JP2008263465A - Image processing system and image processing program - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To provide an image processing system capable of generating a more natural magnified image even in an area where characteristics are not clear such as an edge part by adding a signal of a high frequency to the magnified image. <P>SOLUTION: An image pixel corresponding means of the image processing system associates the pixel value of ambient pixels located around a target pixel with a partial pixel obtained by dividing the target pixel, a pixel value setting means sets a pixel value of the target pixel after magnification processing in accordance with the pixel value of the partial pixel associated by the pixel corresponding means and the scale factor of the magnification processing, and a pixel value converting means converts the pixel value set by the pixel value setting means in accordance with the pixel value of the ambient pixels after the magnification processing. <P>COPYRIGHT: (C)2009,JPO&INPIT

Description

  The present invention relates to an image processing system and an image processing program.

The image enlargement process is one of basic processes for a system that performs image editing, filing, display, printing, and the like. In recent years, with the widespread use of image data mainly for display at display resolutions such as images on the Internet homepage and digital video, these low-resolution images are frequently printed by high-resolution printers. It has been broken. At the time of printing with this printer, it is desired to obtain a high-quality output result, and the importance of the high-quality enlargement process is increasing.
Note that the image enlargement processing here includes high-definition processing of the image.

Typical existing methods for enlarging an image expressed in multiple gradations including color (hereinafter referred to as a multi-valued image) include a nearest neighbor method, a linear interpolation method, and a cubic convolution method.
The nearest neighbor method is a method in which the pixel value of the pixel having the closest distance is used as each enlarged pixel value when the pixel is reversely mapped on the original image. Since this method has a small amount of calculation, it can be processed at high speed.
However, since one pixel of the original image is directly expanded into a rectangular shape, the degree of image quality degradation is small and has little effect when the pixel value difference between adjacent pixels is small. The image quality is greatly deteriorated, for example, when the jaggy on the edge portion is conspicuous or the image has a mosaic shape when the magnification is large.

  In the linear interpolation method, it is assumed that pixel values between pixels change linearly, and pixel values of four pixels in the vicinity of a point obtained by inversely mapping the enlarged pixel are linearly interpolated to obtain a pixel value. It is. Although this method is heavier than the nearest neighbor method, the amount of calculation is relatively small, and jaggies are less likely to occur. On the other hand, there is a drawback that the entire image becomes blurred, centering on the edge portion that does not apply to the assumption that it changes linearly.

  The cubic convolution method defines an interpolation function approximated by a sinc function (sin (x) / x) based on the sampling theorem, and 16 pixels in the vicinity of a point obtained by inversely mapping the enlarged pixel (X and Y directions) This is a method for obtaining an enlarged pixel value by a convolution operation of each of 4 pixels) and the approximate interpolation function. This method has a relatively good image quality compared to the above two methods, but has the characteristic that the high frequency band is emphasized, so there are drawbacks such as light jaggies occurring at the edge and noise components being emphasized. is there.

As an attempt to solve these problems, techniques described in, for example, Patent Literature 1 to Patent Literature 6 have been proposed.
In the technique described in Patent Document 1, first, an original image is binarized, and the direction of an oblique component included in the original image is determined from the binary image to coincide with a two-dimensional pattern (matrix data) prepared in advance. Obtain and perform interpolation processing along the obtained oblique direction. In addition, linear interpolation processing is performed for the other portions. However, since the direction of the diagonal component is determined after binarizing the original image with a predetermined threshold, it is effective for edges with a large density difference, but for reproducing edges with a small density difference. There's a problem.

In the technique described in Patent Document 2, a pixel value of an arrangement file is determined by a dot arrangement file (enlarged pattern file) for each integer magnification corresponding to one-to-one in the pattern file and a pixel value at any position of the pixel block. An enlarged image block is generated based on the pixel reference information. Further, when there is no matching pattern, an enlarged image block is simply generated with the target pixel of the original image block.
However, in Patent Document 2, since the enlarged block is uniquely generated only by pattern matching, the image quality of the enlarged image is determined by the number of pattern files and dot arrangement files. That is, many pattern files are required in advance to improve image quality, and it is not realistic to prepare many pattern files in advance.

In the technique described in Patent Literature 3, edge detection is performed by an edge detection filter as a method for detecting the degree of change in an original image, and edge pixels are defined based on the edge detection result. When it is determined that the pixel is an edge pixel, enlargement is performed by the M-cubic method in which the cubic function shape of the cubic convolution method is adjusted. Otherwise, enlargement is performed by the nearest neighbor method.
However, since the edge portion having a large degree of change is performed by the M-cubic method, the image quality characteristics of the cubic convolution method are followed, and there is a disadvantage that jaggy generation and noise components are emphasized.

  In the technique described in Patent Document 4, the property of an image is measured in advance by a density histogram for each block, and based on the result, a first interpolation process (a pattern matching method or a nearest neighbor method (NN method)) and a second one are performed. The result of interpolation processing (cubic convolution method or M-cubic method) is superimposed. In the pattern matching method, which is one of the first interpolation processes, when a pattern (binarized pattern) generated from an original image block matches a predetermined angle pattern, a predetermined block is used using a reference block including the original image block. An interpolation pixel block for the target pixel is generated by the rule. However, Patent Document 4 also has a problem that jaggy and noise components are emphasized because of superimposition with the M-cubic method.

  In contrast to such a conventional enlargement technique, there is a technique described in Patent Document 5, for example, as a high-quality enlargement technique. This method detects an accurate edge direction and generates an enlarged image from pixel values corresponding to the edge direction, and causes as little image quality defects as blur and jaggy to the input image as much as possible. An enlargement process can be performed.

In the technique described in Patent Document 6, the feature amount of an image region having a predetermined size including the target pixel is calculated by the region feature amount calculation unit, and the enlarged image region generation unit is provided according to the calculated feature amount. A method is shown in which a plurality of enlargement methods are switched to generate an enlarged image region corresponding to an image region, and the obtained enlarged image region is placed by an image placement unit to generate an output image.
JP 2000-228723 A JP 2001-188900 A JP 2000-188681 A JP 2002-165089 A JP 2003-274157 A JP 2004-180171 A

In the related art as described above, a good enlarged image can be generated for a region having a clear feature such as an edge portion in an image. However, in the case of the region other than the edge portion, there is a problem that the image quality remains the same as that of the nearest neighbor method, linear interpolation method, cubic convolution method or the like of the prior art.
These conventional techniques (nearest neighbor method, linear interpolation method, cubic convolution method, etc.) do not infer and generate information with a frequency higher than the frequency of the input image, resulting in a blurred image. There is a problem.
The present invention has been made in consideration of the above-described problems of the prior art, and by adding a high-frequency signal to the enlarged image, even for regions where the features are not clear, such as edge portions, An object of the present invention is to provide an image processing system and an image processing program capable of generating a more natural enlarged image.

The gist of the present invention for achieving the object lies in the inventions of the following items.
[1] Pixel correspondence means for associating pixel values of surrounding pixels located around the target pixel in the target pixel;
An image processing system comprising: enlarging means for enlarging by using the pixel values of surrounding pixels corresponding to the target pixel by the pixel correspondence means.

[2] Pixel correspondence means for associating pixel values of surrounding pixels located around the target pixel with partial pixels obtained by dividing the target pixel;
Pixel value setting means for setting the pixel value of the target pixel after the enlargement process according to the pixel value of the partial pixel associated by the pixel correspondence means and the magnification of the enlargement process;
An image processing system comprising: a pixel value conversion unit that converts a pixel value set by the pixel value setting unit according to a pixel value of a surrounding pixel after the enlargement process.

[3] The pixel value conversion means converts the pixel value of the target pixel so that the average value of the pixel values of the pixel corresponding to the target pixel after the enlargement process is equal to [2]. The image processing system described.

[4] The image processing system according to [2], wherein the pixel value conversion unit multiplies the pixel value set by the pixel value setting unit by a constant value as a multiplier.

[5] The image processing system according to [4], wherein the pixel value conversion unit determines the multiplier according to a value obtained by interpolation processing.

[6] The pixel correspondence means associates a part of surrounding pixels with the partial pixel, and associates a pixel value with the partial pixel using the area of the associated pixel as a weighting factor. [2] The image processing system described in 1.

[7] Enlarged pixel value calculating means for calculating a pixel value obtained by enlarging the target pixel according to the pixel values of surrounding pixels;
Average value calculating means for calculating an average value of pixel values calculated by the enlarged pixel value calculating means;
Interpolation means for performing interpolation processing of the target pixel;
A multiplier calculating means for obtaining a multiplier for multiplying the pixel value calculated by the enlarged pixel value calculating means using a result of the interpolation processing performed by the interpolation means and an average value calculated by the average value calculating means;
An enlargement processing unit that performs an enlargement process of the target pixel according to the pixel value calculated by the enlarged pixel value calculation unit, the average value calculated by the average value calculation unit, and the multiplier calculated by the multiplier calculation unit. An image processing system comprising:

[8] Pixel correspondence means for performing function approximation on pixel values of surrounding pixels located around the target pixel and associating the pixel value with a position in the target pixel;
Pixel value setting means for setting the pixel value of the target pixel after the enlargement process according to the pixel value associated with the pixel correspondence means and the magnification of the enlargement process;
An image processing system comprising: a pixel value conversion unit that converts a pixel value set by the pixel value setting unit according to a pixel value of a surrounding pixel after the enlargement process.

[9] The pixel value setting means sets the pixel value of the target pixel after the enlargement process by setting the average value of the pixel values after the enlargement process to the pixel value of the target pixel and multiplying by a multiplier. The image processing system according to [8].

[10] The computer
Pixel correspondence means for associating pixel values of surrounding pixels located around the target pixel in the target pixel;
An image processing program that causes the pixel correspondence means to function as an enlargement means for enlarging using pixel values of surrounding pixels corresponding to a target pixel.

[11] Connect the computer
Pixel correspondence means for associating pixel values of surrounding pixels located around the target pixel with partial pixels obtained by dividing the target pixel;
Pixel value setting means for setting the pixel value of the target pixel after the enlargement process according to the pixel value of the partial pixel associated by the pixel correspondence means and the magnification of the enlargement process;
An image processing program for causing a pixel value set by the pixel value setting means to function as a pixel value conversion means for converting the pixel value according to the pixel values of surrounding pixels after the enlargement process.

[12] The pixel value conversion means converts the pixel value of the target pixel so that the average value of the pixel values of the pixel corresponding to the target pixel after the enlargement processing is equal to [11]. The image processing program described.

[13] The image processing program according to [11], wherein the pixel value conversion unit multiplies the pixel value set by the pixel value setting unit by a constant value as a multiplier.

[14] The image processing program according to [13], wherein the pixel value conversion means determines the multiplier according to a value obtained by interpolation processing.

[15] The pixel correspondence unit associates a part of surrounding pixels with the partial pixel, and associates a pixel value with the partial pixel using the area of the associated pixel as a weighting factor. [11] The image processing program described in 1.

[16]
An enlarged pixel value calculating means for calculating a pixel value obtained by enlarging the target pixel according to a pixel value of surrounding pixels;
Average value calculating means for calculating an average value of pixel values calculated by the enlarged pixel value calculating means;
Interpolation means for performing interpolation processing of the target pixel;
A multiplier calculating means for obtaining a multiplier for multiplying the pixel value calculated by the enlarged pixel value calculating means using a result of the interpolation processing performed by the interpolation means and an average value calculated by the average value calculating means;
As an enlargement processing means for performing enlargement processing of the target pixel according to the pixel value calculated by the enlarged pixel value calculation means, the average value calculated by the average value calculation means, and the multiplier calculated by the multiplier calculation means An image processing program characterized by causing it to function.

[17]
Pixel correspondence means for performing a function approximation on the pixel values of surrounding pixels located around the target pixel and associating the pixel value with a position in the target pixel;
Pixel value setting means for setting the pixel value of the target pixel after the enlargement process according to the pixel value associated with the pixel correspondence means and the magnification of the enlargement process;
An image processing program for causing a pixel value set by the pixel value setting means to function as a pixel value conversion means for converting the pixel value according to the pixel values of surrounding pixels after the enlargement process.

[18] The pixel value setting means sets the pixel value of the target pixel after the enlargement process by setting the average value of the pixel values after the enlargement process to the pixel value of the target pixel and multiplying by a multiplier. The image processing program according to [17].

  According to the image processing system and the image processing program according to the present invention, by adding a signal having a high frequency to the enlarged image as compared with the case where the present configuration is not provided, the features such as the edge portion are not clear. A more natural enlarged image can be generated even for a region that is not present.

<1. Overview>
The present embodiment relates to an image processing technique for performing image enlargement processing.
In the following, various preferred embodiments for realizing the present invention will be described with reference to the drawings.
First, the concept of the present embodiment will be described. This description does not directly describe the invention described in the claims, but is limited to the description of the concept of the present embodiment.

In the present embodiment, high-frequency signal generation using the fractal nature of an image is performed. In this embodiment, one pixel is regarded as a region having a rectangular area. One pixel of the input image is considered as one rectangle (pixel 11) as shown in FIG.
At the time of enlarging, the one pixel is considered to be divided into a plurality (one or more) of pixels. For example, in the case of enlarging twice vertically and horizontally, it can be considered that one pixel is divided into four pixels of 2 pixels vertically and 2 pixels horizontally. In FIG. 1B, the boundary of one pixel (pixel 12) before enlargement is represented by a thick line, and the boundary of four pixels (pixels 121, 122, 123, and 124) after enlargement is represented by a thin line.
When enlarging in this way, one pixel is divided into a plurality of pixels.
Before the enlargement, since one pixel is only one pixel, it can be considered that all the pixels are filled with the same pixel value. After enlarging, the pixel becomes a plurality of pixels, so that it is filled with a plurality of pixel values.

At this time, there is a problem as to what pixel value is used to fill each enlarged pixel.
In the background art, when there is no clear information such as the edge direction, pixel values are determined based on the sampling theorem using values of surrounding pixels.
As described above, when enlarging is considered as “division of a pixel region”, if the pixel value is determined based on the sampling theorem, there is no difference between the frequency information of the image before and after enlarging.
Furthermore, actual enlargement is performed by returning the pixels divided as described above to the pixel size of the input image. A pixel obtained by enlarging FIG. 1B is shown in FIG. That is, enlarging the pixel 12 shown in FIG. 1B to the pixel 13 shown in FIG. 1C means that the four pixels (pixels 121, 122, 123, and 124) dividing the pixel 12 are changed. 4 pixels (pixels 131, 132, 133, and 134) that are enlarged and have the same size as the pixel 12.

Before the pixel is enlarged as described above, “there is no difference between the frequency information of the image before enlargement and the image after enlargement”. High frequency information is missing from the frequency information. If the magnification is doubled, the final magnified image does not have the upper half frequency information at all.
For the above reasons, phenomena such as “blurring” and “missing texture” occur.

In the present embodiment, the following processing is performed to suppress phenomena such as “blur” and “texture loss”.
The above-mentioned problem is caused by painting one pixel before enlargement with one pixel value. Therefore, one pixel before enlargement may be painted with a plurality of pixel values.
The plurality of pixel values are generated using surrounding pixel blocks of one pixel before enlargement.
Note that similar surrounding pixel blocks are not searched as in the case of enlargement using a fractal. The surrounding pixel block is fixed until the input image is processed. This is because it is impossible to determine the feature amount of the target region because the target region is only one pixel. Another reason is to eliminate the load of searching for similar surrounding pixel blocks.
In addition, if the pixel values of the surrounding pixel blocks are simply replaced, the continuity of the pixel values is lost. Therefore, correction is performed to maintain a certain degree of continuity.

Hereinafter, the above concept will be described by taking a one-dimensional signal as an example. However, since it is an image enlargement process, a process for two dimensions is actually required, but here, in order to facilitate understanding, the description is simplified to illustrate a one-dimensional process.
First, as shown in FIG. 2A, it is assumed that five pixels (pixels 21 to 25) are arranged in one dimension. Here, it is assumed that the center pixel (pixel 23) is enlarged five times.
When enlargement is performed using a background technique, for example, a linear interpolation method, the enlargement result of the target pixel is shown in FIG. In other words, since the pixel 23 is enlarged five times, the pixel 23 is divided into five pixels 2301 to 2305 and linear interpolation is performed. Therefore, the pixel 2301 and the pixel 2302 are affected by the pixel value of the pixel 22, and the pixel 2304 The pixel 2305 is influenced by the pixel value of the pixel 24. Therefore, as shown in FIG. 2B, the enlarged image becomes a relatively smooth image.
However, the image before enlargement is an image with many irregularities, as shown in FIG. Therefore, in the present embodiment, enlargement is performed while reproducing such unevenness as much as possible.

Therefore, in the present embodiment, the surrounding five pixels before enlargement are reduced and fitted into the target pixel. For example, in this example, there are five surrounding pixels, but the surrounding pixel region is not limited.
3A shows the pixel values of the five pixels before enlargement, and the target pixel is the pixel 23, as in FIG.
FIG. 3B shows that five pixels (pixels 21, 22, 23, 24, and 25) around the target pixel (pixel 23) are reduced to one pixel width. That is, the pixel value of the pixel 211 is the pixel value of the pixel 21, the pixel value of the pixel 221 is the pixel value of the pixel 22, the pixel value of the pixel 231 is the pixel value of the pixel 23, and the pixel value of the pixel 241 is This is the pixel value of the pixel 24, and the pixel value of the pixel 251 is the pixel value of the pixel 25.
FIG. 3C is obtained by fitting the pixel of FIG. 3B into the position of the pixel 23 which is the target pixel of FIG. However, in this state, the continuity between the pixel value of the inserted pixel and the pixel values of the surrounding pixels (for example, the pixels 22 and 24) of the target pixel (pixel 23) is not maintained, resulting in a deteriorated image.

  In order to ensure continuity, first, the average value of the pixel values of the inserted pixels (pixel 212 to pixel 252) and the pixel value of the target pixel (pixel 23) are matched. That is, conversion is performed so that the pixel value of the target pixel (pixel 23) is equal to the pixel value of the pixels (pixel 212 to pixel 252) corresponding to the target pixel after the enlargement process. FIG. 4D shows this state, and the average value of the pixel values of the pixels 213 to 253 is equal to the pixel value of the pixel 23.

Next, the pixel value of the inserted pixel is multiplied by a around the pixel value of the target pixel so that the average value of the pixel values does not change. That is, the difference from the pixel value of the target pixel is multiplied by a for each of the five pixels. FIG. 4E shows the state of this processing. The average value of the pixel values of the pixel 214 to the pixel 254 is equal to the pixel value of the pixel 23, and the pixel 214 to the pixel 254 have the same value. The process of multiplying the pixel value by a is shown. FIG. 4F actually shows a state after multiplying each of the five pixels by a.
The magnification a is determined so that a square error between a pixel value created by a highly continuous interpolation method (for example, linear interpolation) and a pixel value multiplied by a is minimized.
By doing so, unevenness can be preserved, and an enlarged image with high continuity can be obtained (see FIG. 4F). This unevenness becomes a factor that improves the texture of the enlarged image.

<2. First Embodiment>
FIG. 5 shows a conceptual module configuration diagram of the first embodiment.
The module generally refers to a component such as software or hardware that can be logically separated. Therefore, the module in the present embodiment indicates not only a module in a program but also a module in a hardware configuration. Therefore, the present embodiment also serves as an explanation of a program, a system, and a method. In addition, the modules correspond almost one-to-one with the functions. However, in mounting, one module may be composed of one program, or a plurality of modules may be composed of one program. A plurality of programs may be used. The plurality of modules may be executed by one computer, or one module may be executed by a plurality of computers in a distributed or parallel environment. Note that one module may include other modules. In the following, “connection” includes not only physical connection but also logical connection (data exchange, instruction, etc.).
The system includes a configuration in which a plurality of computers, hardware, devices, and the like are connected by communication means such as a network, and also includes a case where the system is realized by a single computer, hardware, devices, and the like.

  As shown in FIG. 5, the first embodiment includes a pixel replacement module 51, a pixel value projection module 52, and a continuation processing module 53. The pixel replacement module 51 is connected to the pixel value projection module 52, the pixel value projection module 52 is connected to the pixel replacement module 51 and the continuation processing module 53, and the continuation processing module 53 is connected to the pixel value projection module 52. It is connected. The input image is processed by the pixel replacement module 51, and the enlarged image that is the final output image is output from the continuation processing module 53.

Input images are processed in raster scan order. Then, the pixels in the input image are enlarged (the pixels to be enlarged change one after another in the raster scan order).
As shown in FIG. 6A, surrounding pixel regions (surrounding pixels 61, 62, 63, 64, 65, 66, 67, 68, 60) are set around the target pixel (target pixel 60). The relative position between the surrounding pixel area and the target pixel is fixed. That is, the surrounding pixels are not changed according to the target pixel.
Since a plurality of pixels are included in the surrounding pixel region, it can be expected that the image region has a high frequency component. Further, if the distance between the target pixel and the surrounding pixel area is short, it is expected that the image shape of the surrounding pixel area is similar to the image shape of the enlarged target pixel. Therefore, the pixel value in the target pixel is replaced with the pixel value in the surrounding pixel region.
The size of the surrounding pixel area will be exemplified below as 3 × 3.

  In the pixel replacement module 51, the pixel values of the surrounding pixels located around the target pixel are associated with the division into which the target pixel is divided. That is, one pixel of the target pixel is filled with 9 pixel areas of 3 × 3 pixels with pixel values of surrounding pixels. At this time, the pixel value in the surrounding pixel area is used as it is. FIG. 6B shows the target pixel 60 shown in FIG. 6A processed by the pixel replacement module 51. That is, the target pixel 601 shown in FIG. 6B is divided into nine sections, and the respective values are the surrounding pixels 61, 62, 63, 64, 60, 65, 66, and 67 shown in FIG. , 68 pixel values.

  In the pixel value projection module 52, the pixel value of the target pixel after the enlargement process is set according to the pixel value of the section associated by the pixel replacement module 51 and the magnification of the enlargement process. That is, pixel value projection processing is performed so as to achieve final pixel value division. For example, in the event that the enlargement is performed twice in the vertical and horizontal directions, the target pixel is divided into vertical and horizontal pixel values of 2 × 2. The target pixel (target pixel 601) is divided into 2 × 2 pixels by performing division by the broken vertical lines 71 and horizontal lines 72 as shown in FIG. The pixel value of each pixel after the enlargement process may be determined by a projection method according to the area of the pixel value in the broken line.

The continuation processing module 53 converts the pixel values set by the pixel replacement module 51 according to the pixel values of the surrounding pixels after the enlargement processing. That is, the pixel value is converted so that the pixel value after projection has continuity with the surrounding pixel values after enlargement. Here, an enlarged pixel value that satisfies the following condition is adopted.
-The pixel value of the target image is equal to the average value of the pixel values after the enlargement process.
A square error between the enlarged image when the enlarged image is created using the linear interpolation method and the enlarged image after projection is small.

The embodiment shown in FIG. 5 will be described more specifically using numerical calculation.
The pixel values in the surrounding pixel area are S1 to Sn. Numbers 1 to n are assigned to the pixels in the surrounding pixel area. The pixel value of the target pixel is S0.
The pixel values of the final enlarged image are X1 to Xm. Numbers 1 to m are assigned to the pixels of the final enlarged image.
The surrounding pixel region may not include the entire pixels S1 to Sn. For example, the surrounding pixel area 81 may be a part of a 3 × 3 pixel area as shown in FIG. That is, the surrounding pixel region 81 has a part of the surrounding pixels 61 to 68 and the target pixel 60.

なお、（１）式内のａとｂは、各対象画素毎に決定される定数である。 Next, a method for calculating the pixel values X1 to Xm will be described.
X1 to Xm are created by projecting S0 to Sn.
It is assumed that the area ratio Wij (weight coefficient) of Sj is included in Xi. Xi is created by converting Sj using the projection formula (1).

Note that a and b in the equation (1) are constants determined for each target pixel.

Here, by using the expression (2), the expression (1) can be simply described as the expression (3).

（４）式より、（５）式のようになる。

ここで、（６）式とすると、ｂは（７）式のようになる。

したがって、（３）式は、（８）式のようになる。つまり、最終的に求める拡大画像の画素値Ｘｉは、（８）式で求められることになる。

Next, in order to determine a and b, the following restrictions are placed.
First, a condition (equation (4)) is given that the pixel value of the target pixel matches the average value of X1 to Xm.

From equation (4), equation (5) is obtained.

Here, if it is set as (6) Formula, b will become like (7) Formula.

Therefore, the equation (3) becomes the equation (8). That is, the pixel value Xi of the enlarged image that is finally obtained is obtained by Expression (8).

このようなａは、（１０）式で与えることができる。

まとめると、（２）式でＰｉを求め、（６）式でμを求め、別途Ｙｉを求めておき、さらに、（１０）式でａを求め、最終的に、（８）式でＸｉを求めればよい。
これに即したブロック構成は図９のようになる。図９に示すものは、Ｐｉ算出モジュール９１、μ算出モジュール９２、ａ算出モジュール９３、Ｘｉ算出モジュール９４、Ｙｉ算出モジュール９５を有しており、Ｐｉ算出モジュール９１は、μ算出モジュール９２と接続されている。μ算出モジュール９２は、Ｐｉ算出モジュール９１、ａ算出モジュール９３と接続されている。ａ算出モジュール９３は、μ算出モジュール９２、Ｘｉ算出モジュール９４、Ｙｉ算出モジュール９５と接続されており、Ｘｉ算出モジュール９４はａ算出モジュール９３と接続されており、Ｙｉ算出モジュール９５はａ算出モジュール９３と接続されている。入力画像は、Ｐｉ算出モジュール９１、Ｙｉ算出モジュール９５で処理され、最終的な出力画像である拡大画像は、Ｘｉ算出モジュール９４から出力される。
すなわち、Ｐｉ算出モジュール９１は、（２）式でＰｉを求めることによって、対象画素の拡大処理による画素値を周囲画素の画素値に応じて算出する。μ算出モジュール９２は、（６）式でμを求めることによって、Ｐｉ算出モジュール９１によって算出された画素値の平均値を算出する。Ｙｉ算出モジュール９５は、補間処理によってＹｉを求める。ａ算出モジュール９３は、（１０）式でａを求めることによって、Ｙｉ算出モジュール９５によって行われた補間処理の結果及びμ算出モジュール９２によって算出された平均値を用いて、Ｐｉ算出モジュール９１によって算出された画素値に乗ずる乗数を求める。Ｘｉ算出モジュール９４は、（８）式でＸｉを求めることによって、Ｐｉ算出モジュール９１によって算出された画素値、μ算出モジュール９２によって算出された平均値及びａ算出モジュール９３によって算出された乗数に応じて、対象画素の拡大処理を行う。 Next, a is calculated.
First, using a linear interpolation method (or cubic convolution method or the like) which is a kind of interpolation processing, pixel values of pixels located at the same positions as X1 to Xm are calculated. These pixel values are Y1 to Ym.
In the present embodiment, a constant a is set such that the difference between the pixel values of Xi and Yi is as small as possible. That is, equation (9) is obtained.

Such a can be given by equation (10).

In summary, Pi is obtained from equation (2), μ is obtained from equation (6), Yi is separately obtained, a is obtained from equation (10), and finally Xi is obtained from equation (8). Find it.
A block configuration corresponding to this is as shown in FIG. 9 includes a Pi calculation module 91, a μ calculation module 92, an a calculation module 93, an Xi calculation module 94, and a Yi calculation module 95. The Pi calculation module 91 is connected to the μ calculation module 92. ing. The μ calculation module 92 is connected to the Pi calculation module 91 and the a calculation module 93. The a calculation module 93 is connected to the μ calculation module 92, the Xi calculation module 94, and the Yi calculation module 95. The Xi calculation module 94 is connected to the a calculation module 93, and the Yi calculation module 95 is connected to the a calculation module 93. Connected with. The input image is processed by the Pi calculation module 91 and the Yi calculation module 95, and the enlarged image that is the final output image is output from the Xi calculation module 94.
In other words, the Pi calculation module 91 calculates Pi according to the pixel values of the surrounding pixels by obtaining Pi in Expression (2), thereby calculating the pixel value based on the target pixel enlargement process. The μ calculation module 92 calculates an average value of the pixel values calculated by the Pi calculation module 91 by obtaining μ by the equation (6). The Yi calculation module 95 obtains Yi by interpolation processing. The a calculation module 93 calculates the Pi by the Pi calculation module 91 using the result of the interpolation process performed by the Yi calculation module 95 and the average value calculated by the μ calculation module 92 by obtaining a in Expression (10). A multiplier for multiplying the obtained pixel value is obtained. The Xi calculation module 94 obtains Xi according to the equation (8), thereby depending on the pixel value calculated by the Pi calculation module 91, the average value calculated by the μ calculation module 92, and the multiplier calculated by the a calculation module 93. The target pixel is enlarged.

Although the calculation path is as described above, in practice, the relationship between Pi-μ and Sj may be calculated in advance so that the value of Pi-μ can be directly calculated from the value of Sj. These relationships are linear equations.
For example, Pi-μ may be directly calculated as shown in FIG. In FIG. 10, the Pi-μ calculation module 101 is connected to the a calculation module 93, and the a calculation module 93 is connected to the Pi-μ calculation module 101, the Xi calculation module 94, and the Yi calculation module 95. The Xi calculation module 94 is connected to the a calculation module 93, and the Yi calculation module 95 is connected to the a calculation module 93. The input image is processed by the Pi-μ calculation module 101 and the Yi calculation module 95, and the enlarged image that is the final output image is output from the Xi calculation module 94. In addition, the same code | symbol is attached | subjected to the same kind of module, and the overlapping description is abbreviate | omitted.
Alternatively, as shown in FIG. 11 includes an expression calculation module 111, an expression calculation module 112, an expression calculation module 113, an expression calculation module 113, and an Xi calculation module 114. The (54) formula calculation module 111 is connected to the (10) formula calculation module 113, the (55) formula calculation module 112 is connected to the (10) formula calculation module 113, and the (10) formula calculation module 113. Is connected to the expression calculation module 111, the expression calculation module 112, and the Xi calculation module 114. The Xi calculation module 114 is connected to the expression calculation module 113. The input image is processed by the formula (54) calculation module 111 and the formula (55) calculation module 112, and the enlarged image that is the final output image is output from the Xi calculation module 114.
In other words, the equation (54), which is the numerator on the right side of the equation (10), and the equation (55), which is the denominator on the right side of the equation (10), may be calculated in advance as a secondary equation of Sj Therefore, the modules of the formula calculation module 111 and the formula calculation module 112 may be used.

（１１）〜（１３）式より、（１４）〜（１７）式のようになる。

（１５）式に示すように、Ｐｉ−μを直接Ｓｊから算出することが可能である。
また、前記の式を（１０）式に代入すれば、（１０）式の右辺の分子（（５４）式）、分母（（５５）式）はそれぞれ、Ｓ０〜Ｓ８の２次式として表すことができる。 Here, a specific numerical example is shown.
Assume that the surrounding pixel region is 3 × 3 and the target pixel is enlarged twice. Yi is assumed to be created by linear interpolation. The 3 × 3 pixel value is as shown in FIG.
The pixel value of the output enlarged image is as shown in FIG. That is, this is a case where the target pixel S0 shown in FIG. 12 is enlarged to the pixels X1 to X4.
In this case, X1 to X4 are represented by S0 to S8.
First, Equation (11) is obtained, which is Equation (12), and Equation (13) is obtained.

From equations (11) to (13), equations (14) to (17) are obtained.

As shown in the equation (15), Pi-μ can be directly calculated from Sj.
Also, if the above equation is substituted into equation (10), the numerator ((54) equation) and denominator ((55)) on the right side of equation (10) are expressed as secondary equations of S0 to S8, respectively. Can do.

さらに、（１９）〜（２１）式のようになる。

他の値は、前述の数値計算例と同じである。 Another numerical calculation example is shown.
It is also possible to make the surrounding pixel area part of a 3 × 3 pixel block. The thick line in FIG. 14 is the surrounding pixel area. That is, the target pixel is S0, and the surrounding pixel area includes all of S0, 1/2 of S1 to S4, and 1/4 of S5 to S8.
At this time, equation (18) is obtained.

Furthermore, it becomes like (19)-(21) Formula.

Other values are the same as those in the above numerical calculation example.

<3. Second Embodiment>
In the first embodiment, the pixel value of the surrounding pixel area is directly included in the target pixel. However, in the second embodiment, the surrounding pixel area is temporarily approximated by a function.
By performing function approximation, it is possible to generate a well-interpolated enlarged image even when the number of pixels in the surrounding pixel region is smaller than the number of pixels after enlargement.
Further, when the unevenness of the surrounding pixel area is large, the unevenness can be reduced at the time of function approximation.
Furthermore, the calculation amount can be reduced by appropriately determining the function.

  As shown in FIG. 15, the second embodiment includes a function approximating module 151, a function reducing module 152, and an enlarged pixel value creating module 153. The function approximating module 151 is connected to the function reducing module 152, the function reducing module 152 is connected to the function approximating module 151 and the enlarged pixel value creating module 153, and the enlarged pixel value creating module 153 is connected to the function reducing module 152. Has been. The input image is processed by the function approximation module 151, and an enlarged image that is a final output image is output from the enlarged pixel value creation module 153.

First, the function approximation module 151 performs function approximation on the pixel values of surrounding pixels located around the target pixel, and associates the pixel value with a position in the target pixel. That is, the surrounding pixel area is approximated by a function from the pixel values of the pixels in the surrounding pixel area located around the target pixel. For example, it approximates with a quadric surface.
Next, the function reduction module 152 sets the pixel value of the target pixel after the enlargement process in accordance with the pixel value associated with the function approximation module 151 and the magnification of the enlargement process. That is, the function is reduced so that it fits within the target pixel. Further, the output value of the function is multiplied by α and shifted by C, and the average value of the enlarged pixel values is the same as that of the target pixel and is as continuous as possible with the surrounding pixels as in the first embodiment. Make connections.
Further, the function reduction module 152 may set the pixel value of the target pixel after the enlargement process by setting the average value of the pixel values after the enlargement process to the pixel value of the target pixel and multiplying by the multiplier.
Finally, the enlarged pixel value creation module 153 converts the pixel values set by the function reduction module 152 according to the pixel values of the surrounding pixels after the enlargement process. That is, the enlarged pixel position is input to the function to generate an enlarged pixel value.

  At the time of actual calculation, as in the first embodiment, the relationship between Ti and Sj may be obtained in advance so that the output pixel value Ti can be directly calculated from the input pixel value Sj. In the first embodiment, the pixel values after enlargement are Y1 to Y4. In the second embodiment, T0 to T3.

Hereinafter, specific examples of numerical calculation will be shown.
Here, it relates to the following.
Block B is 3 × 3 pixels.
Block X is the central pixel of block B
-The approximate function is a quadric surface.
・ Enlargement ratio is the same in all directions. Furthermore, the enlargement ratio is 2.

<3.1 Preparation>
The size of each pixel is defined as a 1 × 1 rectangle. At this time, the pixels are arranged with the center position of the 3 × 3 block as the origin (x, y) = (0, 0). The relationship between the pixel value and the x and y coordinates is as shown in FIG. That is, the coordinates of the center of the pixel values S0 to S8 are as shown in Equation (56).

Furthermore, the purpose here is to enlarge the pixel S0 twice. The pixel S0 is enlarged to pixels T0 to T3 as shown in FIG. The coordinates of the center of the pixels T0 to T3 are as shown in equation (57).

また、２次曲面係数ベクトルをａとすると、ベクトルａは（２３）式のようになる。

このとき、（２４）式のようになる。

いま、（２５）式とする。

<3.2 Quadratic surface approximation>
The quadratic curved surface is represented by equation (22).

Further, when the quadric surface coefficient vector is a, the vector a is expressed by equation (23).

At this time, equation (24) is obtained.

Now, the equation (25) is assumed.

（２６）式は、２次曲面係数ベクトルａに関する連立方程式であり、（２７）式で解くことができる。

ただし、２次曲面近似の範囲は−１≦ｘ≦１、−１≦ｙ≦１、であり、重み行列Ｗは（２８）式とする。

具体的なＳｉの座標を入力して、（５８）式を計算すると（２９）式となる。

Since the equation (24) can be obtained at a plurality of points (i = 0, 1, 2,...), The equation (26) can be obtained.

Equation (26) is a simultaneous equation related to the quadric surface coefficient vector a, and can be solved by Equation (27).

However, the range of quadratic curved surface approximation is −1 ≦ x ≦ 1, −1 ≦ y ≦ 1, and the weight matrix W is expressed by equation (28).

By inputting specific Si coordinates and calculating equation (58), equation (29) is obtained.

（４）さらに、拡大後の画素値の平均値を、元の中心画素の画素値に合わせ（平均値シフト）、かつ、周囲画素値との差分が最小となるように振幅変換を行う。 <3.3 Explanation of processing>
(1) First, a quadratic function approximation is performed on a part of a 3 × 3 block area (−1 ≦ x ≦ 1, −1 ≦ y ≦ 1). Let this function be g (x, y). However, since the constant term at this time does not represent a shape and has no meaning, it is assumed that the constant term is not included in g (x, y).
(2) Next, a part of the 3 × 3 block area is transformed into a central 1 × 1 block (−0.5 ≦ x ≦ 0.5, −0.5 ≦ y ≦ 0.5). To do. Similar conversion is performed in the x direction and the y direction (ie, 1/2 times). Such a function can be expressed as g (2x, 2y).
(3) Further, the center pixel is enlarged twice in the vertical and horizontal directions. Such a function can be expressed as equation (59).

(4) Further, the average value of the enlarged pixel values is matched with the pixel value of the original central pixel (average value shift), and amplitude conversion is performed so that the difference from the surrounding pixel values is minimized.

ここで、Ｃは、Ｔ０〜Ｔ３の平均値がＳ０となるように設定する。
まず、準備として、（３１）式とする。

さらに、表記の簡略化のために、（３２）式とする。

これを用いてＣを求める。 The average value shift and amplitude conversion will be described in further detail below.
The function expanded as described above is multiplied by the amplitude conversion coefficient α. Further, a function created by adding the constant term C and shifting the average value is defined as h (x, y). That is, it becomes like (30) Formula.

Here, C is set so that the average value of T0 to T3 is S0.
First, as preparation, formula (31) is used.

Furthermore, in order to simplify the notation, the equation (32) is used.

C is obtained using this.

さらに、（３４）式であるから、（３５）式のようになる。

よって、Ｃは（３６）式のようにαで表すことができる。

したがって、２次曲面ｇ（ｘ，ｙ）を（３７）式のようにすると、ｈ（ｘ，ｙ）は（３８）式となる。

なお、αは、拡大後の画像ができるだけ滑らかに接続されるように設定する。 S0 can be expressed as shown in equation (33).

Furthermore, since it is (34) Formula, it becomes like (35) Formula.

Therefore, C can be represented by α as shown in Equation (36).

Therefore, when the quadric surface g (x, y) is expressed by the equation (37), h (x, y) is expressed by the equation (38).

Α is set so that the enlarged image is connected as smoothly as possible.

（４０）式を用いて、ＴｉをＳｉで表す。

さらに、（２７）式を代入すると、（４１）式のようになる。

Further, as a preparation, Hi is represented by Si. From equation (32), equation (39) is obtained.

Ti is represented by Si using the equation (40).

Further, when the equation (27) is substituted, the equation (41) is obtained.

各画素位置ｉ＝０〜３における誤差をＺｉとする。各誤差量は（４２）式のようになる。

αは、（４３）式に示す評価関数Ｉ（α）を最小化するように設定すればよい。

（４４）式、（４５）式とすると、（４６）式のようになる。

これを最小化するαは、（４７）式のようになる。

ちなみに、（４８）式である。

このようにして求めたαと（４１）式を用いて、Ｔ０〜Ｔ１を算出することにより、拡大後の画素値を求めることができる。 Furthermore, here, in order to create a smooth image, α is set so that the square error with the pixel value of the enlarged image created by linear interpolation is minimized. As an example, α is set so as to minimize the square error with the linearly interpolated pixel value in equation (60).

Let Zi be the error at each pixel position i = 0-3. Each error amount is expressed by equation (42).

α may be set so as to minimize the evaluation function I (α) shown in the equation (43).

If it is set as (44) type | formula and (45) type | formula, it will become like (46) Formula.

Α that minimizes this is expressed by equation (47).

Incidentally, equation (48).

The pixel value after enlargement can be obtained by calculating T0 to T1 using α thus obtained and Equation (41).

<3.4 How to apply to actual images>
Based on the above, a specific filtering method for an image will be described. Hereinafter, calculation is performed with N = 2.
(1) Raster scan the image to be enlarged. Now, let S0 be the pixel value of the pixel to be enlarged. The pixel values of the upper, lower, left and right pixels are defined as shown in FIG.
(2) Enlarge the center pixel (pixel value S0) twice vertically and horizontally. The enlarged pixel value is defined as shown in FIG.
(3) α is obtained using equation (47).
(4) The pixel values of T0 to T3 are obtained using equation (41).
(5) Round the resulting Ti to a pixel value of 0-255.

  FIG. 20 shows a block configuration when the second embodiment is viewed from another viewpoint. 20 includes a function approximation module 201 for the surrounding pixel area, a scaling module 202 for the approximation function, and an output pixel value creation module 203. The function approximation module 201 for the surrounding pixel area is the scaling module 202 for the approximation function. The approximation function scaling module 202 is connected to the surrounding pixel area function approximation module 201 and the output pixel value creation module 203, and the output pixel value creation module 203 is connected to the approximation function scaling module 202. ing. The input image is processed by the function approximation module 201 in the surrounding pixel area, and the enlarged image that is the final output image is output from the output pixel value creation module 203. The function approximation module 201 for the surrounding pixel area is the same as the function approximation module 151, and the output pixel value creation module 203 is the same as the enlarged pixel value creation module 153.

さらに、この関数の振幅をα倍し、定数項Ｃを加えて、シフトする。
結局、この近似関数のスケーリングでは、αとＣを算出し、さらに、（５０）式を計算することになる。

ここで、（５０）式は（３０）式を一般化したものである。
また、（３１）式の一般化は（５１）式のようになる。

出力画素値作成モジュール２０３では、出力画素の存在する位置（ｘ，ｙ）を（５１）式の関数に代入して、出力値を作成する。 The scaling of the approximate function by the scaling module 202 of the approximate function is performed as follows.
First, let g (x, y) be an approximate function.
Assuming that the scaling factor when the surrounding pixel area is reduced to the central 1 × 1 block is p and the enlargement magnification is N, the surrounding pixel area is first reduced so as to be pushed into the central 1 × 1 area, and further N To double the magnification, the function is scaled as in equation (49).

Further, the amplitude of this function is multiplied by α, and a constant term C is added to shift.
Eventually, in the scaling of this approximate function, α and C are calculated, and further equation (50) is calculated.

Here, the equation (50) is a generalization of the equation (30).
Further, the generalization of equation (31) is as shown in equation (51).

The output pixel value creation module 203 creates an output value by substituting the position (x, y) where the output pixel exists in the function of the equation (51).

FIG. 21 shows a block configuration when the second embodiment is viewed from another viewpoint. 21 includes an α calculation module 291, a C calculation module 292, and an output pixel value creation module 293. The α calculation module 291 is connected to the C calculation module 292, and the C calculation module 292 includes an α calculation module 292. The calculation module 291 and the output pixel value creation module 293 are connected, and the output pixel value creation module 293 is connected to the C calculation module 292. The input image is processed by the α calculation module 291, and the enlarged image that is the final output image is output from the output pixel value creation module 293. The output pixel value creation module 293 is the same as the output pixel value creation module 203.
In the α calculation module 291, α is calculated by equation (47).
In the C calculation module 292, C is calculated by Expression (36).
When calculating α, matrix A and matrix B are defined as shown in equation (45). Thereby, when the surrounding pixel area and the enlargement ratio are fixed, they can be fixedly calculated in advance. That is, by calculating and storing the matrix A or the matrix B (equation (47)) in the equation (45) in advance, the speed of the calculation process can be improved using the stored value. .
Further, if the matrix A and the matrix B are fixed, the equations (52) and (53) can be calculated in advance. That is, by calculating and storing Formula (52) or Formula (53) in advance, it is possible to improve the speed of the calculation process using the stored value.

  According to the above-described embodiment, when one pixel before enlargement is enlarged, frequency information higher than the sampling theorem can be given, so that blur of the enlarged image can be suppressed or texture can be given.

  With reference to FIG. 22, a hardware configuration example of the above-described embodiment will be described. The configuration illustrated in FIG. 22 is configured by, for example, a personal computer (PC), and illustrates a hardware configuration example including a data reading unit 2217 such as a scanner and a data output unit 2218 such as a printer.

  The CPU (Central Processing Unit) 2201 includes various modules described in the above-described embodiments, that is, the pixel replacement module 51, the pixel value projection module 52, the continuous processing module 53, the Pi calculation module 91, the μ calculation module 92, This is a control unit that executes processing according to a computer program that describes the execution sequence of each module such as the Pi-μ calculation module 101, the (54) expression calculation module 111, and the function approximation module 151.

  A ROM (Read Only Memory) 2202 stores programs, calculation parameters, and the like used by the CPU 2201. A RAM (Random Access Memory) 2203 stores programs used in the execution of the CPU 2201, parameters that change as appropriate during the execution, and the like. These are connected to each other by a host bus 2204 including a CPU bus.

  The host bus 2204 is connected to an external bus 2206 such as a PCI (Peripheral Component Interconnect / Interface) bus via a bridge 2205.

  A keyboard 2208 and a pointing device 2209 such as a mouse are input devices operated by an operator. The display 2210 includes a liquid crystal display device, a CRT (Cathode Ray Tube), or the like, and displays various types of information as text or image information.

  An HDD (Hard Disk Drive) 2211 includes a hard disk, drives the hard disk, and records or reproduces a program executed by the CPU 2201 and information. The hard disk stores an input image, an enlarged image that is an output image, and the like. Further, various computer programs such as various other data processing programs are stored.

  The drive 2212 reads data or a program recorded on a removable recording medium 2213 such as a magnetic disk, an optical disk, a magneto-optical disk, or a semiconductor memory, and the data or program is read out to the interface 2207 and the external bus 2206. , The bridge 2205, and the RAM 2203 connected via the host bus 2204. The removable recording medium 2213 can also be used as a data recording area similar to a hard disk.

  The connection port 2214 is a port for connecting the external connection device 2215 and has a connection unit such as USB or IEEE1394. The connection port 2214 is connected to the CPU 2201 and the like via the interface 2207, the external bus 2206, the bridge 2205, the host bus 2204, and the like. A communication unit 2216 is connected to the network and executes data communication processing with the outside. The data reading unit 2217 is a scanner, for example, and executes document reading processing. The data output unit 2218 is a printer, for example, and executes document data output processing.

  Note that the hardware configuration shown in FIG. 22 shows one configuration example, and the present embodiment is not limited to the configuration shown in FIG. 22, and is a configuration capable of executing the modules described in the previous embodiments. If it is. For example, some modules may be configured with dedicated hardware (for example, Application Specific Integrated Circuit (ASIC), etc.), and some modules are in an external system and connected via a communication line In addition, a plurality of systems shown in FIG. 22 may be connected to each other through communication lines so as to cooperate with each other. Further, it may be incorporated in a copying machine, a fax machine, a scanner, a printer, a multifunction machine (also called a multi-function copying machine, which has functions of a scanner, a printer, a copying machine, a fax machine, etc.).

  In the above-described embodiment, the description has been made using mathematical expressions, but the mathematical expressions may include those equivalent to the mathematical expressions. The equivalent includes not only the mathematical formula itself, but also transformation of the mathematical formula to the extent that the final result is not affected, or solving the mathematical formula by an algorithmic solution.

The program described above may be provided by being stored in a recording medium, or the program may be provided by communication means. In that case, for example, the above-described program may be regarded as an invention of a “computer-readable recording medium recording the program”.
The “computer-readable recording medium on which a program is recorded” refers to a computer-readable recording medium on which a program is recorded, which is used for program installation, execution, program distribution, and the like.
The recording medium is, for example, a digital versatile disc (DVD), which is a standard established by the DVD Forum, such as “DVD-R, DVD-RW, DVD-RAM,” and DVD + RW. Standards such as “DVD + R, DVD + RW, etc.”, compact discs (CDs), read-only memory (CD-ROM), CD recordable (CD-R), CD rewritable (CD-RW), etc. MO), flexible disk (FD), magnetic tape, hard disk, read only memory (ROM), electrically erasable and rewritable read only memory (EEPROM), flash memory, random access memory (RAM), etc. It is.
The program or a part of the program may be recorded on the recording medium for storage or distribution. Also, by communication, for example, a local area network (LAN), a metropolitan area network (MAN), a wide area network (WAN), a wired network used for the Internet, an intranet, an extranet, etc., or wireless communication It may be transmitted using a transmission medium such as a network or a combination of these, or may be carried on a carrier wave.
Furthermore, the program may be a part of another program, or may be recorded on a recording medium together with a separate program. Moreover, it may be divided and recorded on a plurality of recording media. Further, it may be recorded in any manner as long as it can be restored, such as compression or encryption.

The present embodiment is also an image processing system, an image processing program, and an image processing method having the following characteristics.
(A) pixel correspondence means for associating pixel values of surrounding pixels located around the target pixel in the target pixel;
The pixel correspondence means includes an enlargement means for enlarging using pixel values of surrounding pixels corresponding to the target pixel.
(B) Further, the item (a) is characterized in that the positional relationship between the target pixel and the surrounding pixels is fixed.
(C) an enlarged pixel value calculating means for calculating a pixel value obtained by enlarging the target pixel according to the pixel values of surrounding pixels and calculating a value obtained by subtracting the average value of the calculated pixel values;
Interpolation means for performing interpolation processing of the target pixel;
A multiplier calculating means for obtaining a multiplier for multiplying the pixel value calculated by the enlarged pixel value calculating means using a result of the interpolation processing performed by the interpolation means and an average value calculated by the average value calculating means;
An enlargement processing unit that performs an enlargement process of the target pixel according to the pixel value calculated by the enlarged pixel value calculation unit, the average value calculated by the average value calculation unit, and the multiplier calculated by the multiplier calculation unit. It is characterized by comprising.
(D) first calculation means for calculating a value by applying the equation (54) using pixels in the image;
Second calculation means for calculating a value by applying equation (55) using pixels in the image;
Third calculation means for calculating a value by applying equation (10) using the values calculated by the first calculation means and the second calculation means;
It is characterized by comprising fourth calculation means for calculating the value of the enlarged pixel using the value calculated by the third calculation means.
(E) pixel correspondence means for performing function approximation on the pixel values of surrounding pixels located around the target pixel and associating the pixel value with a position in the target pixel;
A pixel value setting unit that sets a pixel value using the equation (49) in accordance with the pixel value and the magnification of the enlargement process that are associated by the pixel correspondence unit;
It further comprises pixel value conversion means for converting the pixel value set by the pixel value setting means in accordance with the pixel values of the surrounding pixels after the enlargement process.
(F) first calculation means for calculating a value by applying the equation (47) using pixels in the image;
Using the value calculated by the first calculating means, a second calculating means for calculating a value by applying equation (36);
It is characterized by comprising third calculation means for calculating the value of the enlarged pixel using the value calculated by the second calculation means.
(G) Further, the first calculation means of the item (f) stores the value of the matrix A or the matrix B in the equation (47), and calculates using the stored value. It is characterized by that.
(H) Further, the first calculation means of the item (f) stores the value of the formula (52) or the formula (53) in the formula (47), and uses the stored value. This is characterized by the calculation.

It is a conceptual explanatory diagram showing the relationship between the pixel before the enlargement process and the pixel after the enlargement process. It is a conceptual explanatory drawing at the time of enlarging processing by a linear interpolation method. It is a conceptual explanatory drawing at the time of enlarging processing in the present embodiment. It is a conceptual explanatory drawing at the time of enlarging processing in the present embodiment. It is a conceptual module block diagram about the structural example of 1st Embodiment. It is a conceptual explanatory view showing the relationship between the target pixel and surrounding pixels and the association of pixel values. It is a conceptual explanatory drawing which shows the process of a pixel value projection module. It is explanatory drawing which showed another example of the surrounding pixel. It is a notional module block diagram about another structural example of 1st Embodiment. It is a notional module block diagram about another structural example of 1st Embodiment. It is a notional module block diagram about another structural example of 1st Embodiment. It is explanatory drawing which shows a 3 * 3 pixel value. It is explanatory drawing which shows the pixel value of an expansion pixel. It is explanatory drawing which shows the case where a surrounding pixel area | region is made into a part of 3x3 block. It is a conceptual module block diagram about the structural example of 2nd Embodiment. It is explanatory drawing which shows the relationship between a pixel value and an X, Y coordinate. It is explanatory drawing which shows the relationship between the pixel value of an expansion pixel, and X, Y coordinate. It is explanatory drawing which shows the pixel value of the pixel which is the object of an expansion process. It is explanatory drawing which shows the pixel value after an expansion process. It is a conceptual module block diagram about another structural example of 2nd Embodiment. It is a conceptual module block diagram about another structural example of 2nd Embodiment. It is a block diagram which shows the hardware structural example of the computer which implement | achieves this Embodiment.

Explanation of symbols

DESCRIPTION OF SYMBOLS 51 ... Pixel replacement module 52 ... Pixel value projection module 53 ... Continuation processing module 91 ... Pi calculation module 92 ... μ calculation module 93 ... a calculation module 94 ... Xi calculation module 95 ... Yi calculation module 101 ... Pi-μ calculation module 111 (54) Formula calculation module 112 (55) Formula calculation module 113 (10) Formula calculation module 114 ... Xi calculation module 151 ... Function approximation module 152 ... Function reduction module 153 ... Expanded pixel value creation module 201 ... Surrounding pixel area Function approximation module 202 ... Scaling module of approximation function 203 ... Output pixel value creation module 291 ... α calculation module 292 ... C calculation module 293 ... Output pixel value creation module

Claims (18)

Pixel correspondence means for associating pixel values of surrounding pixels located around the target pixel in the target pixel;
An image processing system comprising: enlarging means for enlarging by using the pixel values of surrounding pixels corresponding to the target pixel by the pixel correspondence means. Pixel correspondence means for associating pixel values of surrounding pixels located around the target pixel with partial pixels obtained by dividing the target pixel;
Pixel value setting means for setting the pixel value of the target pixel after the enlargement process according to the pixel value of the partial pixel associated by the pixel correspondence means and the magnification of the enlargement process;
An image processing system comprising: a pixel value conversion unit that converts a pixel value set by the pixel value setting unit according to a pixel value of a surrounding pixel after the enlargement process. The image according to claim 2, wherein the pixel value conversion means converts the pixel value of the target pixel so that an average value of pixel values of pixels corresponding to the target pixel after the enlargement processing is equal. Processing system. The image processing system according to claim 2, wherein the pixel value conversion unit multiplies the pixel value set by the pixel value setting unit by a constant value as a multiplier. The image processing system according to claim 4, wherein the pixel value conversion unit determines the multiplier according to a value obtained by an interpolation process. The pixel correspondence unit associates a part of surrounding pixels and the partial pixel, and associates a pixel value with the partial pixel by using an area of the associated pixel as a weighting factor. Image processing system. An enlarged pixel value calculating means for calculating a pixel value obtained by enlarging the target pixel according to a pixel value of a surrounding pixel;
Average value calculating means for calculating an average value of pixel values calculated by the enlarged pixel value calculating means;
Interpolation means for performing interpolation processing of the target pixel;
A multiplier calculating means for obtaining a multiplier for multiplying the pixel value calculated by the enlarged pixel value calculating means using a result of the interpolation processing performed by the interpolation means and an average value calculated by the average value calculating means;
An enlargement processing unit that performs an enlargement process of the target pixel according to the pixel value calculated by the enlarged pixel value calculation unit, the average value calculated by the average value calculation unit, and the multiplier calculated by the multiplier calculation unit. An image processing system comprising: Pixel correspondence means for performing a function approximation on the pixel values of surrounding pixels located around the target pixel and associating the pixel value with a position in the target pixel;
Pixel value setting means for setting the pixel value of the target pixel after the enlargement process according to the pixel value associated with the pixel correspondence means and the magnification of the enlargement process;
An image processing system comprising: a pixel value conversion unit that converts a pixel value set by the pixel value setting unit according to a pixel value of a surrounding pixel after the enlargement process. The pixel value setting means sets the pixel value of the target pixel after the enlargement process by setting the average value of the pixel values after the enlargement process to the pixel value of the target pixel and multiplying by a multiplier. 9. The image processing system according to 8. Computer
Pixel correspondence means for associating pixel values of surrounding pixels located around the target pixel in the target pixel;
An image processing program that causes the pixel correspondence means to function as an enlargement means for enlarging using pixel values of surrounding pixels corresponding to a target pixel. Computer
Pixel correspondence means for associating pixel values of surrounding pixels located around the target pixel with partial pixels obtained by dividing the target pixel;
Pixel value setting means for setting the pixel value of the target pixel after the enlargement process according to the pixel value of the partial pixel associated by the pixel correspondence means and the magnification of the enlargement process;
An image processing program for causing a pixel value set by the pixel value setting means to function as a pixel value conversion means for converting the pixel value according to the pixel values of surrounding pixels after the enlargement process. The image according to claim 11, wherein the pixel value conversion unit converts the pixel value of the target pixel so that an average value of pixel values of pixels corresponding to the target pixel after the enlargement process is equal. Processing program. The image processing program according to claim 11, wherein the pixel value conversion unit multiplies the pixel value set by the pixel value setting unit by a constant value as a multiplier. The image processing program according to claim 13, wherein the pixel value conversion unit determines the multiplier according to a value obtained by an interpolation process. 12. The pixel correspondence unit associates a part of surrounding pixels and the partial pixel, and associates a pixel value with the partial pixel by using an area of the associated pixel as a weighting factor. Image processing program. Computer
An enlarged pixel value calculating means for calculating a pixel value obtained by enlarging the target pixel according to a pixel value of a surrounding pixel;
Average value calculating means for calculating an average value of pixel values calculated by the enlarged pixel value calculating means;
Interpolation means for performing interpolation processing of the target pixel;
A multiplier calculating means for obtaining a multiplier for multiplying the pixel value calculated by the enlarged pixel value calculating means using a result of the interpolation processing performed by the interpolation means and an average value calculated by the average value calculating means;
As an enlargement processing means for performing enlargement processing of the target pixel according to the pixel value calculated by the enlarged pixel value calculation means, the average value calculated by the average value calculation means, and the multiplier calculated by the multiplier calculation means An image processing program characterized by causing it to function. Computer
Pixel correspondence means for performing a function approximation on the pixel values of surrounding pixels located around the target pixel and associating the pixel value with a position in the target pixel;
Pixel value setting means for setting the pixel value of the target pixel after the enlargement process according to the pixel value associated with the pixel correspondence means and the magnification of the enlargement process;
An image processing program for causing a pixel value set by the pixel value setting means to function as a pixel value conversion means for converting the pixel value according to the pixel values of surrounding pixels after the enlargement process. The pixel value setting means sets the pixel value of the target pixel after the enlargement process by setting the average value of the pixel values after the enlargement process to the pixel value of the target pixel and multiplying by a multiplier. The image processing program according to 17.

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