JP3544566B2 - Image enlargement method - Google Patents

Description

【００４０】
ここで ｇ_ｉ （ｐ 、ｑ ）は、分類領域Ｒ_ｉ に属している注目画素を中心とした ｒ×ｒ 画素の矩形領域の参照領域であり、 ｇ_ｉ （ｐ 、ｑ ）の平均をｇ の上にｂａｒ （￣）をつけて表している。又、ｐ 、ｑ をそれぞれ１から ｍＮまでスキャンする。ｒ は３以上の奇数であればよいが、本実施例ではｒ ＝５とする。
【００４１】
次いで、ステップ２３において、σ_ｇ （ｐ 、ｑ ）を用い、閾値 ｔ_ａ 、 ｔ_ｂ によって領域分類し、注目画素（ｐ 、ｑ ）がどの領域に属すかを示す領域マップを作成し、次のステップ２４で、平均値マップを作成する。このときステツプ２３及び２４において、ｐ 、ｑ はそれぞれ１から ｍＮまでスキャンされる。
【００４２】
上記領域分類は、次の（１１）式により行われる。本実施例ではエッジ部Ｒ_１ 、テクスチュア部Ｒ_２ 、平坦部Ｒ_３ へと分類される。
【００４３】
【数２】

【００４４】
次に、ステップ２５において、各領域毎に偏差境界値Ｂ_ｉ を計算する。この計算は、次の（１２）式によって行われる。（１２）式が示すように、この偏差境界値Ｂ_ｉ は、ある領域内で許される平均値からの濃度変化の最大値を表わし、ある領域内の平均濃度（画素値）（ｇ _ｉ のｂａｒ ）と実際に処理中の画像濃度ｇ との変動（変化）量‖ｇ −（ｇ _ｉ のｂａｒ ）‖に、濃度変動の許容範囲を調整するパラメータβ_ｉ をかけることによって求められる。
【００４５】
【数３】

【００４６】
ここでβ_ｉ は適切な境界値を設定するためのパラメータであり、ノルムは、＊を複素共役としたとき次の（１３）式で定義され、積分範囲は分類領域Ｒｉ に属する全ての（ｐ ，ｑ ）にわたる。
【００４７】
【数４】

【００４８】
再び図３のフローチャートに戻り、ステップ５において画像の空間的な拡がりを限定するために、Ｎ×Ｎ画素の原画像の周りにグレイレベル（ｇｒａｙ ｌｅｖｅｌ）をｌ （エルの小文字）とした画像を付加し、図２（Ｂ）に示したｎ Ｎ×ｎ Ｎ画素の画像に拡張する。ここで、グレイレベルｌ は、実数であればどのような値を用いてもよく、ｌ （エル）を０に設定したときには、ＤＣＴ演算の負荷を減らすことができる。又、ｎ は１より大きな実数であって、ｎ Ｎが整数になる値であればよい。更に、ｎｍＮが２の巾乗（累乗）になるようにｎ を設定すると、ＤＣＴの高速演算アルゴリズムを用いることができる。
【００４９】
上記図２（Ｂ）の画像を２次元ＤＣＴにより、同図（Ｃ）に示した周波数成分ａ に変換する（ステップ６）。この周波数成分ａ がＤＣＴ領域における既知情報であり、空間的低周波成分に相当する。この周波数成分ａ は反復演算中に使用するため、メモリ上に保存する（ステップ７）。
【００５０】
次いで、上記周波数成分ａ について、図２（Ｄ）に示すように、拡大率に応じた高周波帯まで周波数領域を拡張する（ステップ８）。このとき、高周波成分の初期値を０とし、拡張されたサイズがｎｍＮ×ｎｍＮ画素分になるようにする。この図２（Ｄ）のように、周波数拡張されたＤＣＴシーケンス（ｓｅｑｕｅｎｃｅ）を２次元逆ＤＣＴ（ＩＤＣＴ）し、画像領域に戻す（ステップ９）。このとき得られる画像はｎｍＮ×ｎｍＮ画素の画像であり、その中心部のｍ Ｎ×ｍ Ｎ画素分αが拡大画像である。
【００５１】
次いで、現在の反復数を更新し（ステップ１０）、上記ステップ９で得られた図２（Ｅ）の画像中心部のｍ Ｎ×ｍ Ｎ画素分αの外側に拡張された×印を付した領域は、上記ＩＤＣＴによりレベルが不明となっているが、この領域では既にそのレベルが図２（Ｂ）の画像からｌ （エル）であることが分かっているので、そのレベルを正しい値、即ちｌ （エル）に修正し、同図（Ｆ）の状態にする（ステップ１１）。この操作が空間的領域制限である。
【００５２】
更に、拡張領域を修正した上記図２（Ｆ）の画像をＤＣＴすることにより、同図（Ｇ）に示す周波数成分ｂ を得る（ステップ１２）。この周波数成分ｂ では、低周波側は既知情報として前記図２（Ｃ）に示した周波数成分ａ であることが分かっているので、その低周波成分を該周波数成分ａ で置き換えて同図（Ｈ）に示したＤＣＴシーケンスとし（ステップ１３）、周波数成分ａ 及びｂ からなる該ＤＣＴシーケンスを更にＩＤＣＴして、同図（Ｉ）の画像とする（ステップ１４）。こうして得られた図２（Ｉ）の画像の中心部分βが拡大画像であり、この画像は前記同図（Ｅ）の拡大画像αより更に解像度が向上している。
【００５３】
次に、ステップ１５において、ステップ４で得たデータを用い、リンギングを抑制する。この処理は図６に示すように各分類領域Ｒ_１ 、Ｒ_２ 、Ｒ_３ 毎にリンギングの修正を行うものである。
【００５４】
各分類領域Ｒ_ｉ に対して行われる詳細な処理を表わすフローチャートを図７に示す。以下、図７を用いて、リンギング修正処理について説明する。
【００５５】
まず、ステップ３１において、処理対象画像ｈ と参照画像から得られた平均値データ（ ｇ_ｉ のｂａｒ ）によってノルムを計算する。ノルムを計算するための積分範囲は分類領域Ｒ_ｉ に属する全ての（ｐ 、ｑ ）である。又、処理対象画像は外側に拡張された領域があり、参照画像とサイズが異なっているので注目画素の位置を揃えるためにｈ に対して（ｄｘ，ｄｙ）画素ずらした位置を注目するようにしている。 ｄｘ 、ｄｙは次の（１４）式で与えられる。
【００５６】
ｄｘ＝ ｍＮ（ｎ −１）／２
ｄｙ＝ ｍＮ（ｎ −１）／２ …（１４）
【００５７】
次に、ステップ３２で、次の（１５）式により、ステップ３１で計算したノルムの２乗（（１５）式の左辺）と、ステップ４で得たＢ_ｉ の２乗を比較する。
【００５８】
【数５】

【００５９】
（１５）式が成り立つとき、即ちノルムの２乗のほうが大きくないときは、この処理は全て終了となり、その他の場合は画素値の変化量が変化量の最大許容値（Ｂｉ ^２ ）を越えているため（リンギングが発生しているため）リンギングを修整する処理を行う必要があり、修正処理の最初として、次のステップ３３へ進み、注目画素位置（ｐ 、ｑ ）を初期化する。
【００６０】
次に、ステップ３４で、注目画素位置（ｐ 、ｑ ）を更新する。即ちｐ 、ｑ のスキャン範囲はそれぞれ１から ｍＮまでとし、全領域がスキャンできるように更新される。
【００６１】
ステップ３５において、ステップ４で作成された領域マップを参照して、現在の注目画素が分類領域Ｒ_ｉ に属しているかどうか判定する。ここで、属していないと判定された場合にはステップ３７へ進み、属している場合には次のステップ３６へ進む。
【００６２】
ステップ３６では、これまでの判定条件によってリンギングの発生が認められているので、次の（１６）式によって処理対象画像を修正する。
【００６３】
【数６】

【００６４】
ここで、（１６）式において、第１項の濃度平均値（ｇ _ｉ のｂａｒ ）に、第２項の画素の平均からの変化量を加えているが、もし第２項で、もとの画像の変化量を加えてしまうとリンギングが発生したままになってしまう。そこで（１６）式に示すように、もとの変化量を線形に縮めた（抑制した）量を第２項で加えるようにしたためリンギングが抑制される。
【００６５】
ステップ３７で全ての（ｐ 、ｑ ）がスキャン済みかどうか判定し、Ｎｏ の場合には、ステップ３４に戻り、Ｙｅｓの場合にはリンギング修正処理を終了する。
【００６６】
ここでの処理が終了した次点で、図２のγはβよりリンギングの少ない画像になっている。
【００６７】
このリンギング修正処理の模式図を図８に示す。図８において、左側が修正前の画像（図２のβ）であり、右側が、これに参照画像のデータを用いてリンギングの修正（図３のステップ１５の処理）を行った修正後の画像（図２のγ）である。図８に示すように、リンギングの修正により平坦部ではリンギングが少なくなり、エッジ部ではエッジが立つようになる。このため、より一層鮮鋭化された画像が得られる。
【００６８】
次に図３のステップ１６で、現在の反復数が設定された反復数に達しているかどうか判定する。判定の結果、Ｎｏ の場合にはステップ１０へ戻り、Ｙｅｓの場合にはステップ１７へ進み、拡大画像を出力し、全ての処理を終了する。
【００６９】
通常のＧ・Ｐ反復法では、フーリエ変換を使用しているが、本実施例では実際に処理される画像が非負の整数で表現されていることを考慮して、フーリエ変換の代わりに離散的コサイン変換（ＤＣＴ）を用いることにより、記憶容量や演算量の点で負荷を低減することを可能とした。
【００７０】
なお、前述したＧ・Ｐ反復法の反復回数としては適切な回数を設定すればよいが、通常１０回以下で十分である。
【００７１】
又、本実施例では分類する領域数が３の場合を示したが、更に細かく分類してもよい。分類する領域数をｉ としたときｉ −１種の閾値（ ｔ_１ 、・・・、 ｔ_ｉ−１ ）、ｉ 種のパラメータβ_ｉ を設定しておけばよい。
【００７２】
次に、本実施例で採用した２次元ＤＣＴと、その逆変換であるＩＤＣＴについて説明する。離散関数ｉ （ｘ ，ｙ ）、０≦ｕ ，ｖ ≦Ｎ−１のＮ×Ｎ点の２次元ＤＣＴは、以下の（１７）、（１８）式で定義される。
【００７３】

【００７４】
【数７】

【００７５】
ここで、０≦ｕ ，ｖ ≦Ｎ−１である。
【００７６】
又、ｃ （ｕ ）は次の（１９）式、（２０）式で定義される。なお、ｃ （ｖ ）も上記ｃ （ｕ ）と同様に定義される。これら関数ｃ （ｕ ）、ｃ （ｖ ）は、逆変換でも使用される。
【００７７】
ｃ （ｕ ）＝１／√２ （ｕ ＝０） …（１９）
ｃ （ｕ ）＝１ （ｕ ＝１，２，・・・，Ｎ−１） …（２０）
【００７８】
２次元ＤＣＴの逆変換ＩＤＣＴは、次の（２１）式、（２２）式で定義される。
【００７９】

【００８０】
【数８】

【００８１】
ここで、０≦ｘ ，ｙ ≦Ｎ−１である。
【００８２】
本実施例においては、ＤＣＴを上記定義のまま用いることもできるが、前述した如く、前記図２に示した画素数ｎｍＮを２の巾乗とする場合に、ＤＣＴには高速演算アルゴリズムが存在するので、この高速演算アルゴリズムのＤＣＴを実際に演算で用いることが好ましい。
【００８３】
図９は、本発明に係る第２実施例に適用される装置構成の概略を示すブロック図である。
【００８４】
本実施例は、カラー画像を拡大する場合の例で、この場合は原画像格納部１０からＲ（赤）、Ｇ（緑）、Ｂ（青）の各信号について、拡大処理部１２でそれぞれ前記第１実施例の場合と同様のリンギング抑制処理を含んだＧ・Ｐ反復法を実行することにより拡大画像を作成することができるようにしたものである。
【００８５】
本実施例によれば、カラー画像についても、各色成分をそれぞれモノクロ画像とみなして前記第１実施例と同様の処理を行うことができるので従来の補間法に比べて極めて高画質で、且つリンギングの少ない拡大画像を作成することが可能となる。
【００８６】
図１０は、本発明に係る第３実施例に適用される装置の基本構成を示したブロック図である。
【００８７】
本実施例は、印刷用カラー画像を拡大する場合の例で、原画像格納部１０からＣ（シアン）、Ｍ（マゼンタ）、Ｙ（イエロー）及びＫ（ブラック）の各色の原信号に対して、拡大処理部１２で前記第１実施例の場合と同様のリンギング抑制処理を含んだＧ・Ｐ反復法を実行することにより、拡大画像が作成されるようになっている。
【００８８】
本実施例によれば、前記第２実施例と同様に各色成分について前記第１実施例と同様に処理することができるので、同様に極めて高画質でリンギングの少ない拡大された印刷用カラー画像を作成することができる。
【００８９】
以上、本発明について具体的に説明したが、本発明は、前記実施例に示したものに限られるものでなく、その要旨を逸脱しない範囲で種々変更可能である。
【００９０】
例えば、Ｇ・Ｐ反復法にて採用する直交変換としてはＤＣＴを用いる場合についてのみ説明したが、これに限られるものでなく、拡大した画像と原画像との間にエネルギーのマッチングが取れるような直交変換であれば、フーリエ変換等の他の直交変換をも採用することができる。
【００９１】
又、色空間が、ＲＧＢ及びＣＭＹＫの場合について説明したが、特定の色空間に限定されるものでなく、いかなる色空間に対しても適用することができる。
【００９２】
又、Ｇ・Ｐ反復法による画像拡大法の場合について説明したが、ディジタルフィルタを用いた画像拡大法にリンギング抑制処理を適用することができる。
【００９３】
【発明の効果】
以上説明した通り、本発明によれば、リンギング発生のない参照画像を用いて、リンギングを抑制する処理を行っているため、リンギングが発生せず、鮮鋭感の向上した拡大画像を得ることができる。
【００９４】
又、参照画像をバイリニア法で作成する場合には、簡単な演算で、平坦部ではリンギングのない滑かな画像が得られるため、処理対象画像のリンギング抑制をより効率良く行うことができる。
【００９５】
又、原画像をサンプリングした際に失われた空間的高周波成分を復元するようにした場合には、ジャギーのないエッジが再現され、テクスチュアの再現性、ハイライトの抜けがよく、高拡大率に強いという、多くの性質を持つ極めて高画質の拡大画像を作成することができるという優れた効果を有する。
【図面の簡単な説明】
【図１】Ｇ・Ｐ反復法の原理を示す説明図
【図２】本発明に係る第１実施例の処理の工程を模式的に示す説明図
【図３】上記実施例の処理の流れを示すフローチャート
【図４】上記実施例に適用される装置の基本構成を示すブロック図
【図５】上記実施例で用いられる参照用データ作成処理を示すフローチャート
【図６】分類領域に対する修正処理を示すフローチャート
【図７】上記分類領域の修正処理の詳細を示すフローチャート
【図８】リンギング修正処理を模式的に示す説明図
【図９】本発明に係る第２実施例に適用される装置の基本構成を示すブロック図
【図１０】本発明に係る第３実施例に適用される装置の基本構成を示すブロック図
【符号の簡単な説明】
１０…原画像格納部
１２…拡大処理部
１４…拡大画像格納部[0001]
[Industrial applications]
The present invention relates to an image enlargement method, and more particularly to an image enlargement method capable of obtaining a clear high-quality enlarged image.
[0002]
[Prior art]
In the fields of image processing systems, image database systems, and high-definition color printing, various high-quality image processing functions are required. One of them is image enlargement. This image enlargement is not only important as one function of the image processing system, but also media having different resolutions (for example, HDTV (high resolution television), NTSC television, electronic still camera, medical imaging system, printing imaging system). ) Is a very important function that can also be used as the resolution conversion required to connect
[0003]
As a conventional image enlargement method, an interpolation method of simply interpolating pixels has been adopted. As a representative interpolation method, a nearest neighbor, a bilinear, and a cubic convolution are known. These interpolation methods are based on the basic concept of interpolation using a sinc function {sinc (x) = sin (x) / x} based on the sampling theorem, and approximated the sinc function to reduce the computational load. By convolving the interpolation function with respect to the sample points of the original image, interpolation is performed between the sample points of the original image to increase the number of pixels.
[0004]
The nearest neighbor uses a rectangular function as an interpolation function, and uses the nearest sample value as an interpolation value. The bilinear uses a triangle function as an interpolation function. The cubic convolution uses a cubic function as an interpolation function, and in the case of one-dimensional, a value interpolated from four neighboring points is used as an interpolation value. .
[0005]
The idea of enlargement by each interpolation method is that an ideal original image before the original image to be enlarged is observed (sampled by scanning) is composed of only frequencies (low frequency components) equal to or less than half the Nyquist frequency. If you are correct. However, although an ideal original image generally has infinitely high frequency components, a low-pass filter (LPF) is used to prevent aliasing (a phenomenon such as moiré or beat) from occurring in the sampled observation image. ) To remove unnecessary high-frequency components. Therefore, the original high-resolution image to be enlarged has already lost spatial high-frequency components that contribute to the sharpness and detail of the image at the time of sampling.
[0006]
As described above, the high-frequency component removed at the time of observation (sampling) is unnecessary for an original image that is not enlarged, but is an essential element for creating a high-resolution enlarged image.
[0007]
[Problems to be solved by the invention]
However, since the spatial high-frequency components lost at the time of sampling cannot be restored by the interpolation method, when the original image is enlarged by interpolation, the spatial high-frequency components originally required are deleted. Will be.
[0008]
Therefore, when the original image is enlarged by the above-mentioned conventional interpolation method, since the spatial high-frequency component is missing, deterioration of the image quality such as blurring, smoothing, or rattling of the edge, and the expression of details are improper. There was a problem that sufficient images were obtained.
[0009]
On the other hand, the present inventor has disclosed in Japanese Patent Application Laid-Open No. 6-54172 that the spatial information lost at the time of sampling is used by using two constraints that the information of the pass frequency range is correct and the spread of the image is limited. Although an image enlarging method for restoring high frequency components has been proposed, there is a problem that ringing still occurs in a flat portion.
[0010]
SUMMARY OF THE INVENTION The present invention has been made to solve the above-mentioned conventional problems, and an object of the present invention is to provide an image enlargement method that improves the quality of an enlarged image, does not cause blurring or jaggy, and has no image quality deterioration due to ringing. And
[0011]
[Means for Solving the Problems]
The present invention provides an image enlarging method for enlarging an image based on image information included in a sampled original image, wherein a reference image having no ringing in a flat portion is prepared for an image to be processed, and the image to be processed is Divided into a plurality of regions having different properties, and for each pixel in each region, the density change from the average density of the corresponding region of the reference image is calculated in advance for each region from the average density in the small region of the reference image. Set based on the integral of the pixel value variation, On a flat part Ringing Restrainable The above object has been achieved by performing processing for limiting the deviation to within an allowable deviation and suppressing ringing.
The present invention also achieves the above object by classifying the processing target pixel into a flat portion, a texture portion, and an edge portion by using a deviation for each small region of the reference image and a preset threshold value. It is.
The present invention also obtains, for each of the classified flat portions, texture portions, and edge portions, an integrated value of a variation amount of a pixel value from an average density in a small area of a reference image, and sets a predetermined allowable range of density variation. The above object is similarly achieved by setting the permissible deviation by multiplying the parameter by adjusting.
The present invention is also directed to a case where the variation amount of the pixel value from the average density in the small region of the reference image in the small region of the processing target image exceeds the allowable deviation, To the density average value, by adding a value obtained by range-compressing the difference between the processing target image and the average value based on the allowable deviation, an error in a small region of the processing target image is included in the allowable deviation, Similarly, the object has been achieved.
[0012]
The present invention also relates to the image enlargement method, wherein the original image before enlargement is provided. Density of each pixel in From By using an interpolation function having a low-pass characteristic, the density values of pixels that do not exist in the original image of the enlarged image are interpolated, The above object is similarly achieved by creating the reference image by an interpolation method.
[0013]
According to the present invention, in the image enlarging method, an image signal to which an image whose initial value for limiting a range of spatial expansion is known is added outside an image signal to be enlarged is defined as an original image signal g. The original image signal g is orthogonally transformed into original frequency information G band-limited to a pass frequency band, and information obtained by expanding a high-frequency band to the original frequency information G according to a desired enlargement ratio is defined as first frequency information F1. After the first frequency information F1 is subjected to inverse orthogonal transformation to obtain a first image signal f1, a second image signal f2 obtained by modifying the value of the limited area of spatial expansion of the first image signal f1 to an initial value is obtained. The second image signal f2 is subjected to orthogonal transformation to obtain second frequency information F2, information The range corresponding to the pass frequency band of F2 is replaced with the original frequency information G, which is information of a correct pass frequency range, and the third frequency information F3 and the third frequency information After applying the same spatial area restriction as the original image signal f1 to the third image signal f3 obtained by inversely orthogonally transforming F3, in the process of repeating the normal transform and the inverse transform by the orthogonal transform as in the orthogonal transform. The spatial high-frequency component (Fi-G) lost at the time of sampling is restored using the two constraints that the information of the pass frequency range is correct and the spatial spread of the image is limited, and the image is enlarged. By doing so, the above-mentioned object is also achieved.
[0014]
[Action]
According to the present invention, when an image to be processed is enlarged, in order to suppress ringing occurring in a flat portion, a reference image created by an appropriate method and having no ringing in the flat portion is prepared. This is created using an interpolation method such as a bilinear method or a cubic method.
[0015]
The edge of the reference image obtained by this interpolation method is dull due to the low-pass filter (LPF) effect of the interpolation method, and there is a problem in image quality. However, in the flat part of the reference image, an image which is free of ringing and which is smoothly expressed can be obtained. The present invention uses the flat portion of the reference image for the purpose of suppressing the occurrence of ringing in the flat portion of the image to be processed.
[0016]
For example, the processing target image is classified into local regions such as flat portions, texture portions, and edge portions, and the processing target image and the reference image are compared and repaired for each region. Correct To determine the maximum value of a certain allowable deviation. At this time, the maximum value of a certain allowable deviation is determined so as to severely limit the error with respect to the reference image so that ringing does not occur in the flat portion. In addition, a loose restriction is imposed on an edge portion with respect to an error from a reference image. Repair within this fixed deviation Correct The ringing energy that appeared on the flat part Gi Energy is added to the edge to make the edge stand out, so that ringing is reduced in the flat portion and the edge is raised in the edge portion. Therefore, a sharp image can be obtained and ringing can be suppressed.
[0017]
In particular, when the reference image is created by the bilinear method, the calculation is easy and the frequency characteristics in the pass frequency range are suppressed, so that the image has LPF-like properties and a smooth image can be obtained.
[0018]
Also, in the process of repeating the forward transform and the inverse transform by, for example, the orthogonal transform, asymptotically by an iterative operation using two constraints that the information of the pass frequency band is correct and the spread of the image is limited. Applying the Gerchberg-Papoulis iterative method (hereinafter abbreviated as GP iterative method) as a basic principle of frequency domain extension to restore information to the image to be processed, and to enlarge the image to be processed For example, by restoring the spatial high-frequency component lost at the time of sampling, estimating and restoring the detail information and edge information of the image, it is possible to further improve the image quality of the enlarged image.
[0019]
Hereinafter, the GP iteration method will be described with reference to FIG.
[0020]
In FIG. 1, (A), (C), (E), and (G) on the left correspond to the frequency domain, and (B), (D), (F), and (H) on the right correspond to the real space domain. FIG. 7B shows the original signal f (x), and the space | x | ≦ x ₀ (Corresponding to the object being limited to a certain size). FIG. 1A shows a Fourier transform F (u) of the original signal f (x), which includes an infinitely high frequency component because the original signal f (x) is region-limited. Will be.
[0021]
FIG. 1C shows the section | u | ≦ u of F (u). ₀ Indicates that only the portion G (u) is observed. That is, the following equation (3) using the window function defined by the following equations (1) and (2) holds.
[0022]
W (u) = 1 (| u | ≦ u ₀ …… (1)
W (u) = 0 (| u |> u ₀ …… (2)
G (u) = W (u) F (u) (3)
[0023]
The inverse Fourier transform of G (u) is g (x) in FIG. 1 (D). Here, it is problematic to find F (u) or f (x) from G (u) or g (x).
[0024]
The first stage of the GP iteration method is as follows. G (u) is | u | ≦ u ₀ , G (x) spreads infinitely. However, the original signal f (x) is in the interval | x | ≦ x ₀ Since the region is known to be limited to the above, the same region limitation is performed for g (x). That is, the section | x | ≦ x of g (x) ₀ Take out only the part of f ₁ (X). This f ₁ When (x) is represented by an expression using a window function w (x) in the spatial domain represented by the following expressions (4) and (5), the following expression (6) is obtained. This is the f shown in FIG. ₁ (X).
[0025]
w (x) = 1 (| x | ≦ x ₀ …… (4)
w (x) = 0 (| x |> x ₀ …… (5)
f ₁ (X) = w (x) g (x) (6)
[0026]
The above f ₁ By performing Fourier transformation on (x), F in FIG. ₁ (U). f ₁ Since (x) is area-limited, F ₁ (U) extends indefinitely. However, the section | u | ≦ u ₀ Since the correct value G (u) = F (u) is already known for ₁ | U | ≦ u in (u) ₀ Is replaced with G (u). The waveform thus formed is represented by G in FIG. ₁ (U). This relationship is expressed by the following equations (7) to (9). And the above G ₁ The inverse Fourier transform of (u) is g in FIG. ₁ (X).
[0027]
G ₁ (U) = G (u) + (1-W (u)) F ₁ (U) ... (7)
G ₁ (U) = G (u) (| u | ≦ u ₀ …… (8)
G ₁ (U) = F ₁ (U) (| u |> u ₀ …… (9)
[0028]
In the above description, (C) and (D) to (G) and (H) in FIG. 1 are the first stage of the GP iteration method. Then, g in FIG. ₁ From (x) to the interval | x | ≦ x ₀ And take out only the part ₁ F corresponding to (x) ₂ (X) (not shown), and this f ₂ (X) is subjected to Fourier transform to obtain an F corresponding to FIG. ₂ By repeating the same operation of calculating (u) (not shown) infinitely, the original signal can be completely restored.
[0029]
【Example】
Hereinafter, embodiments of the present invention will be described in detail with reference to the drawings.
[0030]
FIG. 2 is an explanatory diagram schematically showing a flow of a process executed in the image enlarging method according to the first embodiment of the present invention, and FIG. 3 is a flowchart showing a flow of the process of FIG. is there.
[0031]
In the present embodiment, a monochrome image is enlarged by applying DCT to the GP repetition method. The apparatus having the basic configuration shown in FIG. 12, the enlargement processing unit 12 performs a process described in detail below to create an enlarged image, and performs an operation of storing the enlarged image in the enlarged image storage unit 14.
[0032]
The original image storage unit 10 may be, for example, a magnetic disk, the enlargement processing unit 12 may be an engineering workstation (EWS), and the enlarged image storage unit 14 may be a magnetic disk. Further, the enlarged image created by the enlargement processing unit 12 may be output to an output device such as a display or a printer.
[0033]
The series of processing shown in FIGS. 2 and 3 is executed in the enlargement processing unit 12. Hereinafter, the process of this processing will be described in detail. In FIG. 2, the left side represents the image area, and the right side represents the DCT area.
[0034]
Now, it is assumed that an original image of N × N pixels as shown in FIG. 2A is magnified m times to create an image of m N × m N pixels. The numbers in parentheses in FIG. 2 correspond to the step numbers in the flowchart in FIG.
[0035]
First, in step 1, the number of times of repeating the operation by the GP repetition method and the enlargement ratio are set. _i Threshold t for classification into _a , T _b And boundary value B of deviation _i Parameter β for setting _i Is set, and in step 3, the original image to be enlarged shown in FIG. 2A is read.
[0036]
Next, in step 4, data to be referred to when correcting ringing is created.
[0037]
FIG. 5 is a flowchart showing detailed processing of the reference data creation process. Hereinafter, this process will be described with reference to FIG.
[0038]
First, in step 21, an m 2 reference image is created by the bilinear method, and in the next step 22, the deviation σ for each rectangular area of r × r pixels around the pixel of interest (p 1, q 2) _g Calculate (p, q). The calculation of this deviation is performed by the following equation (10).
[0039]
(Equation 1)

[0040]
Where g _i (P, q) is the classification area R _i Is a reference area of a rectangular area of r × r pixels centering on a pixel of interest belonging to _i The average of (p 1, q 2) is represented by adding bar (￣) above g 1. Also, p and q are each scanned from 1 to mN. Although r may be an odd number of 3 or more, r is set to 5 in this embodiment.
[0041]
Next, in step 23, σ _g Using (p, q), the threshold t _a , T _b A region map indicating which region the pixel of interest (p 1, q 2) belongs is created, and an average value map is created in the next step 24. At this time, in steps 23 and 24, p and q are scanned from 1 to mN, respectively.
[0042]
The area classification is performed by the following equation (11). In this embodiment, the edge portion R ₁ , Texture R ₂ , Flat part R ₃ Classified as
[0043]
(Equation 2)

[0044]
Next, in step 25, the deviation boundary value B is set for each region. _i Is calculated. This calculation is performed by the following equation (12). As shown in equation (12), this deviation boundary value B _i Represents the maximum value of the density change from the average value allowed in a certain area, and the average density (pixel value) (g _i (Bar) and the image density g during the actual processing (change) Δg− (g _i Bar) ‖ is a parameter β for adjusting the allowable range of concentration fluctuation. _i Is obtained by multiplying by
[0045]
[Equation 3]

[0046]
Where β _i Is a parameter for setting an appropriate boundary value, and the norm is defined by the following equation (13) when * is a complex conjugate, and the integration range extends over all (p 1, q) belonging to the classification region Ri. .
[0047]
(Equation 4)

[0048]
Returning to the flowchart of FIG. 3 again, in step 5, in order to limit the spatial spread of the image, an image in which the gray level (gray level) is 1 (lower case letter) is set around the original image of N × N pixels. In addition, the image is expanded to an image of n N × n N pixels shown in FIG. Here, any value may be used as the gray level l as long as it is a real number. When l (ell) is set to 0, the load of the DCT operation can be reduced. Also, n may be a real number greater than 1 and a value where n N is an integer. Furthermore, when n is set so that nmN is a power of 2 (power), a high-speed DCT algorithm can be used.
[0049]
The image shown in FIG. 2B is converted into the frequency component a shown in FIG. 2C by two-dimensional DCT (step 6). This frequency component a 1 is known information in the DCT domain, and corresponds to a spatial low frequency component. This frequency component a is stored in the memory for use during the repetitive operation (step 7).
[0050]
Next, as shown in FIG. 2D, the frequency domain of the frequency component a 1 is extended to a high frequency band corresponding to the magnification (step 8). At this time, the initial value of the high frequency component is set to 0, and the expanded size is set to be nmN × nmN pixels. As shown in FIG. 2D, the frequency-expanded DCT sequence (sequence) is subjected to two-dimensional inverse DCT (IDCT) and returned to the image area (step 9). The image obtained at this time is an image of nmN × nmN pixels, and α of mN × mN pixels at the center thereof is an enlarged image.
[0051]
Next, the current number of repetitions is updated (step 10), and an extended x mark is added to the outside of m N × m N pixels α in the center of the image in FIG. Although the level of the region is unknown by the IDCT, the level is already known to be l (ell) from the image of FIG. 2B in this region. 1 (L), and the state is changed to the state shown in FIG. This operation is a spatial area limitation.
[0052]
Further, the image of FIG. 2F in which the extended area is corrected is subjected to DCT to obtain a frequency component b 2 shown in FIG. 2G (step 12). In this frequency component b 1, it is known that the low frequency side is the frequency component a 2 shown in FIG. 2 (C) as known information, so that the low frequency component is replaced with the frequency component a 2 (H ) (Step 13), and the DCT sequence composed of the frequency components a and b is subjected to IDCT to obtain an image shown in FIG. 1I (step 14). The central portion β of the image of FIG. 2 (I) thus obtained is an enlarged image, and this image has a further improved resolution than the enlarged image α of FIG. 2 (E).
[0053]
Next, in step 15, ringing is suppressed using the data obtained in step 4. This processing is performed for each classification area R as shown in FIG. ₁ , R ₂ , R ₃ The ringing is corrected every time.
[0054]
Each classification area R _i FIG. 7 is a flow chart showing a detailed process performed for. Hereinafter, the ringing correction processing will be described with reference to FIG.
[0055]
First, in step 31, the average value data (g obtained from the processing target image h and the reference image) _i Is calculated by bar). The integration range for calculating the norm is the classification region R _i (P 1, q 2). Also, since the image to be processed has a region extended outside and has a size different from that of the reference image, a position shifted by (dx, dy) pixels with respect to h in order to align the position of the pixel of interest. ing. dx and dy are given by the following equation (14).
[0056]
dx = mN (n-1) / 2
dy = mN (n-1) / 2 (14)
[0057]
Next, in step 32, the following equation (15) is used to calculate the square of the norm calculated in step 31 (the left side of equation (15)) and the B obtained in step 4 _i Are compared.
[0058]
(Equation 5)

[0059]
When the expression (15) is satisfied, that is, when the square of the norm is not larger, this processing is all terminated. In other cases, the amount of change in the pixel value is equal to the maximum allowable value of the amount of change (Bi ² ) Is exceeded (since ringing has occurred), it is necessary to perform processing for correcting ringing. As a first step of the correction processing, the process proceeds to the next step 33, where the pixel position of interest (p 1, q) is initialized. I do.
[0060]
Next, in step 34, the target pixel position (p, q) is updated. That is, the scan ranges of p and q are set to 1 to mN, respectively, and are updated so that the entire area can be scanned.
[0061]
In step 35, referring to the area map created in step 4, the current pixel of interest is _i Judge whether it belongs to. Here, if it is determined that they do not belong, the process proceeds to step 37, and if they do, the process proceeds to the next step.
[0062]
In step 36, since the occurrence of ringing is recognized according to the determination conditions so far, the processing target image is corrected by the following equation (16).
[0063]
(Equation 6)

[0064]
Here, in equation (16), the density average value (g _i Is changed from the average of the pixels in the second term, but if the change in the original image is added in the second term, ringing remains generated. Therefore, as shown in Expression (16), the amount of the original change is linearly reduced (suppressed) is added in the second term, so that ringing is suppressed.
[0065]
In step 37, it is determined whether or not all the (p, q) have been scanned. If No, the process returns to step 34, and if Yes, the ringing correction process ends.
[0066]
At the next point after the processing here is completed, γ in FIG. 2 is an image with less ringing than β.
[0067]
FIG. 8 shows a schematic diagram of the ringing correction process. In FIG. 8, the left side is an image before correction (β in FIG. 2), and the right side is an image after correction in which ringing correction (processing in step 15 in FIG. 3) is performed using the reference image data. (Γ in FIG. 2). As shown in FIG. 8, the ringing is corrected so that the ringing is reduced in the flat portion and the edge is raised in the edge portion. Therefore, a sharpened image can be obtained.
[0068]
Next, in step 16 of FIG. 3, it is determined whether the current number of iterations has reached the set number of iterations. If the result of determination is No, the process returns to step 10, and if Yes, the process proceeds to step 17 to output an enlarged image and end all the processing.
[0069]
In the normal GP iteration method, the Fourier transform is used. However, in this embodiment, considering that an image to be actually processed is represented by a non-negative integer, a discrete transform is used instead of the Fourier transform. By using the cosine transform (DCT), it is possible to reduce the load in terms of storage capacity and calculation amount.
[0070]
The number of repetitions of the above-described GP repetition method may be set to an appropriate number, but usually 10 or less is sufficient.
[0071]
Further, in the present embodiment, the case where the number of regions to be classified is 3 is shown, but it is also possible to further finely classify. When the number of regions to be classified is i, i −1 kinds of thresholds (t ₁ , ..., t _i-1 ), I kinds of parameters β _i Should be set.
[0072]
Next, the two-dimensional DCT employed in this embodiment and the IDCT which is the inverse transform thereof will be described. A two-dimensional DCT of N × N points of discrete function i (x, y) and 0 ≦ u, v ≦ N−1 is defined by the following equations (17) and (18).
[0073]

[0074]
(Equation 7)

[0075]
Here, 0 ≦ u and v ≦ N−1.
[0076]
Also, c (u) is defined by the following equations (19) and (20). Note that c (v) is also defined in the same manner as c (u). These functions c (u) and c (v) are also used in the inverse transformation.
[0077]
c (u) = 1 / √2 (u = 0) (19)
c (u) = 1 (u = 1, 2,..., N−1) (20)
[0078]
The inverse transform IDCT of the two-dimensional DCT is defined by the following equations (21) and (22).
[0079]

[0080]
(Equation 8)

[0081]
Here, 0 ≦ x, y ≦ N−1.
[0082]
In the present embodiment, the DCT can be used as defined above. However, as described above, when the number of pixels nmN shown in FIG. 2 is set to a power of 2, the DCT has a high-speed operation algorithm. Therefore, it is preferable that the DCT of this high-speed operation algorithm is actually used in the operation.
[0083]
FIG. 9 is a block diagram showing an outline of a device configuration applied to the second embodiment according to the present invention.
[0084]
The present embodiment is an example of enlarging a color image. In this case, each of the R (red), G (green), and B (blue) signals from the original image storage unit 10 is processed by the enlarging processing unit 12. An enlarged image can be created by executing a GP repetition method including a ringing suppression process similar to the case of the first embodiment.
[0085]
According to the present embodiment, the same processing as that of the first embodiment can be performed on a color image by regarding each color component as a monochrome image. Thus, it is possible to create an enlarged image with few images.
[0086]
FIG. 10 is a block diagram showing a basic configuration of an apparatus applied to the third embodiment according to the present invention.
[0087]
The present embodiment is an example of enlarging a print color image. The original image storage unit 10 stores an original signal of each color of C (cyan), M (magenta), Y (yellow) and K (black). The enlargement processing unit 12 executes the GP repetition method including the ringing suppression processing similar to that of the first embodiment, thereby creating an enlarged image.
[0088]
According to this embodiment, each color component can be processed in the same manner as in the first embodiment, as in the second embodiment, so that an enlarged printing color image with extremely high image quality and little ringing can be obtained. Can be created.
[0089]
As described above, the present invention has been specifically described. However, the present invention is not limited to the above-described embodiment, and can be variously modified without departing from the gist thereof.
[0090]
For example, although the orthogonal transform employed in the GP repetition method has been described only for the case of using DCT, the present invention is not limited to this case, and energy matching between an enlarged image and an original image can be obtained. If it is an orthogonal transform, other orthogonal transforms such as a Fourier transform can be adopted.
[0091]
Also, the case where the color space is RGB and CMYK has been described, but the present invention is not limited to a specific color space, and can be applied to any color space.
[0092]
Although the case of the image enlargement method by the GP repetition method has been described, the ringing suppression processing can be applied to the image enlargement method using a digital filter.
[0093]
【The invention's effect】
As described above, according to the present invention, since processing for suppressing ringing is performed using a reference image having no ringing, an enlarged image with no sharpness and no ringing can be obtained. .
[0094]
Further, when the reference image is created by the bilinear method, a smooth image without ringing can be obtained in a flat portion by a simple operation, so that the ringing of the processing target image can be more efficiently suppressed.
[0095]
Also, when the spatial high-frequency components lost when the original image was sampled are restored, edges without jaggies are reproduced, texture reproducibility, highlight omissions are good, and high magnification is achieved. It has an excellent effect that an extremely high-quality enlarged image having many properties can be created.
[Brief description of the drawings]
FIG. 1 is an explanatory diagram showing the principle of the GP iteration method.
FIG. 2 is an explanatory view schematically showing processing steps of a first embodiment according to the present invention.
FIG. 3 is a flowchart showing a flow of processing of the embodiment.
FIG. 4 is a block diagram showing a basic configuration of an apparatus applied to the embodiment.
FIG. 5 is a flowchart showing reference data creation processing used in the embodiment.
FIG. 6 is a flowchart showing a correction process for a classification area.
FIG. 7 is a flowchart showing details of the above-described classification area correction processing;
FIG. 8 is an explanatory diagram schematically showing a ringing correction process.
FIG. 9 is a block diagram showing a basic configuration of an apparatus applied to a second embodiment according to the present invention.
FIG. 10 is a block diagram showing a basic configuration of an apparatus applied to a third embodiment according to the present invention;
[Brief description of reference numerals]
10. Original image storage
12 Enlargement processing section
14 ... Enlarged image storage

Claims (6)

In an image enlarging method for enlarging an image based on image information included in a sampled original image,
For the image to be processed, prepare a reference image without ringing in the flat part,
Dividing the processing target image into a plurality of regions having different properties,
For each pixel in each area, the density change from the average density of the corresponding area of the reference image is determined in advance for each area by integrating the variation of the pixel value from the average density in the small area of the reference image. set based on, performs a process of limiting the ringing suppressible acceptable in deviation the flat portion,
An image enlargement method characterized by suppressing ringing. 2. The image enlargement method according to claim 1, wherein the processing target pixel is classified into a flat portion, a texture portion, and an edge portion using a deviation of each small region of the reference image and a preset threshold. In Claim 2, for each of the classified flat portion, texture portion, and edge portion, an integrated value of a variation amount of a pixel value from an average density in a small region of a reference image is obtained,
By applying a parameter that adjusts the allowable range of concentration fluctuation set in advance,
An image enlargement method, wherein the allowable deviation is set. The method according to any one of claims 1 to 3, wherein in a small area of the processing target image, a variation amount of a pixel value from an average density in the small area of the reference image exceeds the allowable deviation.
The error in the small area of the processing target image is added to the density average value in the small area of the reference image by adding a value obtained by range-compressing the difference between the processing target image and the average value based on the allowable deviation. An image enlargement method characterized in that it is within an allowable deviation. 2. The reference image according to claim 1, wherein a density value of a pixel that does not exist in the original image of the enlarged image is interpolated from an intensity of each pixel in the original image before enlargement by an interpolation function having a low-pass characteristic. An image enlarging method characterized in that is created by an interpolation method. In any one of claims 1 to 5,
An image signal to which an image whose initial value is known to limit the range of spatial expansion outside the image signal to be enlarged is added is defined as an original image signal g,
The original image signal g is orthogonally transformed into original frequency information G band-limited to a pass frequency band,
Information obtained by extending a high-frequency band to the original frequency information G according to a desired enlargement factor is referred to as first frequency information F1,
After the first frequency information F1 is subjected to inverse orthogonal transform to obtain a first image signal f1,
A second image signal f2 in which the value of the limited area of the spatial spread of the first image signal f1 is adjusted to an initial value;
The second image signal f2 is orthogonally transformed into second frequency information F2,
A range corresponding to the pass frequency band of the second frequency information F2 is replaced with the original frequency information G, which is information of a correct pass frequency band, to obtain third frequency information F3,
For the third image signal f3 obtained by inverse orthogonally transforming the third frequency information F3,
After applying the same spatial area restriction as the original image signal f1, orthogonal transformation is performed,
In the process of repeating normal and inverse transformations by orthogonal transformation,
The spatial high-frequency component (Fi-G) lost at the time of sampling is restored and the image is enlarged using two constraints that the information of the pass frequency range is correct and the spatial spread of the image is limited. An image enlarging method characterized in that:

Images