JP4223789B2 - Quantizer - Google Patents

Description

この様に、確率密度分布関数ｇ′が連続空間［−∞，∞］上で定義される連続関数として定義されると、フーリェ変換が可能となる。従って、フーリェ変換器１７は、確率密度分布関数ｇ′を次の式（５）に従って解析的にフーリェ変換し、
図９に示す様な、パワースペクトルＰ（ν）＝｜Ｇ（ν）｜を生成する。
【００２３】
【数２】

図８の（ｂ）は、図８の（ａ）に示す矩形関数ｒｅｃｔ（ｘ）のフーリェ変換したものであり、ｓｉｎｃ（ν）＝ｓｉｎπν／πνであることを利用している。尚、当然のことながら、ｓｉｎｃ（ν）の逆フーリェ変換は、前記矩形関数ｒｅｃｔ（ｘ）である。
【００２４】
次に、カットオフ設定器１８は、前記パワースペクトルＰ（ν）から、例えば、次の（Ａ），（Ｂ）若しくは（Ｃ）の何れかの方法を使って、カットオフ周波数Ｕｃを求める。
【００２５】
（Ａ）予め設定されたεを用いて、Ｐ（ν）≦εとなる周波数νをカットオフ周波数Ｕｃとする。
（Ｂ）スペクトル強度の最大値Ｐｍａｘに予め設定されたαを掛けた値α・Ｐｍａｘをεとして用いて、Ｐ（ν）＝εとなる周波数νをカットオフ周波数Ｕｃとする。
（Ｃ）予め設定されたスペクトル強度分布面積比βを用いて、次の式（６）を満たす周波数νｃをカットオフ周波数Ｕｃとする。
【００２６】
【数３】

カットオフ設定器１８は、この様にして求められたカットオフ周波数Ｕｃから、最適量子化ステップ幅Δｄ′（≦１／（２Ｕｃ））求める。
【００２７】
次に、第２の量子化器１９は、前記第１の量子化器１３の出力である量子化サイズＬのデジタル画像信号を、濃度方向に、前記量子化保証器１４で算出された最適量子化ステップ幅Δｄ′で量子化する。尚、Δｄ′は実数値なので、実際には、式、Δｄ′′＝［Δｄ′］（［ ］は最も近い整数値を表す）によって、整数化した最適量子化ステップ幅Δｄ′′を用いて量子化する。
【００２８】
本発明による量子化器によれば、画像信号の確率密度分布を１次元信号と考えることが出来る為、公知の標本化定理をそのまま適用することが出来、カットオフ周波数ＵＣが分かれば、１／（２Ｕｃ）のステップでサンプリングすれば、サンプリングされたデータから、カットオフ周波数Ｕｃで帯域制限された元の１次元信号（確率密度分布）を完全に復元することが出来る。つまり、濃度方向の量子化を、確率密度分布の再現問題に置きかえれば、標本化定理と同等に扱え、濃度方向の量子化の再現性を保証した量子化器を提供することが出来る。
【００２９】
尚、本発明による量子化器は、二次元のアナログ画像信号の量子化に限定されるものではなく、１次元のアナログ信号（例えば時系列信号）の量子化にも適用出来る。
【００３０】
例えば第１０図に、１次元アナログ信号の量子化に本発明による量子化器を適用した場合の例を示す。図中、図３で使用した記号と同一記号が付されたものは同一構成要素である。
入力信号は有限な観測区域［ｔｏ，ｔｅ］にある１次元アナログ信号であれば、その区間におけるヒストグラムを生成することが出来、前記二次元のアナログ画像信号の量子化の場合と同様にして確率密度分布を得ることが出来、画像の量子化の場合と同等の処理となる。
尚、標本化・量子化のステップにおいて、各強度区間（画像信号においては、各濃度区間）における強度の代表値は、単純に、その区間の中心における強度値か、或いは、重心値（区間内の各強度値の平均値に対応する）を採用する。
又、前記例では、確率密度分布生成器１６によりヒストグラムから確率密度分布関数を生成する場合、ヒストグラムから、矩形関数の集合と見なせる確率密度分布を生成するように成したが、これに限定されず、要は、ヒストグラムから、解析的にフーリェ変換可能な関数の線形結合で表される確率密度分布を生成するように成せば良い。従って、ヒストグラムから、ガウス分布の集合と見なせる確率密度分布を生成するように成しても良いし、或いは、ヒストグラムから、ｓｉｎｃ関数｛ｓｉｎｃ＝ｓｉｎ（πｘ）／πｘ｝の集合と見なせる確率密度分布を生成するように成しても良いし、或いは、ヒストグラムから、三角形関数Λ（ｘ）｛Λ（ｘ）は、｜ｘ｜≦１／２の時には１−｜ｘ｜、｜ｘ｜＞１／２の時には０｝の集合と見なせる確率密度分布を生成するように成しても良いし、或いは、ヒストグラムから、指数関数の集合と見なせる確率密度分布を生成するように成しても良い。
【００３１】
【発明の効果】
本発明によれば、連続座標上に連続な強度値を持つアナログ信号の情報を劣化させることなく、最適な量子化数を提供出来るようになり、記憶容量を大幅に小さく出来る。
又、本発明による量子化器は、公知の標本化定理を強度方向の分割ステップ幅に応用しているので、最適量子化ステップ幅で量子化しても、アナログ信号のヒストグラムが再現されることが保証され、更に、アナログ信号の情報を保存しつつ記憶容量を大幅に小さく出来る。
【図面の簡単な説明】
【図１】 従来の量子化器の構成を示している。
【図２】 従来の量子化器の構成を示している。
【図３】 本発明による量子化器の１構成例を示している。
【図４】 標本化器の１概略例を示している。
【図５】 図３に示す量子化器の量子化保証器の１構成例を示す。
【図６】 画像信号のヒストグラムの一例を示している。
【図７】 画像信号の確率密度分布の一例を示している。
【図８】 矩形関数ｒｅｃｔ（ｘ）と関数ｓｉｎｃ（ν）の関係を示している。
【図９】 パワースペクトルの一例を示している。
【図１０】本発明を他の信号へ適用した例を示している。
【符号の説明】
１…標本化器
２…ＡＤ変換器
３…最適量子化器
１２…標本化器
１３…第１の量子化器
１４…量子化保証器
１５…ヒストグラム生成器
１６…確率密度分布生成器
１７…フーリェ変換器
１８…カットオフ設定器
１９…第２の量子化器[0001]
[Field of the Invention]
The present invention relates to a quantizer for obtaining a digital signal from an analog signal.
[0002]
[Prior art]
FIG. 1 and FIG. 2 show a configuration example of a conventional quantizer for converting an analog image signal having continuous density values on two-dimensional continuous coordinates into a digital image signal having integer density values on two-dimensional discrete coordinates. Indicates.
[0003]
In the quantizer shown in FIG. 1, an analog image signal is sampled by a sampler 1, and the sampled image signal is converted into a digital image signal by an AD converter 2 that quantizes in the density direction.
[0004]
In the quantizer shown in FIG. 2, the digital image signal output from the AD converter 2 in the quantizer shown in FIG. 1 is regarded as a preprocessed image signal, and an optimum quantum for optimizing the quantization step width is obtained. Sent to the digitizer 3 to obtain a new digital image signal.
[Patent Document 1]
JP-A-4-67275 [0005]
[Problems to be solved by the invention]
In the quantizer having the configuration shown in FIG. 1, since the quantization step width is a preset value, the obtained digital image signal has a quantization step that depends on the peak-to-peak value of the density of the sampled image signal. Denseness comes out.
[0006]
On the other hand, in the quantizer having the configuration shown in FIG. 2, the peak-to-peak value of the density of the sampled image signal is obtained by using a known method (for example, vector quantization) for spatially optimizing the quantization step width. According to the above, quantization is performed with an optimum step width, but in reality, quantization may not always be performed with an ideal step width. In that case, for example, it is a big problem that the density distribution of the obtained digital image signal becomes sparse.
Therefore, in order to prevent the amount of information of the obtained digital image from being deteriorated, there is a problem in that the storage capacity is greatly increased if the setting is made in advance so that the quantization step width is considerably small.
In addition, since both of the quantizers shown in FIGS. 1 and 2 cannot perform reversible conversion, there is a problem in that the original sampled image signal cannot be reproduced from the finally obtained digital image signal. there were.
The present invention solves the above-described problems, sets a suitable quantization step width irrespective of the input image signal, and has a novel quantization having a reversible transformation function that can restore the input image signal from the output image signal The purpose is to provide a vessel.
[0007]
[Means for Solving the Problems]
The quantizer according to the present invention is a sampling unit that samples an analog signal in a quantizer that converts an analog signal having continuous intensity values on continuous coordinates into a digital signal having integer intensity values on discrete coordinates. A first quantizer for quantizing the sampled signal in the intensity direction, a histogram generator for generating a histogram from the sampled and quantized signal, and a probability density distribution for converting the histogram into a distribution function A generator, a Fourier transformer that generates a spectrum by performing Fourier transform on the probability density distribution, a cutoff setter that sets a cutoff frequency from the spectrum and sets a quantization step width from the cutoff frequency, and a first quantum And a second quantizer for re-quantizing the output signal of the quantizer in the intensity direction with a set quantization step width.
[0008]
A quantizer according to the present invention converts an analog image signal having continuous density values on two-dimensional continuous coordinates into a digital image signal having integer density values on two-dimensional discrete coordinates. A sampler that samples a signal in a two-dimensional spatial direction, a first quantizer that quantizes the sampled signal in a concentration direction, and a histogram that generates a histogram from the sampled and quantized image signal A generator, a probability density distribution generator that converts the histogram into a distribution function, a Fourier transformer that generates a spectrum by performing a Fourier transform on the probability density distribution, and sets a cutoff frequency from the spectrum, and a quantization step width from the cutoff frequency And a second quantizer that quantizes the output image signal of the first quantizer again in the density direction with the set quantization step width. Characterized by comprising a vessel.
[0009]
DETAILED DESCRIPTION OF THE INVENTION
Hereinafter, embodiments of the present invention will be described in detail with reference to the drawings. FIG. 3 shows one schematic example of the quantizer of the present invention.
[0010]
In the figure, reference numeral 12 denotes a two-dimensional (x, y) space direction sampling of a finite continuous two-dimensional analog original image signal (the density value is a positive continuous value) having an infinitely continuous density value in the density direction. A sampler having a structure as shown in FIG. 4, for example, is composed of a plurality of minute light receiving elements, and the spatial sampling interval is determined by the size and number of the light receiving elements. The optical signal of the analog original image is converted into an electric signal. Normally, the number of light receiving elements is the maximum number of samplings, and the number of samplings can be reduced by regarding the signals of adjacent light receiving elements as the same signal region.
[0011]
Reference numeral 13 denotes a first quantizer that quantizes the sampled signal in the concentration direction.
[0012]
Reference numeral 14 denotes a quantization guarantor for calculating the optimum quantization step width Δd ′ of the output of the first quantizer 13 (for example, it can be regarded as a digital image signal having a quantization size L). 5, a histogram generator 15 that generates a histogram from a digital image signal of a quantization size L from the first quantizer 13, and a probability density distribution that converts the histogram generated by the histogram generator 15 into a distribution function The generator 16 includes a Fourier transformer 17 that performs Fourier transform on the probability density distribution to generate a spectrum, and a cutoff setter 18 that sets a cutoff frequency from the spectrum and sets a quantization step width from the cutoff frequency.
[0013]
19 quantizes the digital image signal of the quantization size L, which is the output of the first quantizer 13, in the density direction with the optimum quantization step width Δd ′ calculated by the quantization guarantor 14. A second quantizer.
[0014]
In the quantizer having such a configuration, a finite continuous two-dimensional (x, y) analog original image signal is sampled in the (x, y) space direction by the sampler 12. That is, a spatial sampling interval (for example, 100 pixels × 100 pixels) is defined.
[0015]
The sampled analog original image signal is quantized in the density direction by the first quantizer 13. That is, an image signal that is spatially sampled by the sampler 12 but has a continuous value Dij = D (xi, yj) {i, j is a spatial sampling index} in the density direction. The density value Dij is quantized into a quantized density value dij by the following equation (1).
[0016]
dij = d (xi, yj) = n (Dij) = nij (1)
Note that n is an integer value determined by Dij. Normally, the coordinate system of the continuous value D is a finite area of [0, Dmax], the area [0, Dmax] is divided into L sections, numbered, and the density value is converted to an integer by the following equation (2). To do.
[0017]
nij = [Dij] (2)
[Dij] indicates the number (quantum number) of the section to which the numbered Dij belongs.
[0018]
Also, the density value Dij of the image signal can be expressed as Δd · nij, where the quantization step width is Δd (= Dmax / L). Note that L is called a quantization size.
[0019]
Next, the histogram generator 15 of the quantization guarantee device 14 generates a histogram gk (k is a quantum number) as shown in FIG. 6 from the digital image signal of the quantization size L from the first quantizer 13. To do. Note that gk represents the frequency of occurrence of the quantum number k.
[0020]
Next, the probability density distribution generator 16 generates a probability density distribution function g ′ based on the linear sum of rectangular functions rect (x) as shown in FIG. 7 from the histogram gk. This rectangular function rect (x) is defined as in the following equation (3), and its shape is as shown in FIG.
[0021]
rect (x) = 1 (| x | ≦ 1/2) or 0 (| x |> 1/2) (3)
Here, assuming that the continuous density coordinate space is d [−∞, ∞], the probability density distribution function g ′ is expressed as the following equation (4).
[0022]
[Expression 1]

As described above, when the probability density distribution function g ′ is defined as a continuous function defined on the continuous space [−∞, ∞], Fourier transform is possible. Therefore, the Fourier transformer 17 analytically Fourier transforms the probability density distribution function g ′ according to the following equation (5):
As shown in FIG. 9, a power spectrum P (ν) = | G (ν) | is generated.
[0023]
[Expression 2]

FIG. 8B is a Fourier transform of the rectangular function rect (x) shown in FIG. 8A and utilizes the fact that sinc (ν) = sinπν / πν. As a matter of course, the inverse Fourier transform of sinc (ν) is the rectangular function rect (x).
[0024]
Next, the cut-off setting unit 18 obtains the cut-off frequency Uc from the power spectrum P (ν) using, for example, any one of the following methods (A), (B), or (C).
[0025]
(A) Using a preset ε, a frequency ν satisfying P (ν) ≦ ε is set as a cutoff frequency Uc.
(B) Using a value α · Pmax obtained by multiplying a maximum value Pmax of spectral intensity by a preset α as ε, a frequency ν at which P (ν) = ε is set as a cutoff frequency Uc.
(C) Using a preset spectral intensity distribution area ratio β, a frequency νc satisfying the following equation (6) is set as a cutoff frequency Uc.
[0026]
[Equation 3]

The cut-off setting unit 18 obtains the optimum quantization step width Δd ′ (≦ 1 / (2Uc)) from the cut-off frequency Uc thus obtained.
[0027]
Next, the second quantizer 19 outputs the digital image signal of the quantization size L that is the output of the first quantizer 13 in the density direction in the optimum quantum calculated by the quantization guarantor 14. Quantization is performed with the quantization step width Δd ′. Since Δd ′ is a real value, in practice, the optimum quantization step width Δd ″ converted to an integer by the equation, Δd ″ = [Δd ′] ([] represents the nearest integer value) is used. Quantize.
[0028]
According to the quantizer according to the present invention, since the probability density distribution of the image signal can be considered as a one-dimensional signal, a well-known sampling theorem can be applied as it is, and if the cutoff frequency UC is known, 1 / If sampling is performed in step (2Uc), the original one-dimensional signal (probability density distribution) band-limited by the cut-off frequency Uc can be completely restored from the sampled data. That is, if the quantization in the concentration direction is replaced with a probability density distribution reproduction problem, a quantizer that can be handled in the same manner as the sampling theorem and guarantees the reproducibility of the quantization in the concentration direction can be provided.
[0029]
The quantizer according to the present invention is not limited to the quantization of a two-dimensional analog image signal, and can be applied to the quantization of a one-dimensional analog signal (for example, a time series signal).
[0030]
For example, FIG. 10 shows an example in which the quantizer according to the present invention is applied to the quantization of a one-dimensional analog signal. In the figure, components having the same symbols as those used in FIG. 3 are the same components.
If the input signal is a one-dimensional analog signal in a finite observation area [to, te], a histogram in that section can be generated, and the probability is the same as in the case of quantization of the two-dimensional analog image signal. A density distribution can be obtained, and the processing is the same as in the case of image quantization.
In the sampling / quantization step, the representative value of the intensity in each intensity interval (in the image signal, each density interval) is simply the intensity value at the center of the interval or the centroid value (within the interval). (Corresponding to the average value of each intensity value).
In the above example, when the probability density distribution function 16 generates the probability density distribution function from the histogram, the probability density distribution that can be regarded as a set of rectangular functions is generated from the histogram. However, the present invention is not limited to this. In short, a probability density distribution represented by a linear combination of analytically Fourier transformable functions may be generated from the histogram. Accordingly, a probability density distribution that can be regarded as a set of Gaussian distributions may be generated from the histogram, or a probability density distribution that can be regarded as a set of sinc functions {sinc = sin (πx) / πx} from the histogram. Or the triangular function Λ (x) {Λ (x) is 1− | x |, | x |> 1 when | x | ≦ 1/2. A probability density distribution that can be regarded as a set of 0} at / 2 may be generated, or a probability density distribution that can be regarded as a set of exponential functions may be generated from a histogram.
[0031]
【The invention's effect】
According to the present invention, an optimum quantization number can be provided without degrading information of an analog signal having continuous intensity values on continuous coordinates, and the storage capacity can be greatly reduced.
In addition, since the quantizer according to the present invention applies a well-known sampling theorem to the division step width in the intensity direction, the histogram of the analog signal can be reproduced even if quantization is performed with the optimum quantization step width. Furthermore, the storage capacity can be greatly reduced while preserving analog signal information.
[Brief description of the drawings]
FIG. 1 shows a configuration of a conventional quantizer.
FIG. 2 shows a configuration of a conventional quantizer.
FIG. 3 shows a configuration example of a quantizer according to the present invention.
FIG. 4 shows one schematic example of a sampler.
FIG. 5 shows one configuration example of a quantization guarantee device of the quantizer shown in FIG. 3;
FIG. 6 shows an example of a histogram of an image signal.
FIG. 7 shows an example of a probability density distribution of an image signal.
FIG. 8 shows a relationship between a rectangular function rect (x) and a function sinc (ν).
FIG. 9 shows an example of a power spectrum.
FIG. 10 shows an example in which the present invention is applied to other signals.
[Explanation of symbols]
DESCRIPTION OF SYMBOLS 1 ... Sampler 2 ... AD converter 3 ... Optimum quantizer 12 ... Sampler 13 ... 1st quantizer 14 ... Quantization guarantee device 15 ... Histogram generator 16 ... Probability density distribution generator 17 ... Fourier Transformer 18 ... Cutoff setting device 19 ... Second quantizer

Claims (17)

In a quantizer that converts an analog signal with continuous intensity values on continuous coordinates to a digital signal with integer intensity values on discrete coordinates, a sampler that samples the analog signal, and a sampled signal A first quantizer that quantizes in the intensity direction, a histogram generator that generates a histogram from the sampled and quantized signal, a probability density distribution generator that converts the histogram into a distribution function, and a probability density distribution A Fourier transform that generates a spectrum by conversion, a cutoff frequency that sets a cutoff frequency from the spectrum, a quantization step width that sets the quantization step width from the cutoff frequency, and an output signal of the first quantizer are set. And a second quantizer that re-quantizes in the intensity direction with the quantization step width. In a quantizer that converts an analog image signal with continuous density values on two-dimensional continuous coordinates to a digital image signal with integer density values on two-dimensional discrete coordinates, the analog image signal is sampled in a two-dimensional spatial direction. , A first quantizer that quantizes the sampled signal in the density direction, a histogram generator that generates a histogram from the sampled and quantized image signal, and a distribution function that converts the histogram into a distribution function A probability density distribution generator that performs a Fourier transform of the probability density distribution to generate a spectrum, a cutoff frequency that sets a cutoff frequency from the spectrum, and sets a quantization step width from the cutoff frequency; And a second quantizer for requantizing the output image signal of the first quantizer in the density direction with a set quantization step width. Quantizer for. 3. The quantizer according to claim 1, wherein the probability density distribution is regarded as original data, and the sampling step width obtained by the sampling theorem is the quantization step width. 3. The quantizer according to claim 1, wherein the probability density distribution is reproduced without losing the amount of information even if Fourier transform and inverse Fourier transform are performed. 3. A quantizer according to claim 1, wherein the probability density distribution is analytically Fourier-transformed. 3. The quantizer according to claim 1, wherein when the spectral intensity is P and the set value is ε, a frequency satisfying P ≦ ε is set as a cutoff frequency. The quantizer according to claim 1 or 2, wherein a frequency based on a product of the spectrum intensity maximum value and the parameter is set as a cutoff frequency. The quantizer according to claim 1 or 2, wherein a frequency based on a spectral intensity distribution area ratio is set as a cut-off frequency. The quantization step width is set from the cutoff frequency so as to satisfy the conditional expression of Δd ′ ≦ 1 / (2UC), where UC is the cutoff frequency and Δd ′ is the quantization step width. The quantizer according to 1 or 2. 2. The quantizer according to claim 1, wherein the intensity representative value of each intensity interval is set to the intensity value at the center of each intensity interval or the gravity center value of the intensity of each intensity interval. The quantizer according to claim 2, wherein the density representative value of each density section is set to a density value at the center of each density section or a centroid value of the density of each density section. 3. The quantizer according to claim 1, wherein a probability density distribution represented by a linear combination of analytically Fourier transformable functions is generated from the histogram. 3. The quantizer according to claim 1, wherein a probability density distribution that can be regarded as a set of rectangular functions is generated from the histogram. 3. The quantizer according to claim 1, wherein a probability density distribution that can be regarded as a set of Gaussian distributions is generated from the histogram. The quantizer according to claim 1 or 2, wherein a probability density distribution that can be regarded as a set of sinc functions {sinc = sin (πx) / πx} is generated from a histogram. From the histogram, the triangular function Λ (x) {Λ (x) is a probability density distribution that can be regarded as a set of 1− | x | when 0 ||| 1/2 and 0} when | x |> ½. 3. The quantizer according to claim 1, wherein the quantizer is generated. 3. The quantizer according to claim 1, wherein a probability density distribution that can be regarded as a set of exponential functions is generated from the histogram.

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