマ変換が実行されたことになる。
【０１１１】
次に、図１８〜２３を参照して、曲線パノラマ投影方法により、複数の断層像から、三次元画像を構成する手順を説明する。なお、図１９〜２３のいずれにおいても、最初に円柱投影面２１上に断層像を投影し、次にパノラマ変換により投影像を展開して投影平面４に変換する。
【０１１２】
図１８は、曲線パノラマ投影方法により、複数の断層像から三次元画像の構成する際に、断層像の画素座標を投影面の画素座標に変換する原理を説明する図である。図１８に示す例では、説明を簡単にするため、円柱投影面２１の中心軸３１と断層像面２３とが平行であり、さらにｘ−ｙ平面Ｔが平行であるように、三次元座標系を定めてある。また、円柱投影面２１の中心線はｘ軸と平行である。図１８において、ｘ，ｙ，ｚは三次元座標系（ｘ，ｙ，ｚ）の各軸、ｅ点（０，０，Ｒ）は視曲線Ｃ上の任意の視点ｅの位置、Ｖは視点ｅにおける曲線Ｃの接線、Ｑ点（ｘ，ｙ，ｚ）は円柱投影面２１上の点、Ｓ点（ｘ_０，ｙ_０，ｚ_０）はｅ点（０，０，Ｒ）とＱ点（ｘ，ｙ，ｚ）とを結ぶ直線２２と断層像２３Ａとが交わる点、Ｒは視点ｅのｚ座標である。
【０１１３】
ここで、直線２２は、視点ｅから視曲線Ｃのｅ点における接線Ｖに対して直角に引く。また、ｄ_０は断層像２３Ａのｚ軸上の位置であり、計算時に決まる。
【０１１４】
図１８において、各視点ｅに着目すれば、扇形の面をｚ軸方向に積み重ねたものとみなすことができる。つまり、扇形の面内で投影計算を実行し、それを積み重ねると、三次元画像を表示できる。
【０１１５】
図１９は、図１８の原理において、断層面と投影面とが平行である場合の曲線パノラマ変換を説明する図である。
【０１１６】
視点ｅを通る曲線Ｃのｅ点における接線Ｖに対してｅ点で直交する平面Ｂに着目する。図１９は、同様の座標系において、断層像２３Ａの他にも断層像２３Ｂ〜２３Ｈを用意し、ｘ軸方向から見た状態を示す。この図１９において、断層像２３Ａ〜２３Ｈは、同一対象物について同一方向に等間隔で得られた断層像であり、断層像２３には臓器領域Ｂ１，Ｂ２，Ｂ３，Ｂ４を強調して書いてある。曲線パノラマ変換により、まず、臓器領域Ｂ１，Ｂ２，Ｂ３，Ｂ４を円柱投影面２１に投影し、さらにそれをパノラマ変換して２次投影平面４に投影すると、Ｂ１’，Ｂ２’，Ｂ３’，Ｂ４’となる。なお、ここでは、等間隔の例を図示してあるが、必ずしも等間隔である必要はない。
【０１１７】
ここで投影データＢ１’，Ｂ２’，Ｂ３’，Ｂ４’を図示しない表示メモリに格納するときは、三次元的効果を出すために、視点ｅからみてより遠くに存在する投影データを先に書き込み、それより近くに存在する投影データは後のタイミングに先の投影データ上に上書きする。その後、陰影付け処理（シェーディング）を実行する。
【０１１８】
図２０は、図１８の原理において、断層面と投影面とが交差している場合の曲線パノラマ変換の原理を説明する図である。図２０は、図１９の例をより一般化し、円柱投影面と断層像面が平行でない例を示している。この場合には、断層像２３Ａ，２３Ｂ，．．．．．．．２３Ｈから、補間演算法により、投影面４と平行な面に向けられた断層像２３ａ，２３ｂ，２３ｃ，．．．．２３ｈを作っておく必要がある。その後の投影計算は、図１９の場合と同様である。
【０１１９】
図２１は、視曲線と断層面と投影面とがより複雑な位置関係にある場合の曲線パノラマ変換を説明する図である。断層像２３上のＳ点（ｘ_０，ｄ_０，ｚ_０）の投影結果が平面Ｔ上の点Ｐ（ｘ，ｙ，ｚ）になることを示す。
【０１２０】
図２１において、曲線パノラマ投影方法による断層像２３の円柱投影面２１への投影に際し、断層像２３の各画素座標の円柱投影面２１上の座標への変換は、次のように行われる。
【０１２１】
ここでは、一般性を失わないようにするために、位置関係を次のように設定する。図２１において、入力の断層像２３は、ｙ軸に垂直な面内にあり、原点からｄ_０の距離にある。複数の断層像は、原点からの距離ｄ_０が変わる。
【０１２２】
視曲線Ｃは、三次元空間の任意の曲線とする。ここで曲線Ｃ上の任意の視点ｅを決め、その点において曲線Ｃに接線Ｖを引く。まず、接線Ｖを中心軸とした円柱投影面２１を仮定する。視点ｅは曲線Ｃ上を移動するので、それにつれて接線Ｖおよびそれと対をなす円柱投影面２１も三次元空間（ｘ，ｙ，ｚ）内を移動していく。ただし、断層像２３は三次元空間（ｘ，ｙ，ｚ）に固定されている。
【０１２３】
次に、接線Ｖ上の視点ｅから、半円柱投影面の中央線Ｃｖに垂線ｈを下ろす。垂線ｈは、トラックボールやマウス等のポインティングデバイスを用いてオペレータが決める。
【０１２４】
半投影面の中央線Ｃｖに接する平面Ｔを仮定する。この平面Ｔが２次投影平面４となる。平面Ｔも視点ｅと共に移動する。
【０１２５】
図２２は、図２１において、三次元空間の視曲線Ｃと視点ｅにおける接線Ｖとの関係を示す図である。
【０１２６】
ここで実際の計算においては、視曲線Ｃ上の視点ｅ（ｘ_１，ｙ_１，ｚ_１）と、視曲線Ｃ上で視点ｅから微小距離Δｓだけ離れた点をｅｓ（ｘｓ，ｙｓ，ｚｓ）とする。ここで、任意に与えられた視曲線Ｃは十分滑らかに変化しているものと仮定する。この曲線は、数式で与えてもよいが、マウスやトラックボール等で与える方が簡便である。マウスやトラックボール等で与えた軌跡を２次曲線で近似したり、局所的に短い直線で近似し、この曲線全体を折れ線近似してもよい。
【０１２７】
ベクトルｅ→ｅｓのｘ，ｙ，ｚ方向の変化分をΔｘ，Δｙ，Δｚとし、ａ_１，ｂ_１，ｃ_１を次のように定義する。
ａ_１＝Δｘ，ｂ_１＝Δｙ，ｃ_１＝Δｚ
そうすると、曲線Ｃ上の点ｅ（ｘ_１，ｙ_１，ｚ_１）における接線Ｖは、係数ａ ，ｂ ，ｃ を用いて次の式で近似できる。
（ｘ−ｘ_１）／ａ_１＝（ｙ−ｙ_１）／ｂ_１＝（ｚ−ｚ_１）／ｃ_１ ……（１２）
視曲線Ｃと視点ｅとを決めると、Ｖが決まるので、ａ_１，ｂ_１，ｃ_１，ｘ_１，ｙ_１，ｚ_１が決まる。また、トラックボール，マウス等により視点ｅの方向を与える方向ベクトルのパラメータａ_２，ｂ_２，ｃ_２も与えられる。
【０１２８】
上述のように視点ｅ（ｘ_１，ｙ_１，ｚ_１）を通り、接線Ｖに直交し、方向がａ_２，ｂ_２，ｃ_２の直線ｈを決めると、Ｖとｈとの直交条件から、次式が成り立つ。
ａ_１ａ_２＋ｂ_１ｂ_２＋ｃ_１ｃ_２＝０
また、直線ｈの式は次のようになる。
【０１２９】
（ｘ−ｘ_１）／ａ_２＝（ｙ−ｙ_１）／ｂ_２＝（ｚ−ｚ_１）／ｃ_２ ……（１３）
ここで、ａ_２，ｂ_２，ｃ_２，ｘ_１，ｙ_１，ｚ_１は決まっている。また、ｈ＝Ｒである。したがって、直線ｈと断層像２３（ｙ_１＝ｄ_０）との交点は、直線ｈの式でｙ＝ｄ_０と置くと、次式で与えられる。
（ｘ−ｘ_１）／ａ_２＝（ｄ_０−ｙ_１）／ｂ_２＝（ｚ−ｚ_１）／ｃ_２
（ｘ−ｘ_１）＝ａ_２（ｄ_０−ｙ_１）／ｂ_２
（ｚ−ｚ_１）＝ｃ_２（ｄ_０−ｙ_１）／ｂ_２
∴ｘ＝ａ_２（ｄ_０−ｙ_１）／ｂ_２＋ｘ_１
ｙ＝ｄ_０
ｚ＝ｃ_２（ｄ_０−ｙ_１）／ｂ_２＋ｚ_１
この座標は、断層像２３との交点の座標であり、ｄ_０が変われば、この座標も変わる。
【０１３０】
Ｖ軸を中心として直線ｈを角度θだけ回転させた直線ｈ’を仮定すると、ｈ’も接線Ｖと直交して、点ｅ（ｘ_１，ｙ_１，ｚ_１）を通る。さらに、断層像２３（ｙ＝ｄ_０）とも交差する。このため、直線ｈ’は（１４）式で与えられる。
（ｘ−ｘ_１）／ａ_３＝（ｄ_０−ｙ_１）／ｂ_３＝（ｚ−ｚ_１）／ｃ_３ ……（１４）
ここでａ_３，ｂ_３，ｃ_３は直線ｈ’の方向ベクトルのパラメータである。
【０１３１】
（１４）式から、直線ｈ’と断層像２３との交点Ｓ’（ｘ，ｙ，ｚ）の座標は、（１５）〜（１７）式で求められる。
ｘ＝ａ_３（ｄ_０−ｙ_１）／ｂ_３＋ｘ ……（１５）
ｙ＝ｄ_０ ……（１６）
ｚ＝ｃ_３（ｄ_０−ｙ_１）／ｂ_３＋ｚ ……（１７）
さらに接線Ｖと直線ｈ，接線Ｖと直線ｈ’の直交条件から、パラメータａ_１，ｂ_１，ｃ_１，ａ_２，ｂ_２，ｃ _２ａ_３，ｂ_３，ｃ_３の間には以下の条件が成り立つ。
ａ_１ａ_３＋ｂ_１ｂ_３＋ｃ_１ｃ_３＝０
ｃｏｓθ＝｜ａ_２ａ_３＋ｂ_２ｂ_３＋ｃ_２ｃ_３｜／√（Ｔ_２×Ｔ_３）
ただし、Ｔ_２，Ｔ_３は次のようにおいた。
Ｔ_２＝ａ_２ ^２＋ｂ_２ ^２＋ｃ_２ ^２
Ｔ_３＝ａ_３ ^２＋ｂ_３ ^２＋ｃ_３ ^２
そうすると、
（ａ_２ａ_３＋ｂ_２ｂ_３＋ｃ_２ｃ_３）^２＝Ｔ_２Ｔ_３・ｃｏｓ^２θ ……（１８）
ここで、
Ｔ_２・ｃｏｓ^２θ＝ｋ
とおくと、（１８）式は（１９）式のようになる。
（ａ_２ａ_３＋ｂ_２ｂ_３＋ｃ_２ｃ_３）^２＝ｋ（ａ_３ ^２＋ｂ_３ ^２＋ｃ_３ ^３） ……（１９）
両辺をｂ_３ ^２で割ると、（２０）式のようになる。
（ａ_１ａ_３／ｂ_３＋ｂ_１＋ｃ_１ｃ_３／ｂ_３）^２＝ｋ（ａ_３ ^２＋１＋ｃ_３ ^２） ……（２０）
また、ａ_１ａ_３＋ｂ_１ｂ_３＋ｃ_１ｃ_３＝０の両辺をｂ_３で割ると、次のようになる。
ａ_１ａ_３／ｂ_３＋ｂ_１＋ｃ_１ｃ_３／ｂ_３＝０
ここで、
ａ_３／ｂ_３＝ｍ
ｃ_３／ｂ_３＝ｎ
と置くと、次の式が成り立つ。
ａ_１ｍ＋ｂ_１＋ｃ_１ｎ＝０
ｎ＝−（ａ_１ｍ＋ｂ_１）／ｃ_１ ……（２１）
（２１）式のｎを（２０）式に代入し、ｍについて解くと、（２２）式のようになる。

ここで、以下のような置き換えを導入する。
ｃ_１ａ_１−ｃ_２ａ_１＝ｔ_１
ｃ_１ｂ_２−ｃ_２ｂ_１＝ｔ_２
ｃ_１ ^２＋ａ_１ ^２＝ｔ_３
ａ_１ ^２＋ｂ_１ ^２＝ｔ_４
そうすると、（２２）式は次のようになる。
（ｔ_１ｍ＋ｔ_２）^２＝ｋ（ｔ_３ｍ ＋２ａ_１ｂ_１ｍ＋ｔ_４）
これを整理すると、（２３）式のようになる。

この式から、ｍは（２４）式により求められる。

（２４）式のｍを用いると、（２１）式のｎが得られる。
【０１３２】
これらの値に基づいて、（１５），（１６），（１７）式を用いると、断層像２３上の交点Ｓ’（ｘ，ｙ，ｚ）が得られる。
【０１３３】
複数の断層像２３に対してはｄ_０が異なるので、複数のｄ_０に対して各々Ｓ’（ｘ，ｙ，ｚ）が得られる。異なる視点ｅ（ｘ_１，ｙ_１，ｚ_１）に対しても同様に異なるＳ’（ｘ，ｙ，ｚ）が得られる。
【０１３４】
一方、θが与えられると、（１５），（１６），（１７）式から、各断層像上の通過点の座標が求まり、その近傍の輪郭点の投影データが求められる。断層像は、複数あるから、輪郭点が複数存在することもある。θが与えられると、これら複数の輪郭点は、同じ位置として円柱投影面２１に投影されるが、視点の遠いところから表示メモリに書き込むようにすれば、視点に一番近い投影像が見える。
【０１３５】
視点ｅからの距離は次のようにして求められる。与えられた視点ｅから任意平面２３上の任意の点Ｓ’までの距離ｅＳ’は、ＳおよびＳ’の座標を用いて、距離ｅＳとＳＳ’とにより、次の式で計算できる。
ｅＳ’＝√｛（ｅＳ）^２＋（ＳＳ’）^２｝ ……（２５）このｅＳ’を利用して視点ｅからの距離を定め、例えば陰影変換を実行する。
【０１３６】
視点ｅを視曲線Ｃ上で表示する長さの領域で少しずつ動かし、各視点ｅの位置において、角度θを０から例えば±９０度または±１８０度の範囲で変えると、１次投影像が円柱投影面２１上に求められる。この投影像をパノラマ変換により２次投影平面４に変換し、対応する画像表示メモリに書き込むと、ＣＲＴに表示される。
【０１３７】
図２３は、２次投影平面上に曲線パノラマ変換された１次投影像の相互の関係を示す図である。長さδＶの円柱投影面２１に投影された１次投影像は、ｘ方向の幅Ｗを５１２点に対応させて画像メモリに書き込む。ｙ軸方向は長さδＶの投影像を曲線Ｃの長さの分だけ並べて５１２点に対応させる。
【０１３８】
陰影変換は、２次投影平面４上で実行する。陰影変換には、視曲線Ｃからの距離に応じて濃淡を着ける方法や、視曲線に直交する各個別平面内での投影直線とのなす角度に応じて輝度変換する方法や、視曲線Ｃからの距離に応じて等高線のように輝度変換する方法等が考えられる。
【０１３９】
《任意曲面を用いるパノラマ投影方法》
上記直線パノラマ投影方法の実施例では、円柱面へのパノラマ投影方法を取り扱ったが、図２４は、任意曲面へのパノラマ投影方法の手順を示すフローチャートである。
【０１４０】
ステップ３０１：任意曲面へのパノラマ投影方法においては、まず、三次元空間に置かれた被投影物体に対して、視点が分布する任意の直線Ｅを引く。ここでは直線の実施例を示すが、曲線であっても曲線上の各点における接線を仮定すれば、本実施例を適用できる。
ステップ３０２：上記直線に対してそれと平行な任意の曲面からなる投影面Ｔを仮定する。この投影面Ｔは平面であってもよい。
ステップ３０３：視直線Ｅの各点で視直線と直交する平面ｔを仮定する。
ステップ３０４：平面ｔと投影対象との交線を求める。また、上記投影面との交さ曲線Ｕを求める。
ステップ３０５：上記交線と交さ曲線Ｕをｘｙ平面に写像する。また、交さ曲線も写像する。
ステップ３０６：ｘｙ平面で投影処理を行う。
ステップ３０７：視直線上の視点を移動し、上記処理を３０３ステップから繰り返す。
ステップ３０８：視線上で必要な区間を計算したら結果を例えば陰影変換してＣＲＴに表示する。
【０１４１】
図２５および図２６を参照して、任意曲面への直線パノラマ変換の原理について説明する。
図２５において、Ｅは視点が連続的に分布する直線であり、ｘｙ平面に平行である。また、直線Ｅ上のｅｉ（ｅ_１，ｅ_２，ｅ_３）は各視点を表す。Ｓは三次元空間内の投影対象を表し、ｓ_１，ｓ_２はＳ内の点を表す。また、Ｔは投影対象を投影する平面であり、ｘｙ平面と同一である。この平面上に投影されたデータは、例えば陰影変換して、ＣＲＴに表示される。
【０１４２】
ここで、直線Ｅ上の各点ｅ_２において直線Ｅに垂直な平面ｔを考える。平面ｔ上の位置関係に着目すると、ｔはｅ_２，ｓ_２を含んでおり、平面ｔ上ではｅ_２を視点とし、ｘｙ平面上の交線Ｕ２を投影線とみなすことができるので、平面ｔ内で１つの投影計算を行う。Ｓ’は平面ｔによる投影対象Ｓの断面である。このような計算を直線Ｅ上の各点ｅｉについて行い、結果として、投影像がｘｙ平面上に得られる。
【０１４３】
図２５において、平面ｔに着目すると、図２６となる。図２６で点ｅ_２は、視線Ｅ上の視点である。また点Ｑは、投影対象Ｓ内の点Ｓ_２の直線Ｕ_２への投影である。図２６において、点Ｏから点Ｑまでの距離Ｌは次の式で表される。
【０１４４】
Ｌ＝ｈ・ｔａｎθ
図２７は、投影面Ｔが曲面の場合の例であり、投影線Ｕ_２は曲線となる。この場合でも考え方は同じであるが、投影面Ｔから平面Ｔ_２への写像が必要となる。この写像の方法には、曲面に沿った距離ＯＰ_１をそのまま直線ＯＱ_２に写像する方法や、平面に垂直に下し、直線ＯＱ_１として写像する方法が考えられる。
【０１４５】
曲線ＯＰ_１の長さは、曲線の関数ｆを用いて計算可能である。計算方法の詳細については、例えば、高木貞治著「解析概論」１３２頁〜１３９頁（１９６８年６月３０日改訂第三版、岩波書店発行）に述べられている。
【０１４６】
図２８〜３４は、複数の断層像から、曲線パノラマ投影方法により三次元画像を構成する方法を説明する。まず、上記三次元画像の構成方法において、曲線パノラマ投影による座標変換について述べる。投影面への各断層像の投影に当たって、各断層像の画素座標を投影面上の座標に変換する操作は、次のように行われる。
【０１４７】
図２８では、説明を簡単にするため、視点が分布する線Ｅは直線であり、さらにｘ軸に平行でｚ軸に交点をもち、断層像２３はｘｙ平面３０に平行であるように座標系をとっている。また、投影面Ｔは平面であり、ｘｙ平面に平行である。
【０１４８】
図２８において、視点ｅの位置は、視直線Ｅ上の任意の位置である。ｘ，ｙ，ｚは三次元座標系（ｘ，ｙ，ｚ）の各軸、ｅ点（ｘ，０，Ｒ）は視直線Ｅ上の任意の視点ｅの位置、Ｑ点（ｘ，ｙ，ｚ）は投影面２１上の点、Ｓ点（ｘ_０，ｙ_０，ｚ_０）はｅ点（ｘ，０，Ｒ）とＱ点（ｘ，ｙ，ｚ）とを結ぶ直線２２と断層像２３Ａとの交点、Ｒは視点ｅのｚ座標である。ここで、直線２２はｅ点から視直線Ｅに対して直角に引く。また、ｄ_０は断層像２３Ａの位置（ｚ軸上）であり、計算時に決まる。
【０１４９】
図２８において、各視点ｅに着目すれば、視点ｅを含み、視直線Ｅに直交する平面ｔを仮定し、その面をｚ軸方向に積み重ねたものといえる。すなわち、平面ｔ内での投影計算を行い、それを積み重ねると、３次元画像を表示できる。
【０１５０】
図２９は、任意方向への投影における本実施例の原理を表す図である。図２８で、３次元座標ｘｙｚの直交座標系において、一般性を失うことなく、複数の断層像２３をｚ軸に垂直におく。複数の断層像２３はお互いに平行であるとを仮定するが、平行でない場合は、三次元空間内での内挿計算により、平行な画像が容易に求められる。また、等間隔を仮定するが、原画像が等間隔でない場合も、内挿計算により、画像が容易に求められる。
【０１５１】
さらに、視点ｅが分布する任意の直線をＥとするが、直線Ｅはｚ軸と交わるように引く。このとき、直線Ｅのｘｙ平面への射影のｘ軸からの回転角をαとする。また、直線Ｅの、ｚ軸からの傾きをωとする。また、原点Ｏから、前記直線Ｅに平行な直線で、直線Ｅを含む平面に存在する直線ｗを引く。そうすると、ｗは、原点０からｘｙ平面でのｘ軸からの回転角がα、ｚ軸からの傾きがωである軸となる。また、ｗ軸の上で原点から距離ｄ_２のところでｗ軸に直交する平面ｔを仮定する。さらに、ｗ軸と視線Ｅとの距離をｈ_１とする。また、ｗ軸に平行でｗ軸から距離ｈ_２のところに投影平面Ｔを仮定する。平面ｔとｗ軸との交点をＯ’とする。投影平面Ｔは、平面ｔ上で視点ｅと０’を結ぶ直線に直交する。
【０１５２】
そうすると、視線Ｅに分布する視点からの投影は各平面ｔ内で考えればよい。すなわち、各平面ｔと複数の断層像２３との交線上の点を、視線Ｅと平面ｔとの交点を視点ｅとして、平面Ｔに投影していけばよい。
【０１５３】
図２８で、平面ｔと複数の断層像２３との交線を４０とし、交線のｘｙ平面への射影を４０’とする。また、Ｏ’のｘｙ平面への射影をＯ”とする。一方、投影平面Ｔと平面ｔの交線と、視点ｅと点Ｏ’とを結んだ直線との交点をＮ、そのｘｙ平面への射影をＮ’とする。また、ｗ軸のｘｙ平面への射影をｕ’、ｘｙ平面上にあり、原点Ｏを通り、直線ｕ’に直交する直線をｖ’とする。
【０１５４】
原点からｄ_１の距離の断層像２３の平面の方程式を（２６）で表す。このとき、複数の断層像に対しては、ｚの値が変わるだけである。
ｚ＝ｄ_１ ……（２６）
また、ｗ軸に直交し、原点Ｏから距離ｄ_２の平面ｔは（２７）式で表す。ただし、直線ＯＯ’と同じ向きの単位ベクトルをｗ（ｌ，ｍ，ｎ）とする。
ｌｘ＋ｍｙ＋ｎｚ＝ｄ_２ ……（２７）
ただし、ｌ，ｍ，ｎはω、αを用いて、次の式で与えられる。
ｌ＝ｓｉｎω・ｃｏｓα
ｍ＝ｓｉｎω・ｓｉｎα
ｎ＝ｃｏｓω
直線Ｅは、操作者がマウス，トラックボールなどで外部から与えるので、直線Ｅを与えると、係数ｌ，ｍ，ｎが決まる。
【０１５５】
図３０は、平面ｔに対して垂直に見た図である。図３０において、２３は複数の断層像、Ｔは投影平面である。平面ｔに対して垂直に見た場合、投影面Ｔは直線に見える。交線４０は平面ｔ上に分布し、その間隔ｄｌは、ｄｌ＝ｄ_１ｃｏｓｅｃωで与えられる。図３０を用いて、交線４０の式ともとのｘｙ平面における関係を説明する。
【０１５６】
まず、ｘｙｚ座標系による３次元空間における断層像２３と平面ｔの交線の式を求める。交線は断層像の数だけ存在する。ここで、（２６）式と（２７）式とで表される２つの平面の交線の方向ベクトルをｋ（ａ，ｂ，ｃ）とすると、ｋは（２６）、（２７）の法線ベクトルｇ_１（０，０，１）、ｇ_２（ｌ，ｍ，ｎ）とそれぞれ垂直であるから、（２８），（２９）式が成り立つ。
ｋｇ_１＝ ｃ＝０ ……（２８）
ｋｇ_２＝ｌａ＋ｍｂ＋ｎｃ＝０ ……（２９）
（２８），（２９）式から、方向ベクトルｋの方向比ａ：ｂ：ｃを、ｌ，ｍ，ｎを用いて求めると、（３０）式となる。
ａ：ｂ：ｃ＝−ｍ：ｌ：０ ……（３０）
交線は、これらａ，ｂ，ｃ（ｌ，ｍ，ｎ）を用いて、（６）式で与えられる。
（ｘ−ｘ_１）／−ｍ＝（ｙ−ｙ_１）／ｌ， ｚ＝ｄ_１ ……（３１）
ここでｙ_１を求めるために、ｘ_１＝０とおき、（２６），（２７）式からｙ_１を求める。
ｚ_１＝ｄ_１ ……（３２）
ｍｙ_１＋ｎｚ_１＝ｄ_２ ……（３３）
（３２）式から、ｚ_１＝ｄ_１を（３３）式に代入して、ｙ_１を求めると、（３４）式となる。
ｙ_１＝（−ｎｄ_１＋ｄ_２）／ｍ ……（３４）
すなわち、２つの平面１、２の交線である（３１）式は、次の（３５）式となる。
ｘ／−ｍ＝｛ｙ＋（ｎｄ_１−ｄ_２）／ｍ｝／ｌ， ｚ＝ｄ_１ ……（３５）
または、変形して（３６）式
ｌｘ＋ｍｙ＋（ｎｄ_１−ｄ_２）＝０， ｚ＝ｄ_１ ……（３６）
となる。
【０１５７】
図３１は、複数の断層像２３，ｗ軸と直交平面ｔ，投影平面Ｔ，視直線Ｅとの間の関係およびそれらのｘｙ平面への射影の関係を説明するため、直線Ｏｕ’を含むｘｙ平面に垂直な面で切断した図である。図３１で、ｖ軸は、（３６）式においてｄ_１＝ｄ_２・ｃｏｓωとおいた（３７）式で表される。
ｌｘ＋ｍｙ＋ｄ_２（ｎ・ｃｏｓω−１）＝０， ｚ＝ｄ_１ ……（３７）
原点Ｏ’のｘｙｚ座標系での座標は、（３８），（３９），（４０）式を用いて、（４１）〜（４３）式で与えられる。
ｚ＝ｄ_１ ……（３８）
ｙ＝ｘ・ｔａｎα ……（３９）
ｌｘ＋ｍｙ＝ｍｄ_２（ｎ・ｃｏｓω−１） ……（４０）
ｘ＝｛ｍｄ_２（ｎ・ｃｏｓω−１）｝／（ｌ＋ｔａｎα ） ……（４１）
ｙ＝｛ｍｄ_２（ｎ・ｃｏｓω−１）｝ｔａｎα／（ｌ＋ｔａｎα） ……（４２）
ｚ＝ｄ_１ ……（４３）
図３２は、図３１と同じ関係を表す図であり、複数の視点に対してｗ軸に直交する複数の平面ｔと投影平面Ｔとの関係を示す。図３２において、投影方向ＰｗとＰｕは平面ｔ上での投影であり、投影方向ＰｚとＰｘはＰｗとＰｕの関係をｘｙ平面に射影したときの投影方向である。すなわち、交線４０，視線Ｅ，投影平面Ｔ等の関係をそのままｘｙ平面に射影し、ｘｙ平面で投影計算を行えばよい。
【０１５８】
図３３は、ｚ軸の上方からｘｙ平面に射影した状態で、ｘｙ軸とｕ’ｖ’軸との関係を説明する図である。両者の関係は、ｘｙ平面において座標回転となる。
ｘｙ平面への射影変換では、平面ｔ上での交線の間隔ｄ_１をｘ−ｙ平面上に変換したときの間隔ｄｄは、（４４）式のようになる。さらに各断層像間の間隔ｄｚを用いて、（４５）式で表せる。
ｄｄ＝ｄ_１・ｃｏｓω ……（４４）
ｄｄ＝ｄｚ／ｔａｎω ……（４５）
また、（ｘａ，ｙａ）を通る直線の式は、次式で表される。
ｙ−ｙａ＝（ｙｉ−ｙａ）（ｘｉ−ｘａ）／（ｘｉ−ｘａ）
ｌｘ＋ｍｙ＋（ｎｄ_１−ｄ_２）＝０
図３４は、平面ｔ上の交線、平面ｔと投影面Ｔの交線、視点等をｘｙ平面に射影した関係を表す図である。
【０１５９】
ここで、ｘ−ｙ平面上での座標回転を考える。関数ｆ（ｘ，ｙ）＝０を原点の周りにαだけ回転して得られる関数の式は、次のようになる。
【０１６０】
ｆ（ｕ，ｖ）＝ｆ（ｘ・ｃｏｓα＋ｙ・ｓｉｎα，−ｘ・ｓｉｎα＋ｙ・ｓｉｎα）＝０
新しいｕ−ｖ軸と、もとのｘ−ｙ 軸との間には、次の（４６），（４７）式の関係が有る。
【０１６１】
ｘ＝ｕ・ｃｏｓα−ｖ・ｓｉｎα ……（４６）
ｙ＝ｕ・ｓｉｎα＋ｖ・ｃｏｓα ……（４７）
（４０）式に（４６），（４７）式のｘ，ｙを代入してｕ，ｖについて表すと、（４８）式になる。
【０１６２】
ｕ・ｓｉｎω＝（ｄ_２−ｎｄ_１）
ｕ＝（ｄ_２−ｎｄ_１）／ｓｉｎω＝（ｄ_２−ｄ_１・ｃｏｓω）／ｓｉｎω ……（４８）
すなわち、（３６）式から、断層像２３と平面ｔとの交線が求まる。次に（４８）式からｕ，ｖの座標を求める。実際には直線はｖ 軸に平行なため、ｖ＝一定となり、ｕのみを変える。次に、（４６），（４７）式により、逆にｘ，ｙの座標を計算して対応する断層像上の点Ｓを求めればよい。この時、対応する点Ｓに座標が一致しなければ、内挿計算により求めることができる。
【０１６３】
以上のことから、平面ｔ上での投影平面Ｔへの投影は、それらのｘｙ平面上への射影により考えることができる。このとき、視点ｅと投影平面Ｔとの距離は、ｃｏｓωだけ短縮されるが、全ての交線も短縮されるため、前記ｘｙ平面への射影像で計算しても、問題はない。
ここで、ｚ＝ｄ_１のときのｕ’は、次のようになる。
ｄ_１＝ｕ’・ｔａｎω＋ｄ_２／ｃｏｓω
したがって、
ｕ’＝（ｄ_１・ｃｏｓω−ｄ_２）／ｓｉｎω
図３５は、投影面が平面の場合の平面ｔ上の関係を、上からｘｙ平面に射影した図であり、投影計算を説明する図である。図３５で、Ｏは、ｘｙｚ軸およびｕ’ｖ’ｗ軸の原点、ｅ’は視点ｅのｘｙ平面への射影、Ｎ’はＮの射影である。ここで、断層像２３と平面ｔとの複数の交線複数のｘｙ平面への射影を２３’とする。また、投影面Ｔと平面ｔとの交線のｘｙ平面への射影を、Ｔ’とする。以下、各記号を図のように仮定する。交線２３’の上の点Ｓと視点の射影ｅ’を結んだ直線を延長し、直線Ｔ’との交点をＰとすれば、ＰがＳの投影点となる。
ｖ＝ｕ・ｔａｎθ−ｄｕ・ｔａｎθ
直線４０と、直線２３’の交点Ｓの座標：ｕ＝ｕｉとの交点のｖｉの座標は、上式にｕｉを代入して、次のようになる。
ｖｉ＝ｕｉ・ｔａｎθ−ｄｕ・ｔａｎθ
直線ＯＮ’の長さは、ｃｏｓωで短縮されているが、断層像２３’および視点ｅ’との距離の関係すなわち比は、そのまま保存されているので、この上で計算しても問題はない。また、直線ＯＮ’に垂直な方向は短縮されないから、Ｔ’上に得られる投影像は、そのまま表示できる。
【０１６４】
図３６は、投影面が曲面の場合の平面ｔ上の関係を、上からｘｙ平面に射影した図であり、投影計算を説明する図である。図３６は、投影面が任意曲面であるが、計算方法は、いままで述べた方法と同じである。ただし、曲面上での点Ｎから点Ｐまでの距離として曲線上の長さを計算する方法、または、Ｐ点をＯｕ’軸に平行な点Ｐ”を用いる方法がある。
【０１６５】
点Ｓ（ｘ_１，ｙ_１）は座標を回転角αだけ回転させた新しいｕ−ｖ座標系においては、（４６），（４７）式で与えられる。このｕ−ｖ座標系では、上記（１１）式は新しいｕ−ｖ座標軸を用いて、ｕ＝一定， ｖ＝変数として表される。ｗ軸の上で、原点Ｏからの距離ｄ_２が変わるに連れて、視点ｅもｘ−ｙ座標上で視線Ｅの上で移動して行く。また、断層像２３との交線も変わっていく。
【０１６６】
図３６は、投影面が任意曲面の場合であるが、計算方法は、これまで述べた方法と同じである。ただし、ＣＲＴに表示するため、投影像を平面に写像する場合、曲面上での点Ｎから点Ｐまでの距離として曲線の長さを利用する方法、または、Ｐ点をＯｕ’軸に平行な点Ｐ”を用いる方法がある。
【０１６７】
直線４０と直線２３’の交点Ｓの座標とは、次のようになる。
ｖ＝ｕ・ｔａｎθ−ｄｕ・ｔａｎθ
ＶＴ＝（Ｒ−ｄｕ）ｖｉ／（ｕｉ−ｄｕ）
ｔａｎθ＝ＶＴ／（Ｒ−ｄｕ）
複数の断層像２３に対しては、各断層像間の距離ｄ１が異なり、また、複数の平面ｔに対しては、原点Ｏからの距離ｄ２が異なる。このようにして、対応する断層像上の点Ｓとその投影点Ｐが求められる。
【０１６８】
視点ｅを視直線Ｅ軸上で表示する長さの部分だけ動かし、各視点ｅにおける平面ｔとその断層像との交線を計算し、ｘｙ平面への投影点を計算し、平面Ｔに投影すると、任意方向への平面パノラマ投影像が得られる。この投影像を対応する画像表示メモリに書き込むと、ＣＲＴに表示できる。
【０１６９】
陰影変換は、投影平面Ｔ上で実行すればよい。この陰影変換には、視直線Ｅからの距離に応じて濃淡を着ける方法，視直線に直交する各個別平面内での投影直線とのなす角度に応じて輝度変換する方法，視直線Ｅからの距離に応じて等高線のように輝度変換を行う方法等が考えられる。
【０１７０】
【発明の効果】
本発明によれば、血管壁，腸壁などの管状の投影対象を投影する際に、直線または曲線に沿って切り開かれたパノラマ写真のように、ゆがみが少なくパノラマ状の広い視野が得られるパノラマ投影方法が得られる。
【０１７１】
また、任意の曲面へのパノラマ投影方法によれば、血管壁，食道壁などの管状の投影対象の投影像が、あたかもその内部に入って見たような立体的な画像として表示されるので、正確かつ迅速な診断に役立つ。
【図面の簡単な説明】
【図１】本発明による直線パノラマ投影方法の手順を示すフローチャートである。
【図２】図１の直線パノラマ投影方法を実行するためのハードウェアの構成の一例を示すブロック図である。
【図３】直線パノラマ投影方法において、視直線が中心軸と一致する円柱投影面の投影像を直線パノラマ変換により平面に展開し、ゆがみを少なくしながら広視野化する原理を説明する図である。
【図４】図３の原理において、円柱投影面の中心角が１８０度である場合の直線パノラマ変換を説明する図である。
【図５】図３の原理において、円柱投影面の中心角が１８０度よりも大きい場合の直線パノラマ変換を説明する図である。
【図６】直線パノラマ投影方法において、視直線が外側にある円柱投影面の投影像を直線パノラマ変換により平面に展開し、ゆがみを少なくしながら広視野化する原理を説明する図である。
【図７】図６の原理において、円柱投影面の中心角が１８０度である場合の直線パノラマ変換を説明する図である。
【図８】直線パノラマ投影方法により、複数の断層像から三次元画像の構成する際に、断層像の画素座標を投影面の画素座標に変換する原理を説明する図である。
【図９】図８の原理において、断層面と投影面とが平行である場合の直線パノラマ変換を説明する図である。
【図１０】図８の原理において、断層面と投影面とが交差している場合の直線パノラマ変換の原理を説明する図である。
【図１１】視直線と断層面と投影面とがより複雑な位置関係にある場合の直線パノラマ変換を説明する図である。
【図１２】本発明による曲線パノラマ投影方法の手順を示すフローチャートである。
【図１３】曲線パノラマ投影方法において、視曲線の接線が中心軸と一致する円柱投影面の投影像を曲線パノラマ変換により平面に展開し、ゆがみを少なくしながら広視野化する原理を説明する図である。
【図１４】図１３の原理において、円柱投影面の中心角が１８０度である場合の曲線パノラマ変換を説明する図である。
【図１５】図１３の原理において、円柱投影面の中心角が１８０度よりも大きい場合の曲線パノラマ変換を説明する図である。
【図１６】曲線パノラマ投影方法において、視曲線が外側にある円柱投影面の投影像を曲線パノラマ変換により平面に展開し、ゆがみを少なくしながら広視野化する原理を説明する図である。
【図１７】図１６の原理において、円柱投影面の中心角が１８０度である場合の曲線パノラマ変換を説明する図である。
【図１８】曲線パノラマ投影方法により、複数の断層像から三次元画像の構成する際に、断層像の画素座標を投影面の画素座標に変換する原理を説明する図である。
【図１９】図１８の原理において、断層面と投影面とが平行である場合の曲線パノラマ変換を説明する図である。
【図２０】図１８の原理において、断層面と投影面とが交差している場合の曲線パノラマ変換の原理を説明する図である。
【図２１】視曲線と断層面と投影面とがより複雑な位置関係にある場合の曲線パノラマ変換を説明する図である。
【図２２】図２１において、三次元空間の視曲線Ｃと視点ｅにおける接線Ｖとの関係を示す図である。
【図２３】２次投影平面上に曲線パノラマ変換された１次投影像の相互の関係を示す図である。
【図２４】任意曲面へのパノラマ投影方法の手順を示すフローチャートである。
【図２５】パノラマ投影方法において、任意曲面から平面に展開し、ゆがみを少なくしながら広視野化する原理を説明する図である。
【図２６】パノラマ投影方法において、任意曲面から平面に展開し、ゆがみを少なくしながら広視野化する原理を説明する図である。
【図２７】パノラマ投影方法において、任意曲面から平面に展開し、ゆがみを少なくしながら広視野化する原理を説明する図である。
【図２８】三次元画像の構成方法において、断層像の画素座標を投影面上の座標に変換する方法を説明する図である。
【図２９】同様に、複数の断層像の画素座標を投影面上の座標に変換する方法を説明する図である。
【図３０】視点，断層像，投影面がより複雑な位置関係にある場合の直線投影による座標変換方法を説明する図である。
【図３１】視点，断層像，投影面がより複雑な位置関係にある場合の直線投影による座標変換方法を説明する図である。
【図３２】視点，断層像，投影面がより複雑な位置関係にある場合の直線投影による座標変換方法を説明する図である。
【図３３】視点，断層像，投影面がより複雑な位置関係にある場合の直線投影による座標変換方法を説明する図である。
【図３４】視点，断層像，投影面がより複雑な位置関係にある場合の直線投影による座標変換方法を説明する図である。
【図３５】投影計算を説明する図である。
【図３６】投影計算を説明する図である。
【図３７】円柱投影面の中心角が１８０度である場合の直線パノラマ投影方法の原理を説明する図である。
【図３８】円柱投影面の中心角が１８０度よりも大きい場合の直線パノラマ投影方法の原理を説明する図である。
【図３９】曲線パノラマ投影方法の全体の概要を示す図である。
【図４０】円柱投影面の中心角が１８０度である場合の曲線パノラマ投影方法の原理を説明する図である。
【図４１】円柱投影面の中心角が１８０度よりも大きい場合の曲線パノラマ投影方法の原理を説明する図である。
【図４２】視曲線に沿う視点と各視点における接線とこの接線を中心軸とする複数の短い円柱投影面との関係を示す図である。
【図４３】任意曲面へのパノラマ投影を説明する図である。
【図４４】任意曲面へのパノラマ投影を説明する図である。
【図４５】従来の中心投影方法における断層像と投影面との関係を示す図である。
【図４６】従来の平行投影方法における断層像と投影面との関係を示す図である。
【図４７】従来の中心投影方法において断層像と投影像との関係が視点からの距離によりどのように変化するかを示す図である。
【図４８】従来の平行投影方法において断層像が投影像としてどのように重ねて表示されるかを示す図である。
【符号の説明】
４ ２次投影平面
２１ 円柱投影面
または接線Ｖを中心軸とする１次円柱投影面
２３ 断層像
Ｃ 視線の分布する三次元曲線
ｅ 直線上の視点または三次元曲線Ｃ上の視点
ｈ 視点ｅと円柱投影面２１との距離
ｈ 視点ｅから投影曲面の中央に引いた垂線
Ｌ 円柱投影面２１上の円弧ＯＱ
Ｌ’ Ｌと同じ長さを持った直線Ｏ２Ｑ”上の線分
またはＬと同じ長さを持った２次投影平面上の線分
Ｐ ２次投影平面４上の点（ｘ ，ｙ ，ｚ ）
Ｑ 投影平面４上のＰ点に対応する円柱投影面２１上の点
（直線Ｐｅと円柱投影面２１の交点）
Ｒ １次円柱投影面２１の半径
Ｖ 視点ｅにおける曲線Ｃの接線
Ｓ 視点ｅから円柱投影面上の点Ｑへ引いた直線と断層像２３が交わる点
θ 直線Ｐ’ｅとｚ軸のなす角
η ＣＲＴのＸ軸に平行に設定された表示アドレス
θ 垂線ｈとｚ軸のなす角
ξ ＣＲＴのＹ軸に平行に設定された表示アドレス
φ 線分Ｑ’Ｏ’とｚ軸とのなす角
ω 線分Ｑ’ｅと線分Ｑ’Ｏ’とのなす角[0001]
[Industrial application fields]
The present invention relates to a panoramic projection method for computer graphics, and more particularly, to a means for ensuring a wide field of view by improving image distortion in a central projection method.
[0002]
[Prior art]
As shown in FIG. 45, the central projection method is a method of obtaining an image by irradiating light rays radially from a viewpoint e and projecting a projection target onto a projection plane. This central projection method is applied to, for example, projecting the images 40a and 40b of the tomographic image 23 in the body onto the projection plane 4 to obtain the projected images 40A and 40B, and is used to construct a three-dimensional image of the tomographic image. It is done.
[0003]
As shown in FIG. 46, the parallel projection method is a method of obtaining an image by irradiating parallel rays and projecting a projection target onto a projection plane. This parallel projection method is also applied to obtain the projection images 40A and 40B by projecting the images 40a and 40b of the tomographic image 23 in the body onto the projection plane 4, and is used to construct a three-dimensional image of the tomogram. .
[0004]
In general, when a viewpoint is brought into the body and a minute part in an organ such as the inner wall of the blood vessel, the esophagus, the intestine, or the bronchus is projected and displayed in three dimensions, the viewpoint is placed inside the target organ, A viewing center projection method is suitable.
[0005]
On the other hand, when observing bones, skin, body surfaces, etc. from the outside, a parallel projection method capable of intuitively understanding the external shape is suitable.
[0006]
In general, the projection plane in the conventional central projection method and the projection plane in the parallel projection method are “Computer Graphics” (by JD Foley & A. Van Dam), which is a representative document relating to computer graphics. As shown in (issued by the Japan Computer Association on July 15, 1984), it was a flat surface.
[0007]
When an object is projected onto the projection plane 4 using the central projection method, the projected image is enlarged from the center of the projection plane 4 to the periphery, and is rapidly moved away from the center 50 of the projection plane 4. Therefore, as compared with the image near the center 50, the distortion of the image increases from the center of the projection plane 4 to the periphery. This tendency becomes more prominent as the distance r between the viewpoint e and the projection target is shorter.
[0008]
In FIG. 47, if the distance from the viewpoint e to the projection plane 4 is R, the distance from the viewpoint e to the projection target in the tomographic image is r, and the distance from the projection center to the circumferential direction is l (constant), The distance H at
H = R · l / r
It becomes. As the distance r to the projection target decreases, the distance H on the projection plane increases rapidly and moves away from the center 50 on the projection plane. For example, when displaying on a CRT screen, since the display area is limited, when the distance H on the projection plane is determined, the area that can be projected is determined according to the distance R from the viewpoint e to the projection plane 4. In order to project a 180 ° width from the viewpoint e, R = 0 must be set, and only a very narrow portion can be projected.
[0009]
On the other hand, in parallel projection, there is little image distortion, but as shown in FIG. 48, when there are complex irregularities inside such as the inside of the esophagus or intestine, the projection objects overlap and there are many invisible parts. There was a drawback.
[0010]
[Problems to be solved by the invention]
The three-dimensional display may be used for tubular objects such as blood vessels and esophagus. Such an object requires a three-dimensional display that gives a panoramic view so that it enters the inside of these tubular objects and a wide range of tube walls of 180 degrees to the left and right can be seen.
[0011]
Furthermore, since blood vessels, intestines, and the like are winding, it is necessary to create a three-dimensional image developed along these tubes.
[0012]
First of the present inventionofThe purpose is a linear panorama projection method that provides a wide panoramic field of view with little distortion.And linear panorama projectorIs to provide.
[0013]
Second of the present inventionofThe purpose is a curved panorama projection method that can obtain a wide panoramic field of view with little distortion while avoiding overlapping of projection objects as much as possible for curved tubular projection objectsAnd curved panorama projectorIs to provide.
[0014]
A third object of the present invention is to obtain a panoramic wide field of view with little distortion by using viewpoints distributed on a straight line and an arbitrary curved surface.Arbitrary curved surfacePanorama projection methodAnd arbitrary curved panorama projectorIs to provide.
[0015]
[Means for Solving the Problems]
In order to achieve the first object, the present invention irradiates light rays in a plane perpendicular to the straight line from each viewpoint continuously distributed on the straight line, and a cylindrical projection plane having the straight line as an axis. A linear panorama projection method is proposed in which a projection target is projected directly onto the projection plane, and the projection result is developed on a projection plane to display a panorama.
[0016]
The present invention also includes a means for setting a straight line, a means for setting a cylindrical projection plane having the straight line as an axis, and a radial direction within a plane orthogonal to the straight line from each viewpoint continuously distributed on the straight line. A linear panorama including means for directly projecting a projection target onto the cylindrical projection plane by irradiating light, means for developing the projection result on a projection plane, and display means for panoramic display of the projection result developed on the projection plane A projection device is proposed.
[0017]
The linear panorama projection methodAnd linear panorama projectorIn the method, at least a part of the projection target may exist between the viewpoint and the cylindrical projection plane.
[0018]
In any of the above linear panorama projection methods, the radius of the cylindrical projection plane may be equal to the distance from the viewpoint to the projection plane, or may be shorter than the distance from the viewpoint to the projection plane. It may be longer than the distance from the viewpoint to the projection plane.
[0019]
On the other hand, the central angle of the cylindrical projection plane can be set to any angle between 0 and 360 degrees.
[0020]
The projection target may be either data input from an input device or data obtained as a result of calculation by a calculation device.
[0021]
Further, the data obtained as a result of calculation by the calculation device is more specifically configured by using a tomographic image including a tomographic image obtained by decomposing a volume image obtained by three-dimensional measurement or a general linear projection method. 3D images can be obtained.
[0022]
In order to achieve the second object, the present invention irradiates light rays from each viewpoint continuously distributed on an arbitrary curve in a plane perpendicular to the tangent at the viewpoint, and the tangent is used as an axis. A curved panorama projection method in which a projection target is directly projected onto a short cylindrical projection surface, a plurality of the short cylindrical projection surfaces are connected to create a projection image along the curve, and the projection result is developed on a projection plane to display a panorama Propose.
[0023]
The present invention further includes means for setting an arbitrary curve, and radiating rays from each viewpoint continuously distributed on the arbitrary curve in a plane perpendicular to the tangent at the viewpoint, and using the tangent as an axis. Means for directly projecting a projection object onto a short cylindrical projection surface, means for connecting a number of the short cylindrical projection surfaces to create a projection image along the curve, means for developing the projection result on a projection plane, A curved panorama projection apparatus including display means for panorama displaying a projection result developed on a projection plane is proposed.
[0024]
SaidcurvePanorama projection methodAnd arbitrary curved panorama projectorIn the method, at least a part of the projection target may exist between the viewpoint and the cylindrical projection plane.
[0025]
In any curved panorama projection method, the radius of the cylindrical projection plane may be equal to the distance from the viewpoint to the projection plane, or may be shorter than the distance from the viewpoint to the projection plane. However, it may be longer than the distance from the viewpoint to the projection plane.
[0026]
On the other hand, the angle of the cylindrical projection plane can be set to an arbitrary angle between 0 and 360 degrees.
[0027]
The projection target may be either data input by an input device or data obtained as a result of calculation by an arithmetic device.
[0028]
Furthermore, the data obtained as a result of calculation by the calculation device is more specifically a tomogram including a tomogram obtained by decomposing a volume image obtained by three-dimensional measurement.
[0029]
In order to achieve the third object, the present invention irradiates light rays in a plane perpendicular to the straight line from each viewpoint continuously distributed on the straight line, and directly projects the projection target onto an arbitrary curved surface. Then, an arbitrary curved surface panorama projection method is proposed in which the projection result is developed on a projection plane and displayed in a panorama manner.
[0030]
The present invention provides a means for setting a straight line and an arbitrary curved surface, and directly irradiates light rays in a plane orthogonal to the straight line from each viewpoint continuously distributed on the straight line and directly projects the projection target onto the arbitrary curved surface. An arbitrary curved surface panorama projection apparatus including means, means for expanding the projection result on a projection plane, and display means for displaying the projection result expanded on the projection plane in a panorama is proposed.
[0031]
SaidArbitrary curved surfacePanorama projection methodAnd arbitrary curved panorama projectorIn the above, at least a part of the projection target may exist between the viewpoint and the arbitrary curved surface.
[0032]
In any panorama projection method, the cross section of the projection plane may be an arbitrary curve other than a plane, and the cross section of the projection plane may change according to the position of the viewpoint. May be changed according to the shape of the projection target and the purpose of observation of the projection target.
[0033]
The projection target may be either data input from an input device or data obtained as a result of calculation by a calculation device. More specifically, the result data calculated by a calculation device is a volume image obtained by three-dimensional measurement. Is a tomographic image including a tomographic image obtained by decomposing the image, and is a three-dimensional image constructed using a general straight line projection method.
[0034]
[Action]
37 and 38 are diagrams for explaining the principle of the linear panorama projection method according to the present invention. The projection surface is a cylindrical projection surface 21 having a straight line perpendicular to the paper surface as the central axis 7. The viewpoint is continuously distributed on the central axis 7 of the cylindrical projection surface 21, and the projection target 5 is projected onto the cylindrical projection surface 21.
[0035]
In FIG. 37, the center angle of the curved surface surrounding the viewpoint is exactly 180 degrees, but the center angle is arbitrary. The three-dimensional image projected onto the cylindrical projection surface 21 is converted into the plane 4 by panoramic projection of the cylindrical projection surface 21 onto the regions 12 to 13.
[0036]
In FIG. 38, the center angle of the curved surface surrounding the viewpoint is larger than 180 degrees, and the end points 10 and 11 are closer to those of the curved surface in FIG. Also in this case, as in the case of FIG. 37, the three-dimensional image projected on the curved surface between the end points 10 and 11 is converted into the plane 4 by panorama projection.
[0037]
When all the viewpoints, that is, the central axis 7 are enclosed, the end points 10 and 11 coincide. In that case, the cylindrical projection surface 21 is the entire circumference. Accordingly, a panoramic three-dimensional image can be obtained as if a projection target such as a blood vessel, an intestine, and an esophagus is opened.
[0038]
The image converted from the image on the cylindrical projection plane 21 to the secondary projection plane 4 is made to correspond to the coordinates on the CRT screen as it is. When the image converted to the secondary projection plane 4 is made to correspond to the coordinates on the CRT screen in this way, distortion that has conventionally occurred in the horizontal direction depending on the projection direction is corrected, and a wide panoramic field of view is obtained. A panoramic projection method giving a three-dimensional image is obtained.
[0039]
39 to 42 are diagrams for explaining the principle of the curved panorama projection method according to the present invention.
[0040]
FIG. 39 is a diagram showing an overview of the entire curved panorama projection method. In the curve panorama projection method of FIG. 39, first, an arbitrary curve C in which the viewpoints e are continuously distributed is drawn on the projection object 23. More specifically, an arbitrary curve C in which the viewpoints are distributed in the tubular projection object 23 is drawn. In order to draw the curve C, it is possible to record a trajectory when searching in the tube by the central projection method and adopt the trajectory. The operator may specify each tomogram with a pointing device such as a mouse or a trackball. Furthermore, a method of causing the computing device to automatically discriminate and trace the tubular projection object 23 can also be used.
[0041]
Next, a tangent line V is drawn on the curve C at an arbitrary viewpoint e on the given curve C. The gradient of the tangent line V in the three-dimensional space changes as the viewpoint e moves on the curve C. Consider a short cylinder having a length δV with the tangent V at each position of the viewpoint e as the central axis. Next, a plane B that passes through the viewpoint e and is orthogonal to the tangent line V is considered, and the curved surface of the cylinder is defined as a cylindrical projection surface 21. Project.
[0042]
A perpendicular line h is drawn from the viewpoint e to the center of the cylindrical projection surface 21. The perpendicular line h is orthogonal to the tangent line V. Let g be the intersection of the straight line h and the cylindrical projection plane 21, and let T be the plane that includes the intersection g and is perpendicular to the perpendicular h. The plane T is the secondary projection plane 4. When the short cylindrical projection surface 21 and the projection plane 4 are created at each viewpoint e on the curve C, a projection image of an object within a predetermined length range on the curve C can be created.
[0043]
40 and 41 are diagrams showing the relationship between the primary projection curved surface 21 on the arbitrary plane B in FIG. 39, the secondary projection plane 4, the projection object 5, and the tangent line V at the viewpoint e on the curve C. is there. The primary projection curved surface is a cylindrical projection surface 21 that is perpendicular to the paper surface and has a tangent line V as a central axis. The viewpoint is continuously distributed on the central axis 7 of the cylindrical projection surface 21, and the projection object 5 is projected onto the cylindrical projection surface 21.
[0044]
In FIG. 40, the center angle of the curved surface surrounding the viewpoint is exactly 180 degrees, but the center angle is arbitrary. The three-dimensional image projected onto the cylindrical projection surface 21 is converted into the plane 4 by panoramic projection of the cylindrical projection surface 21 onto the regions 12 to 13.
[0045]
When all the viewpoints, that is, the central axis 7 are enclosed, the end points 10 and 11 coincide. In that case, the cylindrical projection surface 21 is the entire circumference. Therefore, a panoramic three-dimensional image can be obtained as if a projected object such as a blood vessel, intestine, and esophagus is cut open.
[0046]
The image converted from the image on the cylindrical projection plane 21 to the secondary projection plane 4 is made to correspond to the coordinates on the CRT screen as it is. When the image converted to the secondary projection plane 4 is made to correspond to the coordinates on the CRT screen in this way, distortion that has conventionally occurred in the horizontal direction depending on the projection direction is corrected, and a wide panoramic field of view is obtained. A panoramic projection method giving a three-dimensional image is obtained.
[0047]
In FIG. 41, the center angle of the curved surface surrounding the viewpoint is larger than 180 degrees, and the end points 10 and 11 are closer than those of the curved surface of FIG. Also in this case, as in the case of FIG. 40, the three-dimensional image projected on the curved surface between the end points 10 and 11 is converted into the plane 4 by panorama projection.
[0048]
When all the viewpoints, that is, the central axis 7 are enclosed, the end points 10 and 11 coincide. In that case, the cylindrical projection surface 21 is the entire circumference. Therefore, a panoramic three-dimensional image can be obtained as if a projected object such as a blood vessel, intestine, and esophagus is cut open.
[0049]
The image developed on the secondary projection plane 4 from the image on the cylindrical projection plane 21 is made to correspond to the coordinates on the CRT screen as it is. When the image converted to the secondary projection plane 4 is made to correspond to the coordinates on the CRT screen in this way, distortion that has conventionally occurred in the horizontal direction depending on the projection direction is corrected, and a wide panoramic field of view is obtained. A panoramic projection method giving a three-dimensional image is obtained.
[0050]
FIG. 42 is a diagram showing the arrangement of the viewpoint e along the curve C, the tangent line at each viewpoint, and a plurality of short cylindrical projection planes 21 with the tangent line as the central axis. In order to prioritize ease of explanation and ease of viewing, the space between the short cylindrical projection surfaces 21 is wide, but actually, as shown in the portions 30 to 32, each short cylindrical projection surface 21. The cylindrical projection plane 21 is arranged so that are closely overlapped with each other.
[0051]
When the cylindrical projection surface 21 is a complete cylinder, the central angle surrounding the tangent line V is 360 degrees, but it can be set to an angle of less than 360. When the central angle surrounding the tangent line V is 360 degrees, a panoramic projection image obtained by opening and projecting a tubular projection object along the curve C is obtained.
[0052]
The center of the projection direction can be arbitrarily set by the operator. The center of the projection direction can be determined individually for each cylindrical projection surface or can be determined in common. When determining the center of the projection direction individually, the operator needs to determine the direction for each cylindrical projection plane. In the case where the center of the projection direction is determined in common, the direction is given by a pointing device such as a mouse or a trackball, and the direction is applied to the entire cylindrical projection surface.
[0053]
As shown in FIGS. 40 and 41, individual cylindrical projection images obtained in this way are developed by curve panorama development, rearranged along a straight line, and displayed on a plane.
[0054]
43 and 44 are diagrams for explaining panorama projection onto an arbitrary curved surface according to the present invention. The projection surface 21 is parallel to the line of sight E and has an arbitrary shape including a plane. The light source is continuously distributed in the line of sight E and projects the projection target 5 onto the projection plane 21. In FIG. 43, the projection plane is a plane, and after the projection calculation, the projection image may be subjected to shadow conversion and displayed on the CRT. In FIG. 44, the projection surface is a curved surface, and continuously changes with respect to the position of the line of sight E. The projection target is projected on the projection plane 21. In order to display this primary projection image on the CRT, it is necessary to map the image of the projection surface 21 onto a plane. For this mapping method, a method using a distance along a curved surface from a certain position (straight line η) or a plane η ′ in contact with the projection curved surface 21 at each point of η is assumed, and the projection is perpendicular to η ′. There are ways to do this.
[0055]
The advantage of using a plane as the projection plane is that it is not necessary to calculate the projection from the curved projection plane to the plane, making the calculation simple and effective when you want to see a three-dimensional image of a part that spreads in a plane. .
[0056]
On the other hand, when a curved surface is used, projection calculation from the curved surface is required, but there is an advantage that a stereoscopic image with a wide field of view can be obtained for a spherical or tubular projection target. In addition, when the projection plane is continuously changed with respect to the shape of the projection target, a stereoscopic image that is easy to see may be obtained even for an object having a complicated shape. When this linear light source is used, a projected image can be calculated continuously along the linear light source, so that a stereoscopic image with a wider field of view can be obtained as compared with the central projection.
[0057]
【Example】
An embodiment of the panorama projection method according to the present invention will be described with reference to FIGS.
[0058]
<Linear panorama projection method>
FIG. 1 is a flowchart showing the procedure of an embodiment of the straight panorama projection method according to the present invention. FIG. 2 is a block diagram showing an example of a hardware configuration for executing the linear panorama projection method of FIG.
[0059]
In FIG. 2, a CPU 50, a main memory 51, a magnetic disk 52, a display memory 53, and a mouse controller 55 are connected to each other via a common bus 57. The magnetic disk 52 stores a plurality of tomographic images and a program for executing the linear panorama projection method of the present embodiment.
[0060]
The CPU 50 reads a program for executing a plurality of tomographic images and a linear panorama projection method from the magnetic disk 52, executes operations such as panorama conversion using the main memory 51, sends the result to the display memory 53, and outputs a CRT It is displayed on the monitor 54. A mouse 56 connected to the mouse controller 55 is used for designating a starting point position and the like in calculations such as panorama conversion. The panorama converted image is stored in the magnetic disk 52 as necessary.
[0061]
Step 101: As shown in FIG. 1, in the linear panorama projection method of the present embodiment, first, the projection target is projected onto the cylindrical projection surface by the linear projection method. In other words, light rays are irradiated from a viewpoint continuously distributed on a straight line into a plane orthogonal to the straight line, and a projection target is projected onto a cylindrical projection plane.
Step 102: The coordinates of the cylindrical projection plane image are transformed into a secondary projection plane to obtain a panoramic projection image. If necessary, the panorama projection image is converted into the coordinates of the CRT monitor 54 and displayed.
[0062]
In the present embodiment, panorama conversion refers to a process of projecting a projection target onto a cylindrical projection curved surface, expanding the cylindrical projection plane onto a secondary projection plane, and projecting the projection target onto a secondary projection plane. That is, in the linear panorama projection method, a projection target is linearly projected using a cylindrical projection plane as a projection plane, and the cylindrical projection plane is developed into a plane. In this case, the address of each point along the semi-cylindrical projection plane that is the projection plane corresponds to the address of the display pixel of the CRT. The panoramic image is displayed on the screen of the CRT monitor 54, for example.
[0063]
Next, the principle of linear panorama conversion will be described with reference to FIGS.
FIG. 3 is a diagram for explaining the principle of widening the field of view while reducing the distortion by developing a projection image of a cylindrical projection surface whose line of sight coincides with the central axis into a plane by linear panorama conversion in the linear panorama projection method. . In FIG. 3, a cylindrical projection surface 21 is a cylindrical projection surface having a radius R centered on the intersection O ′ between the visual line V and the Z axis where the viewpoint e is continuously distributed. Here, of the two semi-cylindrical projection surfaces I and II obtained by dividing the cylindrical projection surface 21 into two by a plane passing through the intersection O ′ and parallel to the xy plane, the semi-cylindrical projection closer to the origin O is used. A comedones are shown. The secondary projection plane 4 is a projection plane to be projected after panoramic conversion of the projection image of the cylindrical projection plane 21. The projection plane 4 corresponds to a display screen of a CRT monitor. The radius R of the cylindrical projection surface 21 is also the distance between the visual line V and the projection plane 4 in the example of FIG.
[0064]
X in the X-axis direction from the origin O of the 3D coordinate system₁It is assumed that a projection object at a distance of is projected onto a point Q on the cylindrical projection surface 21 by the linear projection method. The position of Q is a point (x on the cylindrical projection surface 21 by a light ray irradiated from the visual line V.₁, Θ). θ is an angle formed by a line connecting the point Q and the visual line V and the z axis.
[0065]
When the point Q is coordinate-transformed into the secondary projection plane 4, the point P on the secondary projection plane 4 (η₁, Ξ₁). At that time, the arc from the point O ″ to the point Q on the cylindrical projection surface 21, that is, the arc OQ′L on the projection curved surface 21, extends from the point O ″ to the point P having the same length on the secondary projection plane 4. Converted to a line segment L ′. Of the coordinates of point P, η₁Is the X coordinate on the CRT corresponding to point P, ξ₁May be interpreted as the Y coordinate on the CRT corresponding to the P point.
[0066]
FIG. 4 is a diagram for explaining linear panorama conversion when the center angle of the cylindrical projection surface is 180 degrees in the principle of FIG. In FIG. 3, when attention is paid to the yz plane at x = 0, it can be displayed as shown in FIG. In FIG. 4, planes orthogonal to the visual line V, that is, arbitrary yz planes are considered to be independent from each other, and panorama calculation is performed in each yz plane.
[0067]
Focusing on the yz plane at x = 0, the 180-degree range of the semicircular arc is divided into equal angles, and the divided pixels are used as display pixels in the horizontal axis direction of the screen of the CRT monitor 54, that is, in the X-axis direction. Make it correspond. It may be considered that the circumference of the semicircular arc is divided at equal intervals to correspond to the display pixels.
[0068]
FIG. 5 is a diagram for explaining linear panorama conversion when the center angle of the cylindrical projection surface is larger than 180 degrees in the principle of FIG. Also in this case, the panorama conversion method is the same as in FIG.
[0069]
In FIG. 4, the angle between the line connecting the Q point and the viewpoint e and the z axis is θ, the angle per pixel is dθ, and the angle from which the entire semicircular arc is viewed from the visual line V is the horizontal axis on the CRT, that is, the X axis. When the number of display pixels in the direction is N and the number of pixels representing an arbitrary position is n, the following equation is established. However, the angles dθ, θ, and Θ are expressed in radians. Note that the display pixel number N in the X-axis direction is, for example, 512 or 1024.
dθ = Θ / N = π / N
L ′ = L
ξ₁= OQ₁= L = R · n · dθ = π · n · R / N
η₁= X₁
Here, the range of OA = π · R / 2, twice the length of OA is made to correspond to the display length of the horizontal axis of the CRT screen, that is, the X axis. The vertical axis, that is, the Y axis is determined by the number of pixels on the CRT screen.
[0070]
FIG. 6 is a diagram for explaining the principle of widening the field of view while reducing the distortion by developing the projection image of the cylindrical projection surface having the visual line on the outer side into a plane by linear panorama conversion in the linear panorama projection method. FIG. 6 shows a case where the distance between the visual line V and the cylindrical projection surface 21 is larger than the radius R of the cylinder.
[0071]
FIG. 7 is a diagram for explaining linear panorama conversion when the central angle of the cylindrical projection surface 21 is 180 degrees in the principle of FIG. In FIG. 6, when attention is paid to the yz plane at x = 0, it can be displayed as shown in FIG. In FIG. 7, the coordinates on the yz plane of the intersection point Q between the straight line Pe and the cylindrical projection surface 21 are a line O connecting the points P ′ and e on the y-axis and a point O at a distance R from the origin on the z-axis. It becomes the intersection point Q 'with the circumference of radius R centered on'. In FIG. 7, when the distance between the viewpoint e and the projection plane 4 is h, the angle Q′O′O is φ, and the angle eQ′O ′ is ω, the following equation is established.
φ = ω + θ
R / sin θ = (h−R) / sin ω
From these two equations, η₁, Ξ₁Is obtained.
ω = sin￣¹[{(H−R) sin θ} / R]
dθ = Θ / N
θ = n · dθ = n · Θ / N
L ′ = L
therefore
ξ₁= R ・ φ = R (ω + θ)
η₁= L
It becomes.
[0072]
This η₁, Ξ₁Is the pixel address on the display memory. That is, the point P on the projection plane 4 is the point P (η₁, Ξ₁) And panorama conversion has been executed.
[0073]
Next, a method for constructing a three-dimensional image from a plurality of tomographic images by a linear panoramic projection method will be described with reference to FIGS. In any case, the tomographic image is first projected on the cylindrical projection surface 21 and then the tomographic image on the cylindrical projection surface 21 is developed on the secondary projection plane 4 by panorama conversion.
[0074]
First, in the above three-dimensional image construction method, coordinate conversion by linear panorama projection will be described. When projecting each tomographic image onto the projection surface by linear projection, conversion of pixel coordinates of each tomographic image into coordinates on the projection surface is performed as follows.
[0075]
FIG. 8 is a diagram for explaining the principle of converting the pixel coordinates of the tomographic image into the pixel coordinates of the projection plane when a three-dimensional image is constructed from a plurality of tomographic images by the linear panoramic projection method. In the example of FIG. 8, in order to simplify the description, the coordinate system is defined so that the center line 31 of the cylindrical projection surface 21, the tomographic image plane 23, and the xy plane are parallel to each other. Further, the center line 31 of the cylindrical projection surface 21 is on the z axis. In FIG. 8, the viewpoint e is continuously distributed on the visual line V. X, y, and z are the axes of the three-dimensional coordinate system (x, y, z) and the point e (d₀, 0, R) is the position of an arbitrary viewpoint e on the visual line V, Q point (x, y, z) is a point on the cylindrical projection plane 21, and S point (x₀, Y₀, Z₀) Is the point where the straight line 22 connecting the point e (x, 0, R) and the point Q (x, y, z) intersects the tomographic image 23A, and R represents the z coordinate of the viewpoint e. The straight line 22 is drawn from the point e so as to be orthogonal to the visual line V. D₀Is the position on the z-axis of the tomographic image 23A and is determined at the time of calculation.
[0076]
In FIG. 8, if attention is paid to each viewpoint e, it can be seen that fan-shaped surfaces are stacked in the z-axis direction. Therefore, if projection calculations are executed in a sector shape and they are stacked, a three-dimensional image can be displayed.
[0077]
FIG. 9 is a diagram for explaining linear panorama conversion when the tomographic plane and the projection plane are parallel to each other in the principle of FIG. FIG. 9 shows tomographic images 23B to 23H in addition to the tomographic image 23A, viewed from the x-axis direction. In FIG. 9, tomographic images 23A to 23H are tomographic images obtained at equal intervals in the same direction with respect to the same object, and organ regions B1, B2, B3, and B4 are drawn with emphasis on the tomographic image 23. . The tomographic images in this example are equally spaced, but are not necessarily equally spaced.
[0078]
When the organ regions B1, B2, B3, and B4 are projected onto the projection plane 4, B1 ', B2', B3 ', and B4' are obtained. Here, when the projection data B1 ′, B2 ′, B3 ′, and B4 ′ are written in the display memory 53 of FIG. 2, in order to produce a three-dimensional effect, the projection data existing farther from the viewpoint e is first selected. Write and overwrite the projection data closer to it later. Thereafter, the shading process is executed.
[0079]
FIG. 10 is a diagram for explaining the principle of linear panorama conversion when the tomographic plane and the projection plane intersect with each other in the principle of FIG. In this case, it is necessary to create tomographic images 23a, 23b, 23c,..., 23h directed to a plane parallel to the projection surface 21 from the tomographic images 23A, 23B,. Subsequent projection calculations are the same as in FIG.
[0080]
FIG. 11 is a diagram for explaining linear panorama conversion in the case where the visual line, the tomographic plane, and the projection plane have a more complicated positional relationship. In FIG. 11, the S point (x₀, D₀, Z₀) Is a point P (x, y, z) on the plane.
[0081]
When the tomographic image 23 is projected onto the cylindrical projection surface 21 by the straight panorama projection method, the conversion of each pixel coordinate of the tomographic image 23 into the coordinate on the cylindrical projection surface 21 is executed as follows. Here, the positional relationship is set as follows so that the tomographic image can be handled without losing generality. The tomographic image 23 input in FIG. 11 is in a plane perpendicular to the y-axis and d from the origin.₀Is in the distance. For multiple tomographic images, distance d from the origin₀Changes. The visual line V is set to coincide with the central axis of the cylindrical projection plane, and gives an arbitrary direction that is not parallel to any of the x, y, and z axes. This direction can be designated by the operator with a pointing device such as a trackball or a mouse. Next, an arbitrary viewpoint e is determined on the visual line V, and a perpendicular h is lowered from the viewpoint e to the center line Cv of the semicylindrical projection plane. The perpendicular h is also determined by the operator.
[0082]
Here, a plane T in contact with the center line Cv of the semi-projection plane is assumed.
[0083]
The line of sight V is the parameter a of the V direction vector₁, B₁, C₁Is expressed by the following formula.
(Xx₁/ A₁= (Y-y₁) / B₁= (Z-z₁) / C₁                ...... (1)
When the visual line V and the viewpoint e are determined, a₁, B₁, C₁, X₁, Y₁, Z₁Is determined. Also, the direction vector parameter a that gives the direction of the viewpoint e with a pointing device such as a trackball or a mouse.₂, B₂, C₂Is also given.
[0084]
As above, the viewpoint e (x₁, Y₁, Z₁) And perpendicular to the viewing line V and the direction is a₂, B₂, C₂When the straight line h is determined, the following equation is established from the orthogonal condition between V and h.
a₁a₂+ B₁b₂+ C₁c₂= 0
The equation for the straight line h is as follows.
(Xx₁/ A₂= (Y-y₁) / B₂= (Z-z₁) / C₂                (2)
Where a₂, B₂, C₂, X₁, Y₁, Z₁Since h = R, the straight line h and the tomographic image 23 (y₁= D₀) Is the straight line h, y = d₀Is given by the following equation.
(Xx₁/ A₂= (D₀-Y₁) / B₂= (Z-z₁) / C₂
(Xx₁) = A₂(D₀-Y₁) / B₂
(Z-z₁) = C₂(D₀-Y₁) / B₂
∴x = a₂(D₀-Y1) / b₂+ X₁
y = d₀
z = c₂(D₀-Y₁) / B₂+ Z₁
This coordinate is the coordinate of the intersection with the tomographic image 23, and d₀If changes, this coordinate also changes.
[0085]
Next, assuming a straight line h ′ obtained by rotating the straight line h about the V axis by an angle θ, h ′ is also orthogonal to V and a point (x₁, Y₁, Z₁) Furthermore, the tomographic image 23 (y = d₀). For this reason, the following equation holds.
(Xx₁/ A₃= (D₀-Y₁) / B₃= (Z-z1) / c₃            ...... (3)
Where a₃, B₃, C₃Is a parameter of the direction vector of h ′.
[0086]
From the equation (3), the coordinates of S ′ are obtained by the following equation.
x = a₃(D₀-Y₁) / B₃+ X₁                                ...... (4)
y = d₀                                                    ...... (5)
z = c₃(D₀-Y₁) / B₃+ Z₁                                ...... (6)
Further, from the orthogonal condition of V and h, V and h ′, the parameter a₁, B₁, C₁, A₂, B₂, C₂, A₃, B₃, C₃The following conditions hold between:
a₁a₃+ B₁b₃+ C₁c₃= 0
cos θ = | a₂a₃+ B₂b₃+ C₂c₃| / √ (T₂× T₃)
However,
T₂= A₂ ²+ B₂ ²+ C₂ ²
T₃= A₃ ²+ B₃ ²+ C₃ ²
Then
(A₂a₃+ B₂b₃+ C₂c₃)²= T₂・ T₃・ Cos²θ
It becomes.
[0087]
here,
T₂・ Cos²θ = k
The above formula is as follows.
(A₂a₃+ B₂b₃+ C₂c₃)²= K (a₃ ²+ B₃ ²+ C₃ ²)
B on both sides₃ ²Divide by the following.
(A₂a₃/ B₃+ B₂+ C₂c₃/ B₃)²= K (a₃ ²+ 1 + c₃ ²)
A₁a₃+ B₁b₃+ C₁c₃= 0 b on both sides₃Divide by the following.
a₁a₃/ B₃+ B₁+ C₁c₃/ B₃= 0
here,
a₃/ B₃= U ...... (7)
c₃/ B₃= V (8)
Then, the following equation holds.
a₁u + b₁+ C₁v = 0
v =-(a₁u + b₁) / C₁                                    ...... (9)
Substituting this v into the above equation and solving for u,

Equation (10) is obtained.
[0088]
Here we introduce the following replacement.
c₁a₂-C₂a₁= T₁
c₁b₂-C₂b₁= T₂
c₁ ²+ A₁ ²= T₃
a₁ ²+ B₁ ²= T₄
Then, the equation (10) becomes as follows.
(T₁u + t₂)²= K (t₃u²+ 2a₁b₁u + t²)
This is organized as follows.
(T₁ ²-Kt₃) U₂ ²+2 (t₁t₂-A₁b₁k) u + (t₂ ²-Kt₄) = 0
From this equation, u is determined as follows.

If u in equation (11) is used, v in equation (9) can be obtained. Further, S ′ (x, y, z) is obtained by using (4), (5), and (6).
[0089]
D for a plurality of tomographic images 23₀Are different and multiple d₀S 'is obtained for. Similarly, different (x, y, z) can be obtained for different viewpoints e (x1, y1, z).
[0090]
On the other hand, when θ is given, the coordinates of the passing points on each tomographic image are obtained from the equations (4), (5), and (6), and the projection data of the contour points in the vicinity thereof are obtained. Since there are a plurality of tomographic images, there may be a plurality of contour points. When θ is given, the plurality of contour points are projected on the cylindrical projection plane 21 at the same position. However, when writing into the display memory from a position far from the viewpoint, a projected image closest to the viewpoint can be seen.
[0091]
In this way, if the viewpoint e is moved by the length of the display line on the visual line V-axis and the angle θ is changed from 0 to ± 90 degrees at each viewpoint e, a three-dimensional projection image is obtained on the cylindrical projection plane 21. It is done. This projection image is converted into the secondary projection plane 4 by panorama conversion, written into the corresponding image display memory 53, and displayed on the CRT monitor 54.
[0092]
Shading conversion is performed on the secondary projection plane 4. For this shading conversion, a method of applying shading according to the distance from the visual line V, a method of performing luminance conversion according to the angle formed with the projected straight line in each individual plane orthogonal to the visual line, A method of converting the luminance like a contour line according to the distance can be considered.
[0093]
According to the linear panorama projection method of the present embodiment, when projecting a tubular projection target such as a blood vessel wall or an intestinal wall, the panoramic image has little distortion like a panoramic photograph cut along a straight line or a curve. A wide field of view is obtained.
[0094]
《Curve panorama projection method》
FIG. 12 is a flowchart showing the procedure of an embodiment of the curved panorama projection method according to the present invention. Since the hardware configuration to which the curved panorama projection method of the present embodiment is applied is not different from the hardware configuration to which the linear panorama projection method is applied, the description thereof is omitted.
[0095]
Step 201: In the curved panorama projection method according to the present invention, an appropriate visual curve is drawn through a tube with respect to a curved tubular projection object using a pointing device such as a mouse or a trackball. A viewpoint is distributed on this visual curve.
Step 202: An arbitrary point of the visual curve is determined, a tangent line is drawn at the point, and a short cylindrical projection plane with the tangent as the central axis is assumed.
Step 203: Project an object in a short range by the curved panorama projection method using the short cylindrical projection surface as a projection curved surface. In this projection method, first, projection is performed on a projection surface (cylindrical projection surface: a projection plane before correction by panorama conversion described later) formed by a cylindrical projection surface by a linear projection (projection method combining parallel projection and central projection) method. .
Step 204: After the projection, the results of the plurality of projection curved surfaces are developed on a secondary projection plane by panorama transformation, which will be described later, and arranged on a straight line to obtain the projection target projection image.
[0096]
Here, panorama conversion refers to a process of projecting a projection target onto a cylindrical projection curved surface, expanding the cylindrical projection plane into a plane, and projecting the projection target onto a secondary projection plane.
[0097]
That is, in the present invention, after projecting a curve using the cylindrical projection surface as a projection surface, the projection image is developed on a projection plane. In this case, each point distributed on the semi-cylindrical projection plane, which is the projection plane, is associated with the display pixel address of the CRT, and the panoramic image display effect is obtained on the projection plane (CRT screen).
[0098]
Next, the principle of panorama conversion of the above-described inventive method will be described with reference to FIGS.
[0099]
FIG. 13 is a diagram for explaining the principle of widening the field of view while reducing the distortion by developing a projection image of a cylindrical projection surface in which the tangent line of the visual curve coincides with the central axis into a plane by curve panorama conversion in the curve panorama projection method. It is. In FIG. 13, a short cylindrical projection plane 21 is a cylindrical projection plane having a center at a viewpoint e on the visual curve C and a tangent line V passing through the viewpoint e as a central axis. Here, the direction of the tangent line V is set parallel to the x-axis. The plane 4 is a secondary projection plane that is in contact with the origin O of coordinates (x, y, z) and is perpendicular to the z-axis at the origin O, and is a secondary projection plane as a projection plane after correction by panorama transformation. It is. This projection plane 4 corresponds to a CRT display screen.
[0100]
In FIG. 13, x, y, z are axes of the three-dimensional coordinate system, O is the origin of the three-dimensional coordinate system, e is a viewpoint on the curve C, and C is a spatial curve or visual curve in which the viewpoint e is continuously distributed. , V is the tangent of the curve C at the viewpoint e, and R is the radius of the cylindrical projection surface 21. The radius R is also the distance between the visual curve C and the projection plane 4. Q is a point on the cylindrical projection surface (x₁, Θ) and P are points (η on the secondary projection plane 4)₁, Ξ₁), Θ is an angle at which the entire arc is viewed from the viewpoint e, θ is an angle formed by a line connecting the Q point and the V axis and the Z axis, dθ is a unit angle obtained by equally dividing 180 degrees into N, and L is on the cylindrical projection plane 21. The arc OQ, L ′ is a straight line OP, η on the y-axis having the same length as L₁Is the X coordinate on the CRT corresponding to point P, ξ₁Is the Y coordinate on the CRT corresponding to point P.
[0101]
FIG. 14 is a diagram for explaining curve panorama conversion when the center angle of the cylindrical projection surface is 180 degrees in the principle of FIG.
[0102]
In FIG. 13, focusing on the yz plane at x = 0, FIG. 14 is obtained.
[0103]
In FIG. 14, planes orthogonal to the visual curve C (arbitrary yz planes) are independent, and projection calculation may be performed within each plane. Therefore, focusing on the yz plane at x = 0, FIG. 14 is obtained. In FIG. 14, the 180 degree angle of the semicircular arc ridge is divided by equal angles, and this is made to correspond to the horizontal (y-axis) direction display pixel. It may be considered that the circumference of the semicircular arc is divided at equal intervals to correspond to the display pixels.
[0104]
FIG. 15 is a diagram for explaining curve panorama conversion when the central angle of the cylindrical projection surface is larger than 180 degrees in the principle of FIG. FIG. 15 shows an example of division in the case where the angle Θ for viewing the entire arc ridge from the viewpoint e is larger than 180 degrees, but the formula does not change even in this case.
[0105]
In FIG. 14, the angle QeO is θ, the angle per pixel is dθ, and N is the horizontal on the CRT.
When the number of display pixels in the (X axis) direction (example: 512) and n is the number of pixels representing an arbitrary position, the following equation is established.
dθ = Θ / N = π / N
L ′ = L
ξ₁= OQ₁= L = R · ndθ = π · n · R / N
η₁= X₁(Perpendicular to the page)
In FIG. 13, Θ is an angle at which the entire semicircular arc is viewed from the visual curve C, and dθ and θ are expressed in radians. Q is a point on the cylindrical projection surface 21 corresponding to the point P on the projection plane 4, θ is an angle formed by a line connecting the Q point and the V axis and the z axis, and L is a length of an arc on the cylindrical projection surface 21. L ′ is a line segment having the same length as L and is a straight line OP on the y-axis.
[0106]
Here, the range of OA = π · R / 2 and twice the length of OA is made to correspond to the horizontal (X-axis) display length of the CRT screen. The length (Y axis: direction perpendicular to the paper surface) is determined by the number of pixels on the CRT screen.
[0107]
FIG. 16 is a diagram for explaining the principle of widening the field of view while reducing the distortion in the curved panorama projection method by developing a projection image of a cylindrical projection surface having a visual curve on the outside by curved panorama conversion. FIG. 16 shows a case where the distance between the visual curve C and the cylindrical projection surface 21 is larger than the radius of the cylinder.
[0108]
FIG. 17 is a diagram for explaining curve panorama conversion when the center angle of the cylindrical projection surface is 180 degrees in the principle of FIG. That is, when attention is paid to the yz plane at x = 0 in FIG. 16, FIG. 17 is obtained. In FIG. 17, the coordinates on the yz plane of the intersection point Q between the straight line Pe and the cylindrical projection plane are centered on the point O ′ at a distance R from the straight line connecting the points P and e on the y axis and the origin on the z axis. And an intersection point Q with the circumference of the radius R.
[0109]
16 and 17, x, y, z are axes of the three-dimensional coordinate system, O is the origin of the three-dimensional coordinate system, e is a viewpoint, C is a visual curve in which the viewpoint e is continuously distributed, and h is a viewpoint. e is the distance between the projection plane 4, R is the radius of the cylindrical projection plane 21, and P is a point on the projection plane 4 (X₁, Y₁), Θ is the angle at which the entire arc is viewed from viewpoint e, P₁Is the point Q on the cylindrical projection plane 21₁, Θ is the angle formed by the line connecting the Q point and the V axis and the z axis, dθ is the unit angle obtained by equally dividing the angle Θ into N, and L is the cylindrical projection plane 21. Arc OQ₁, L 'is a line segment with the same length as L, and the length OP of the straight line on the y-axis₁It is.
[0110]
In FIG. 17, when the angle QO′O is φ and the angle eQO ′ is ω, the following equation is established.
φ = ω + θ
R / sin θ = (h−R) / sin ω
From these two equations, η₁, Ξ₁Is required.
ω = sin￣¹[{(H−R) sin θ} / R]
dθ = Θ / N
θ = n · dθ = n · Θ / N
L ′ = L
therefore
ξ₁= R ・ φ = R (ω + θ)
η₁= L
This η₁, Ξ₁Becomes the pixel address on the display memory. That is, the point P on the secondary projection plane 4 is a point (η on the CRT screen).₁, Ξ₁) And panorama conversion has been executed.
[0111]
Next, a procedure for constructing a three-dimensional image from a plurality of tomographic images by the curved panorama projection method will be described with reference to FIGS. 19 to 23, a tomographic image is first projected on the cylindrical projection surface 21, and then the projection image is developed by panorama conversion and converted into the projection plane 4.
[0112]
FIG. 18 is a diagram for explaining the principle of converting pixel coordinates of a tomographic image into pixel coordinates on a projection plane when a three-dimensional image is constructed from a plurality of tomographic images by the curved panorama projection method. In the example shown in FIG. 18, in order to simplify the description, the three-dimensional coordinate system is such that the central axis 31 of the cylindrical projection surface 21 and the tomographic image plane 23 are parallel and the xy plane T is parallel. Is defined. The center line of the cylindrical projection surface 21 is parallel to the x axis. In FIG. 18, x, y, z are axes of the three-dimensional coordinate system (x, y, z), e point (0, 0, R) is the position of an arbitrary viewpoint e on the visual curve C, and V is the viewpoint. The tangent of curve C at e, Q point (x, y, z) is a point on the cylindrical projection plane 21 and S point (x₀, Y₀, Z₀) Is a point where the straight line 22 connecting the point e (0, 0, R) and the point Q (x, y, z) and the tomographic image 23A intersect, and R is the z coordinate of the viewpoint e.
[0113]
Here, the straight line 22 is drawn perpendicularly to the tangent line V at the point e of the visual curve C from the viewpoint e. D₀Is the position on the z-axis of the tomographic image 23A and is determined at the time of calculation.
[0114]
In FIG. 18, if attention is paid to each viewpoint e, it can be considered that fan-shaped surfaces are stacked in the z-axis direction. In other words, if projection calculations are executed in a sector-shaped plane and are stacked, a three-dimensional image can be displayed.
[0115]
FIG. 19 is a diagram for explaining curve panorama conversion when the tomographic plane and the projection plane are parallel in the principle of FIG.
[0116]
Attention is paid to a plane B perpendicular to the tangent V at the point e of the curve C passing through the viewpoint e at the point e. FIG. 19 shows a state in which tomographic images 23B to 23H are prepared in addition to the tomographic image 23A and viewed from the x-axis direction in the same coordinate system. In FIG. 19, tomographic images 23A to 23H are tomographic images obtained at equal intervals in the same direction with respect to the same object, and the organ regions B1, B2, B3, and B4 are emphasized and written on the tomographic image 23. is there. By curve panorama conversion, first, organ regions B1, B2, B3, and B4 are projected onto the cylindrical projection plane 21, and further panorama transformed and projected onto the secondary projection plane 4, B1 ′, B2 ′, B3 ′, B4 ′. In addition, although the example of equal intervals is shown here, it does not necessarily need to be equal intervals.
[0117]
Here, when storing the projection data B1 ′, B2 ′, B3 ′, and B4 ′ in a display memory (not shown), in order to produce a three-dimensional effect, the projection data existing farther from the viewpoint e is written first. , Projection data existing in the vicinity is overwritten on the previous projection data at a later timing. Thereafter, shading processing (shading) is executed.
[0118]
FIG. 20 is a diagram for explaining the principle of curve panorama conversion when the tomographic plane and the projection plane intersect in the principle of FIG. FIG. 20 shows an example in which the example of FIG. 19 is more generalized and the cylindrical projection plane and the tomographic image plane are not parallel. In this case, the tomographic images 23A, 23B,. . . . . . . 23H, tomographic images 23a, 23b, 23c,... Directed to a plane parallel to the projection plane 4 by an interpolation calculation method. . . . It is necessary to make 23h. The subsequent projection calculation is the same as in FIG.
[0119]
FIG. 21 is a diagram for explaining curve panorama conversion when the visual curve, the tomographic plane, and the projection plane have a more complicated positional relationship. S point on the tomographic image 23 (x₀, D₀, Z₀) Shows that the projection result is a point P (x, y, z) on the plane T.
[0120]
In FIG. 21, when the tomographic image 23 is projected onto the cylindrical projection surface 21 by the curved panorama projection method, the pixel coordinates of the tomographic image 23 are converted into coordinates on the cylindrical projection surface 21 as follows.
[0121]
Here, in order not to lose generality, the positional relationship is set as follows. In FIG. 21, the input tomographic image 23 is in a plane perpendicular to the y-axis and d from the origin.₀Is in the distance. A plurality of tomographic images are represented by a distance d from the origin.₀Changes.
[0122]
The visual curve C is an arbitrary curve in the three-dimensional space. Here, an arbitrary viewpoint e on the curve C is determined, and a tangent line V is drawn on the curve C at that point. First, a cylindrical projection surface 21 with the tangent line V as the central axis is assumed. Since the viewpoint e moves on the curve C, the tangent line V and the cylindrical projection plane 21 paired therewith also move in the three-dimensional space (x, y, z). However, the tomographic image 23 is fixed in a three-dimensional space (x, y, z).
[0123]
Next, a perpendicular h is dropped from the viewpoint e on the tangent line V to the center line Cv of the semi-cylindrical projection plane. The operator determines the perpendicular h using a pointing device such as a trackball or a mouse.
[0124]
A plane T that is in contact with the center line Cv of the semi-projection plane is assumed. This plane T becomes the secondary projection plane 4. The plane T also moves with the viewpoint e.
[0125]
FIG. 22 is a diagram showing the relationship between the visual curve C in the three-dimensional space and the tangent line V at the viewpoint e in FIG.
[0126]
Here, in the actual calculation, the viewpoint e (x on the visual curve C₁, Y₁, Z₁) And a point on the visual curve C that is a minute distance Δs away from the viewpoint e is defined as es (xs, ys, zs). Here, it is assumed that the arbitrarily given visual curve C changes sufficiently smoothly. This curve may be given by a mathematical formula, but it is easier to give this curve with a mouse or a trackball. The locus given by a mouse, a trackball, or the like may be approximated by a quadratic curve, or may be approximated by a locally short straight line, and the entire curve may be approximated by a broken line.
[0127]
Changes in the vector e → es in the x, y, and z directions are denoted by Δx, Δy, Δz, and a₁, B₁, C₁Is defined as follows.
a₁= Δx, b₁= Δy, c₁= Δz
Then, point e (x on curve C₁, Y₁, Z₁) Can be approximated by the following equation using coefficients a 1, b 2, and c 2.
(Xx₁/ A₁= (Y-y₁) / B₁= (Z-z₁) / C₁              (12)
When the visual curve C and the viewpoint e are determined, V is determined.₁, B₁, C₁, X₁, Y₁, Z₁Is decided. Also, a direction vector parameter a that gives the direction of the viewpoint e with a trackball, a mouse, or the like.₂, B₂, C₂Is also given.
[0128]
Viewpoint e (x as described above₁, Y₁, Z₁), Perpendicular to the tangent line V, and the direction is a₂, B₂, C₂Is determined from the orthogonal condition of V and h.
a₁a₂+ B₁b₂+ C₁c₂= 0
The equation for the straight line h is as follows.
[0129]
(Xx₁/ A₂= (Y-y₁) / B₂= (Z-z₁) / C₂              (13)
Where a₂, B₂, C₂, X₁, Y₁, Z₁Is decided. Further, h = R. Therefore, the straight line h and the tomographic image 23 (y₁= D₀) Is the straight line h, y = d₀Is given by the following equation.
(Xx₁/ A₂= (D₀-Y₁) / B₂= (Z-z₁) / C₂
(Xx₁) = A₂(D₀-Y₁) / B₂
(Z-z₁) = C₂(D₀-Y₁) / B₂
∴x = a₂(D₀-Y₁) / B₂+ X₁
y = d₀
z = c₂(D₀-Y₁) / B₂+ Z₁
This coordinate is the coordinate of the intersection with the tomographic image 23, and d₀If changes, this coordinate also changes.
[0130]
Assuming a straight line h ′ obtained by rotating the straight line h about the V-axis by an angle θ, h ′ is also orthogonal to the tangent line V and points e (x₁, Y₁, Z₁) Furthermore, the tomographic image 23 (y = d₀). Therefore, the straight line h ′ is given by the equation (14).
(Xx₁/ A₃= (D₀-Y₁) / B₃= (Z-z₁) / C₃              (14)
Where a₃, B₃, C₃Is a parameter of the direction vector of the straight line h '.
[0131]
From the equation (14), the coordinates of the intersection S ′ (x, y, z) between the straight line h ′ and the tomographic image 23 are obtained by the equations (15) to (17).
x = a₃(D₀-Y₁) / B₃+ X (15)
y = d₀                                                  ...... (16)
z = c₃(D₀-Y₁) / B₃+ Z (17)
Further, the parameter a₁, B₁, C₁, A₂, B₂, C₂a₃, B₃, C₃The following conditions hold between:
a₁a₃+ B₁b₃+ C₁c₃= 0
cos θ = | a₂a₃+ B₂b₃+ C₂c₃| / √ (T₂× T₃)
T₂, T₃Was as follows.
T₂= A₂ ²+ B₂ ²+ C₂ ²
T₃= A₃ ²+ B₃ ²+ C₃ ²
Then
(A₂a₃+ B₂b₃+ C₂c₃)²= T₂T₃・ Cos²θ …… (18)
here,
T₂・ Cos²θ = k
Then, the equation (18) becomes the equation (19).
(A₂a₃+ B₂b₃+ C₂c₃)²= K (a₃ ²+ B₃ ²+ C₃ ³) (19)
B on both sides₃ ²When divided by, the equation (20) is obtained.
(A₁a₃/ B₃+ B₁+ C₁c₃/ B₃)²= K (a₃ ²+ 1 + c₃ ²) (20)
A₁a₃+ B₁b₃+ C₁c₃= 0 b on both sides₃Divide by the following.
a₁a₃/ B₃+ B₁+ C₁c₃/ B₃= 0
here,
a₃/ B₃= M
c₃/ B₃= N
Then, the following equation holds.
a₁m + b₁+ C₁n = 0
n =-(a₁m + b₁) / C₁                                    (21)
Substituting n in equation (21) into equation (20) and solving for m results in equation (22).

Here, the following replacement is introduced.
c₁a₁-C₂a₁= T₁
c₁b₂-C₂b₁= T₂
c₁ ²+ A₁ ²= T₃
a₁ ²+ B₁ ²= T₄
Then, equation (22) becomes as follows.
(T₁m + t₂)²= K (t₃m + 2a₁b₁m + t₄)
If this is arranged, it will become like (23) Formula.

From this equation, m is obtained from equation (24).

When m in the equation (24) is used, n in the equation (21) is obtained.
[0132]
Based on these values, the intersection S ′ (x, y, z) on the tomographic image 23 is obtained by using the equations (15), (16), and (17).
[0133]
D for a plurality of tomographic images 23₀Are different, so multiple d₀Respectively, S ′ (x, y, z) is obtained. Different viewpoints e (x₁, Y₁, Z₁) Similarly, different S ′ (x, y, z) can be obtained.
[0134]
On the other hand, when θ is given, the coordinates of the passing points on each tomographic image are obtained from the equations (15), (16), and (17), and the projection data of the neighboring contour points are obtained. Since there are a plurality of tomographic images, a plurality of contour points may exist. When θ is given, the plurality of contour points are projected on the cylindrical projection surface 21 at the same position. However, if writing is made to the display memory from a position far from the viewpoint, a projected image closest to the viewpoint can be seen.
[0135]
The distance from the viewpoint e is obtained as follows. A distance eS 'from a given viewpoint e to an arbitrary point S' on the arbitrary plane 23 can be calculated by the following equation using the distances eS and SS 'using the coordinates of S and S'.
eS '= √ {(eS)²+ (SS ')²} (25) Using this eS ', the distance from the viewpoint e is determined, and for example, shading conversion is executed.
[0136]
When the viewpoint e is moved little by little in the region of the length displayed on the visual curve C, and the angle θ is changed from 0 to, for example, ± 90 degrees or ± 180 degrees at the position of each viewpoint e, the primary projection image is obtained. It is obtained on the cylindrical projection surface 21. When this projection image is converted into the secondary projection plane 4 by panorama conversion and written in the corresponding image display memory, it is displayed on the CRT.
[0137]
FIG. 23 is a diagram showing the mutual relationship of the primary projection images that have been subjected to curve panorama conversion on the secondary projection plane. The primary projection image projected onto the cylindrical projection surface 21 having the length δV is written in the image memory with the width W in the x direction corresponding to 512 points. In the y-axis direction, projection images having a length of δV are arranged by the length of the curve C to correspond to 512 points.
[0138]
Shading conversion is performed on the secondary projection plane 4. For shading conversion, a method of applying shading according to the distance from the visual curve C, a method of converting luminance according to an angle formed with a projection line in each individual plane orthogonal to the visual curve, Depending on the distance, a method of converting the luminance like a contour line can be considered.
[0139]
《Panorama projection method using arbitrary curved surface》
In the embodiment of the linear panorama projection method, the panorama projection method onto the cylindrical surface is dealt with. FIG. 24 is a flowchart showing the procedure of the panorama projection method onto the arbitrary curved surface.
[0140]
Step 301: In the panoramic projection method onto an arbitrary curved surface, first, an arbitrary straight line E in which the viewpoint is distributed is drawn on the projection object placed in the three-dimensional space. Although an example of a straight line is shown here, this example can be applied even if it is a curve, assuming a tangent at each point on the curve.
Step 302: Assume a projection plane T composed of an arbitrary curved surface parallel to the straight line. The projection surface T may be a flat surface.
Step 303: A plane t orthogonal to the visual line at each point of the visual line E is assumed.
Step 304: Obtain an intersection line between the plane t and the projection target. Further, an intersection curve U with the projection plane is obtained.
Step 305: The intersection line and the intersection curve U are mapped onto the xy plane. The intersection curve is also mapped.
Step 306: Projection processing is performed on the xy plane.
Step 307: The viewpoint on the line of sight is moved, and the above process is repeated from step 303.
Step 308: After calculating a necessary section on the line of sight, the result is subjected to, for example, shading conversion and displayed on the CRT.
[0141]
The principle of linear panorama conversion to an arbitrary curved surface will be described with reference to FIGS.
In FIG. 25, E is a straight line in which the viewpoints are continuously distributed, and is parallel to the xy plane. In addition, ei (e₁, E₂, E₃) Represents each viewpoint. S represents a projection object in the three-dimensional space, and s₁, S₂Represents a point in S. T is a plane for projecting the projection target and is the same as the xy plane. The data projected on this plane is displayed on the CRT, for example, by shading conversion.
[0142]
Here, each point e on the straight line E₂A plane t perpendicular to the straight line E is considered. Focusing on the positional relationship on the plane t, t is e.₂, S₂And e on the plane t₂And the intersection line U2 on the xy plane can be regarded as a projection line, so one projection calculation is performed in the plane t. S ′ is a cross section of the projection target S along the plane t. Such calculation is performed for each point ei on the straight line E, and as a result, a projected image is obtained on the xy plane.
[0143]
In FIG. 25, focusing on the plane t, FIG. 26 is obtained. Point e in FIG.₂Is a viewpoint on the line of sight E. The point Q is a point S in the projection object S.₂Straight line U₂Is a projection. In FIG. 26, the distance L from the point O to the point Q is expressed by the following equation.
[0144]
L = h · tan θ
FIG. 27 shows an example in which the projection surface T is a curved surface, and the projection line U₂Becomes a curve. In this case, the idea is the same, but the projection plane T to the plane T₂A mapping to is needed. This mapping method includes a distance OP along the curved surface.₁Straight OQ₂Method of mapping to, or perpendicular to the plane, straight line OQ₁A method of mapping is conceivable.
[0145]
Curve OP₁Can be calculated using the function f of the curve. Details of the calculation method are described in, for example, Sadaharu Takagi, “Introduction to Analysis”, pages 132 to 139 (published June 30, 1968, third edition, published by Iwanami Shoten).
[0146]
28 to 34 illustrate a method for constructing a three-dimensional image from a plurality of tomographic images by a curved panorama projection method. First, in the above three-dimensional image construction method, coordinate conversion by curved panorama projection will be described. In projecting each tomographic image onto the projection plane, the operation of converting the pixel coordinates of each tomographic image into coordinates on the projection plane is performed as follows.
[0147]
In FIG. 28, for simplicity of explanation, the coordinate system is such that the line E on which the viewpoint is distributed is a straight line, further has an intersection point on the z axis parallel to the x axis, and the tomographic image 23 is parallel to the xy plane 30. Have taken. The projection plane T is a plane and is parallel to the xy plane.
[0148]
In FIG. 28, the position of the viewpoint e is an arbitrary position on the visual line E. x, y, z are axes of the three-dimensional coordinate system (x, y, z), e point (x, 0, R) is the position of an arbitrary viewpoint e on the visual line E, Q point (x, y, z) z) is a point on the projection plane 21 and an S point (x₀, Y₀, Z₀) Is the intersection of the line 22 connecting the point e (x, 0, R) and the point Q (x, y, z) and the tomographic image 23A, and R is the z coordinate of the viewpoint e. Here, the straight line 22 is drawn at right angles to the visual line E from the point e. D₀Is the position of the tomographic image 23A (on the z-axis) and is determined at the time of calculation.
[0149]
In FIG. 28, if attention is paid to each viewpoint e, it can be said that a plane t including the viewpoint e and orthogonal to the visual line E is assumed and the surfaces are stacked in the z-axis direction. That is, a projection calculation in the plane t is performed and stacked, a three-dimensional image can be displayed.
[0150]
FIG. 29 is a diagram illustrating the principle of this embodiment in projection in an arbitrary direction. In FIG. 28, in the orthogonal coordinate system of the three-dimensional coordinates xyz, a plurality of tomographic images 23 are placed perpendicular to the z-axis without losing generality. Although it is assumed that the plurality of tomographic images 23 are parallel to each other, if they are not parallel, parallel images can be easily obtained by interpolation calculation in a three-dimensional space. In addition, although an equal interval is assumed, even when the original image is not an equal interval, an image can be easily obtained by interpolation calculation.
[0151]
Further, an arbitrary straight line on which the viewpoint e is distributed is defined as E, and the straight line E is drawn so as to intersect with the z axis. At this time, the rotation angle from the x-axis of the projection of the straight line E onto the xy plane is defined as α. Further, the inclination of the straight line E from the z-axis is ω. Further, a straight line w that is parallel to the straight line E and exists on a plane including the straight line E is drawn from the origin O. Then, w is an axis whose rotation angle from the x axis on the xy plane from the origin 0 is α and whose inclination from the z axis is ω. Also, the distance d from the origin on the w axis₂Now assume a plane t orthogonal to the w-axis. Further, the distance between the w axis and the line of sight E is set to h₁And Also, the distance h is parallel to the w axis and from the w axis.₂Suppose a projection plane T. Let O ′ be the intersection of the plane t and the w axis. The projection plane T is orthogonal to a straight line connecting the viewpoints e and 0 'on the plane t.
[0152]
Then, the projection from the viewpoint distributed in the line of sight E may be considered in each plane t. That is, a point on the intersection line between each plane t and the plurality of tomographic images 23 may be projected onto the plane T with the intersection point between the line of sight E and the plane t as the viewpoint e.
[0153]
In FIG. 28, an intersection line between the plane t and the plurality of tomographic images 23 is 40, and a projection of the intersection line onto the xy plane is 40 '. Also, the projection of O ′ onto the xy plane is O ″. On the other hand, the intersection of the intersection line of the projection plane T and the plane t and the straight line connecting the viewpoint e and the point O ′ is N, and the xy plane. Let N ′ be the projection of the w-axis onto the xy plane, and let v ′ be the straight line that is on the xy plane, passes through the origin O, and is orthogonal to the straight line u ′.
[0154]
D from origin₁The equation of the plane of the tomographic image 23 at a distance of is represented by (26). At this time, the value of z only changes for a plurality of tomographic images.
z = d₁                                                  ...... (26)
Also, perpendicular to the w-axis and the distance d from the origin O₂The plane t is expressed by the equation (27). However, a unit vector in the same direction as the straight line OO ′ is w (l, m, n).
lx + my + nz = d₂                                    ...... (27)
However, l, m, and n are given by the following equations using ω and α.
l = sinω ・ cosα
m = sinω · sinα
n = cos ω
The straight line E is given from the outside by an operator using a mouse, a trackball or the like. Therefore, when the straight line E is given, the coefficients l, m, and n are determined.
[0155]
FIG. 30 is a diagram viewed perpendicularly to the plane t. In FIG. 30, 23 is a plurality of tomographic images, and T is a projection plane. When viewed perpendicular to the plane t, the projection plane T looks straight. The intersection line 40 is distributed on the plane t, and the interval dl is dl = d.₁It is given by cosecω. The relationship in the xy plane with the equation of the intersection line 40 will be described with reference to FIG.
[0156]
First, an equation of an intersection line between the tomographic image 23 and the plane t in the three-dimensional space by the xyz coordinate system is obtained. There are as many intersection lines as the number of tomographic images. Here, if the direction vector of the intersection of the two planes expressed by the equations (26) and (27) is k (a, b, c), k is the normal of (26) and (27). Vector g₁(0,0,1), g₂Since it is perpendicular to (l, m, n), equations (28) and (29) hold.
kg₁= C = 0 (28)
kg₂= La + mb + nc = 0 (29)
If the direction ratio a: b: c of the direction vector k is obtained from the equations (28) and (29) using l, m, and n, the equation (30) is obtained.
a: b: c = -m: l: 0 (30)
The intersection line is given by equation (6) using these a, b and c (l, m, n).
(Xx₁) / − M = (y−y₁) / L, z = d₁              ...... (31)
Where y₁To find x₁= 0 and y from the equations (26) and (27)₁Ask for.
z₁= D₁                                                ...... (32)
my₁+ Nz₁= D₂                                        ...... (33)
From equation (32), z₁= D₁Is substituted into equation (33) and y₁Is obtained as equation (34).
y₁= (-Nd₁+ D₂) / M (34)
That is, the equation (31) that is the intersection line of the two planes 1 and 2 becomes the following equation (35).
x / −m = {y + (nd₁-D₂) / M} / l, z = d₁        ...... (35)
Or, transform (36)
lx + my + (nd₁-D₂) = 0, z = d₁        ...... (36)
It becomes.
[0157]
FIG. 31 illustrates a plurality of tomographic images 23, the relationship between the w axis and the orthogonal plane t, the projection plane T, and the visual line E, and the relationship of projection onto the xy plane, including xy including the straight line Ou ′. It is the figure cut | disconnected by the surface perpendicular | vertical to a plane. In FIG. 31, the v-axis is d in the equation (36).₁= D₂-It is expressed by the equation (37) with cos ω.
lx + my + d₂(N · cos ω−1) = 0, z = d₁          ...... (37)
The coordinates of the origin O ′ in the xyz coordinate system are given by equations (41) to (43) using equations (38), (39), and (40).
z = d₁                                                ...... (38)
y = x · tanα (39)
lx + my = md₂(N · cos ω-1) (40)
x = {md₂(N · cos ω−1)} / (l + tan α) (41)
y = {md₂(N · cos ω−1)} tan α / (l + tan α) (42)
z = d₁                                                ...... (43)
FIG. 32 is a diagram illustrating the same relationship as FIG. 31, and shows a relationship between a plurality of planes t orthogonal to the w-axis and the projection plane T with respect to a plurality of viewpoints. In FIG. 32, projection directions Pw and Pu are projections on the plane t, and projection directions Pz and Px are projection directions when the relationship between Pw and Pu is projected onto the xy plane. That is, the relationship between the intersection line 40, the line of sight E, the projection plane T, and the like may be directly projected onto the xy plane and the projection calculation may be performed on the xy plane.
[0158]
FIG. 33 is a diagram for explaining the relationship between the xy axis and the u′v ′ axis in a state of being projected onto the xy plane from above the z axis. The relationship between the two is coordinate rotation in the xy plane.
In the projective transformation to the xy plane, the distance d between the intersecting lines on the plane t₁Is converted to the xy plane, the interval dd is expressed by the equation (44). Furthermore, it can be expressed by equation (45) using the interval dz between the tomographic images.
dd = d₁・ Cos ω (44)
dd = dz / tan ω (45)
Moreover, the equation of the straight line passing through (xa, ya) is expressed by the following equation.
y-ya = (yi-ya) (xi-xa) / (xi-xa)
lx + my + (nd₁-D₂) = 0
FIG. 34 is a diagram illustrating a relationship in which an intersection line on the plane t, an intersection line between the plane t and the projection plane T, a viewpoint, and the like are projected onto the xy plane.
[0159]
Here, coordinate rotation on the xy plane is considered. A function equation obtained by rotating the function f (x, y) = 0 by α around the origin is as follows.
[0160]
f (u, v) = f (x · cos α + y · sin α, −x · sin α + y · sin α) = 0
Between the new uv axis and the original xy axis, there is a relationship of the following equations (46) and (47).
[0161]
x = u · cos α−v · sin α (46)
y = u · sin α + v · cos α (47)
When u and v are expressed by substituting x and y in the equations (46) and (47) into the equation (40), the equation (48) is obtained.
[0162]
u · sin ω = (d₂-Nd₁)
u = (d₂-Nd₁) / Sin ω = (d₂-D₁・ Cosω) / sinω …… (48)
That is, the intersection line between the tomographic image 23 and the plane t is obtained from the equation (36). Next, the coordinates of u and v are obtained from equation (48). Actually, since the straight line is parallel to the v-axis, v = constant and only u is changed. Next, the corresponding point S on the tomographic image may be obtained by calculating the x and y coordinates on the contrary by the equations (46) and (47). At this time, if the coordinates do not coincide with the corresponding point S, it can be obtained by interpolation calculation.
[0163]
From the above, the projection onto the projection plane T on the plane t can be considered by the projection onto the xy plane. At this time, the distance between the viewpoint e and the projection plane T is shortened by cos ω, but since all intersecting lines are also shortened, there is no problem even if calculation is performed with the projection image onto the xy plane.
Where z = d₁The u ′ at that time is as follows.
d₁= U ’· tan ω + d₂/ Cosω
Therefore,
u ′ = (d₁・ Cos ω-d₂) / Sinω
FIG. 35 is a diagram in which the relationship on the plane t when the projection surface is a plane is projected onto the xy plane from above, and is a diagram for explaining the projection calculation. In FIG. 35, O is the origin of the xyz axis and u′v′w axis, e ′ is the projection of the viewpoint e onto the xy plane, and N ′ is the projection of N. Here, a projection of a plurality of intersecting lines of the tomographic image 23 and the plane t onto a plurality of xy planes is 23 '. In addition, the projection of the intersection line between the projection plane T and the plane t onto the xy plane is T ′. Hereinafter, each symbol is assumed as shown in the figure. If a straight line connecting the point S on the intersection line 23 'and the projection e' of the viewpoint is extended and the intersection point with the straight line T 'is P, P becomes a projection point of S.
v = u · tan θ−du · tan θ
The coordinates of the intersection vi of the straight line 40 and the straight line 23 ': u = ui are as follows by substituting ui into the above equation.
vi = ui · tan θ−du · tan θ
Although the length of the straight line ON ′ is shortened by cos ω, the distance relationship, that is, the ratio between the tomographic image 23 ′ and the viewpoint e ′ is preserved as it is, and there is no problem even if it is calculated on this. . Further, since the direction perpendicular to the straight line ON 'is not shortened, the projection image obtained on T' can be displayed as it is.
[0164]
FIG. 36 is a diagram in which the relationship on the plane t when the projection surface is a curved surface is projected onto the xy plane from above, and is a diagram for explaining the projection calculation. In FIG. 36, the projection surface is an arbitrary curved surface, but the calculation method is the same as the method described so far. However, there is a method of calculating the length on the curve as the distance from the point N to the point P on the curved surface, or a method of using the point P ″ parallel to the Ou ′ axis.
[0165]
Point S (x₁, Y₁) Is given by the equations (46) and (47) in the new uv coordinate system in which the coordinates are rotated by the rotation angle α. In this uv coordinate system, the above equation (11) is expressed as u = constant, v = variable using a new uv coordinate axis. The distance d from the origin O on the w axis₂As the angle changes, the viewpoint e also moves on the line of sight E on the xy coordinates. In addition, the line of intersection with the tomographic image 23 also changes.
[0166]
FIG. 36 shows a case where the projection surface is an arbitrary curved surface, but the calculation method is the same as the method described so far. However, when displaying a projection image on a plane for display on a CRT, a method using the length of the curve as the distance from the point N to the point P on the curved surface, or the point P parallel to the Ou ′ axis There is a method using the point P ″.
[0167]
The coordinates of the intersection S of the straight line 40 and the straight line 23 'are as follows.
v = u · tan θ−du · tan θ
VT = (R-du) vi / (ui-du)
tan θ = VT / (R−du)
For a plurality of tomographic images 23, the distance d1 between the tomographic images is different, and for a plurality of planes t, the distance d2 from the origin O is different. In this way, the point S on the corresponding tomographic image and the projection point P are obtained.
[0168]
Move the viewpoint e by the length of the display line E axis, calculate the intersection line between the plane t and its tomogram at each viewpoint e, calculate the projection point on the xy plane, and project to the plane T Then, a planar panoramic projection image in an arbitrary direction is obtained. When this projection image is written in the corresponding image display memory, it can be displayed on the CRT.
[0169]
The shading conversion may be performed on the projection plane T. For this shadow conversion, a method of applying shading according to the distance from the line of sight E, a method of converting luminance according to the angle formed with the projection line in each individual plane orthogonal to the line of sight, A method of performing luminance conversion like a contour line according to the distance can be considered.
[0170]
【The invention's effect】
According to the present invention, when projecting a tubular projection target such as a blood vessel wall or an intestinal wall, a panorama with a wide panoramic field of view with little distortion is obtained, such as a panoramic photograph cut open along a straight line or a curve. A projection method is obtained.
[0171]
In addition, according to the panoramic projection method on an arbitrary curved surface, a projection image of a tubular projection target such as a blood vessel wall or an esophageal wall is displayed as a stereoscopic image as if seen inside. Useful for accurate and quick diagnosis.
[Brief description of the drawings]
FIG. 1 is a flowchart showing a procedure of a linear panorama projection method according to the present invention.
2 is a block diagram showing an example of a hardware configuration for executing the linear panorama projection method of FIG. 1; FIG.
FIG. 3 is a diagram for explaining the principle of widening the field of view while reducing the distortion by developing a projection image of a cylindrical projection surface whose visual line coincides with the central axis into a plane by linear panorama conversion in the linear panorama projection method; .
4 is a diagram for explaining linear panorama conversion when the center angle of a cylindrical projection surface is 180 degrees in the principle of FIG. 3; FIG.
FIG. 5 is a diagram for explaining linear panorama conversion when the center angle of a cylindrical projection surface is larger than 180 degrees in the principle of FIG. 3;
FIG. 6 is a diagram for explaining the principle of widening the field of view while reducing the distortion by developing a projection image of a cylindrical projection surface with a visual line on the outside in a straight panorama projection method into a plane by linear panorama conversion;
7 is a diagram for explaining linear panorama conversion when the center angle of a cylindrical projection surface is 180 degrees in the principle of FIG. 6;
FIG. 8 is a diagram for explaining the principle of converting pixel coordinates of a tomographic image into pixel coordinates of a projection plane when a three-dimensional image is constructed from a plurality of tomographic images by a linear panorama projection method.
9 is a diagram for explaining linear panorama conversion when the tomographic plane and the projection plane are parallel to each other in the principle of FIG. 8;
10 is a diagram for explaining the principle of linear panorama conversion when a tomographic plane and a projection plane intersect with each other in the principle of FIG. 8;
FIG. 11 is a diagram for explaining linear panorama conversion when a visual line, a tomographic plane, and a projection plane have a more complicated positional relationship;
FIG. 12 is a flowchart showing a procedure of a curved panorama projecting method according to the present invention.
FIG. 13 is a diagram for explaining the principle of widening the field of view while reducing the distortion by developing a projection image of a cylindrical projection surface in which the tangent line of the visual curve coincides with the central axis into a plane by curve panorama conversion in the curved panorama projection method; It is.
14 is a diagram for explaining curve panorama conversion when the central angle of a cylindrical projection surface is 180 degrees in the principle of FIG. 13;
15 is a diagram for explaining curve panorama conversion when the center angle of a cylindrical projection surface is larger than 180 degrees in the principle of FIG. 13;
FIG. 16 is a diagram for explaining the principle of widening the field of view while reducing the distortion by developing a projection image of a cylindrical projection surface having a visual curve outside on a plane by curve panorama conversion in the curved panorama projection method.
17 is a diagram for explaining curve panorama conversion when the center angle of a cylindrical projection surface is 180 degrees in the principle of FIG. 16;
FIG. 18 is a diagram for explaining the principle of converting pixel coordinates of a tomographic image into pixel coordinates of a projection plane when a three-dimensional image is constructed from a plurality of tomographic images by a curved panorama projection method.
19 is a diagram for explaining curve panorama conversion when the tomographic plane and the projection plane are parallel in the principle of FIG. 18;
20 is a diagram for explaining the principle of curve panorama conversion when the tomographic plane and the projection plane intersect with each other in the principle of FIG. 18;
FIG. 21 is a diagram for explaining curve panorama conversion when a visual curve, a tomographic plane, and a projection plane are in a more complicated positional relationship;
FIG. 22 is a diagram illustrating a relationship between a visual curve C in a three-dimensional space and a tangent line V at a viewpoint e in FIG.
FIG. 23 is a diagram showing the mutual relationship between primary projection images that have been subjected to curve panorama conversion on the secondary projection plane;
FIG. 24 is a flowchart illustrating a procedure of a panoramic projection method onto an arbitrary curved surface.
FIG. 25 is a diagram for explaining the principle of expanding from an arbitrary curved surface to a plane and widening the field of view while reducing distortion in the panoramic projection method.
FIG. 26 is a diagram for explaining the principle of expanding from an arbitrary curved surface to a plane and widening the field of view while reducing distortion in the panoramic projection method.
FIG. 27 is a diagram for explaining the principle of expanding from an arbitrary curved surface to a flat surface and widening the field of view while reducing distortion in the panoramic projection method.
FIG. 28 is a diagram for explaining a method of converting pixel coordinates of a tomographic image into coordinates on a projection plane in a method of constructing a three-dimensional image.
FIG. 29 is a diagram for explaining a method of converting pixel coordinates of a plurality of tomographic images into coordinates on the projection plane in the same manner.
FIG. 30 is a diagram for explaining a coordinate conversion method by straight line projection when a viewpoint, a tomographic image, and a projection plane are in a more complicated positional relationship.
FIG. 31 is a diagram for explaining a coordinate conversion method by linear projection when a viewpoint, a tomographic image, and a projection plane are in a more complicated positional relationship.
FIG. 32 is a diagram for explaining a coordinate conversion method by linear projection when a viewpoint, a tomographic image, and a projection plane are in a more complicated positional relationship.
FIG. 33 is a diagram for explaining a coordinate conversion method by straight line projection when a viewpoint, a tomographic image, and a projection plane are in a more complicated positional relationship.
FIG. 34 is a diagram for explaining a coordinate conversion method by straight line projection when a viewpoint, a tomographic image, and a projection plane are in a more complicated positional relationship.
FIG. 35 is a diagram illustrating projection calculation.
FIG. 36 is a diagram illustrating projection calculation.
FIG. 37 is a diagram for explaining the principle of the linear panorama projection method when the central angle of the cylindrical projection surface is 180 degrees.
FIG. 38 is a diagram for explaining the principle of the linear panorama projection method when the central angle of the cylindrical projection surface is larger than 180 degrees.
FIG. 39 is a diagram showing an overview of an entire curved panorama projection method.
FIG. 40 is a diagram for explaining the principle of the curved panorama projection method when the central angle of the cylindrical projection surface is 180 degrees.
FIG. 41 is a diagram for explaining the principle of the curved panorama projection method when the central angle of the cylindrical projection surface is larger than 180 degrees.
FIG. 42 is a diagram illustrating a relationship between a viewpoint along a visual curve, a tangent line at each viewpoint, and a plurality of short cylindrical projection planes having the tangent line as a central axis.
FIG. 43 is a diagram illustrating panorama projection onto an arbitrary curved surface.
FIG. 44 is a diagram for explaining panorama projection onto an arbitrary curved surface;
FIG. 45 is a diagram illustrating a relationship between a tomographic image and a projection plane in a conventional central projection method.
FIG. 46 is a diagram showing a relationship between a tomographic image and a projection plane in a conventional parallel projection method.
FIG. 47 is a diagram showing how the relationship between a tomographic image and a projected image changes depending on the distance from the viewpoint in the conventional central projection method.
FIG. 48 is a diagram showing how tomographic images are superimposed and displayed as projection images in the conventional parallel projection method.
[Explanation of symbols]
4 Secondary projection plane
21 Cylindrical projection plane
Or a primary cylindrical projection plane with the tangent V as the central axis
23 Tomographic image
C Three-dimensional curve with gaze distribution
e Viewpoint on straight line or view on 3D curve C
h Distance between viewpoint e and cylindrical projection surface 21
h A perpendicular drawn from the viewpoint e to the center of the projected curved surface
L Arc OQ on the cylindrical projection surface 21
Line segment on straight line O2Q "having the same length as L'L
Or a line on the secondary projection plane with the same length as L
P A point (x 1, y 2, z 2) on the secondary projection plane 4
Q Points on the cylindrical projection plane 21 corresponding to points P on the projection plane 4
(Intersection of straight line Pe and cylindrical projection surface 21)
R Radius of primary cylindrical projection surface 21
V Tangent of curve C at viewpoint e
S The point where the line drawn from the viewpoint e to the point Q on the cylindrical projection plane intersects the tomographic image 23
θ Angle between straight line P'e and z-axis
η Display address set parallel to the X axis of CRT
θ Angle between perpendicular h and z axis
ξ Display address set parallel to Y-axis of CRT
φ Angle between line segment Q'O 'and z-axis
ω Angle between line segment Q'e and line segment Q'O '

Claims (2)

Irradiate light rays radially from a viewpoint distributed continuously on an arbitrary curve into a plane perpendicular to the tangent at the viewpoint,
Project the projection object directly onto a short cylindrical projection plane with the tangent as an axis,
Connect a number of the short cylindrical projection surfaces to create a projection image along the curve,
A curved panorama projection method that displays the projection result on a projection plane to display a panorama. Means for setting an arbitrary curve;
Means for projecting a projection object directly on a short cylindrical projection plane having the tangent as an axis by radiating light rays radially from a viewpoint perpendicular to the tangent at the viewpoint from each viewpoint continuously distributed on the arbitrary curve;
Means for connecting a plurality of the short cylindrical projection planes to create a projection image along the curve;
Means for developing the projection result on a projection plane;
A curved panoramic projection apparatus including display means for panoramic display of the projection result developed on the projection plane.

Images