WO1999064987A1

WO1999064987A1 - Image processor

Info

Publication number: WO1999064987A1
Application number: PCT/JP1999/003043
Authority: WO
Inventors: Kazuo Toraichi; Kouichi Wada
Original assignee: Fluency Research & Development Co., Ltd.
Priority date: 1998-06-10
Filing date: 1999-06-08
Publication date: 1999-12-16
Also published as: JPH11353473A; TW510999B

Abstract

An image processor capable of reducing the distortion of an image due to an error and processing an image with a reduced amount of calculation. When the magnification/reduction ratio of an image is specified, a pixel position calculating unit (20) calculates, according to the specified magnification/reduction ratio, the relative position of each of the pixels constituting the image formed by image processing. A pixel value calculating unit (30) calculates the pixel values of the pixels corresponding to the respective calculated pixel positions by performing predetermined interpolation in the X direction and then in the Y direction by using the pixel values of the pixels of the original image contained in a predetermined area around it. The pixel value calculating unit (30) uses a sampling function differentiatable finite times and having finite values for the interpolation.

Description

Description Image processing equipment Technical field

The present invention relates to an image processing device that performs enlargement or reduction processing of an image composed of a plurality of pixels. In this specification, a case where the value of a function has a limited value other than 0 in a local region and becomes 0 in other regions is referred to as a “finite base” and described. I do. Background art

Conventionally, as a method of performing enlargement or reduction of an image by simple processing, a method of repeating or thinning out the same pixel at a predetermined interval has been known. For example,

By inserting a pixel having the same pixel value as that of the fifth pixel every 5 pixels in each of the X direction and the Y direction, a 20% enlarged image can be easily obtained. On the other hand, by deleting one pixel for every five pixels, a reduced image of 25% can be easily obtained. However, when pixels are inserted or thinned out at regular intervals in this way, the image after enlargement or reduction has a disadvantage that the image is distorted. Techniques that use interpolation processing that does not have such disadvantages are widely used.

By the way, conventionally, as a data interpolation method for obtaining a value between predetermined discrete values, a method of performing data interpolation using a sampling function is known. FIG. 11 is an explanatory diagram of a conventionally known sampling function called a sinc function. This sinc function appears when the Fourier transform of the Dirac delta function is performed, and becomes 1 only at the sample point at t = 0, and becomes 0 at all other sample points. Specifically, the sine function is: (0 () ^S (ί ⁽ )-d) one κΤ)

Represented by According to this equation (1), interpolation by the sinc function shifts the function sin {rc f (t−k T)} / 7r f (t−k T) by k T in the time axis direction, It can be seen that this is realized by performing a so-called convolution operation by multiplying by.

By the way, when the above-mentioned sinc function is used as a sampling function, the value of each sampling function corresponding to the pixel value from -∞ to + ∞ is theoretically added by convolution to obtain an accurate interpolation value. Can be obtained. However, when the above-described interpolation calculation is actually performed by various processors, the processing is terminated in a predetermined finite interval in order to reduce the amount of calculation, so that an error due to the truncation occurs, and furthermore, a small number of pixel values is generated. When the interpolation operation is performed by using, there is a problem that sufficient accuracy cannot be obtained, and distortion occurs in an image after being enlarged or reduced. Disclosure of the invention

The present invention has been made in view of the above points, and an object of the present invention is to provide an image processing apparatus capable of reducing image distortion due to an error and reducing the amount of calculation.

The image processing apparatus according to the present invention calculates the pixel positions of a plurality of pixels constituting the image after the image processing when a predetermined magnification for performing the enlargement processing or the reduction processing on the original image is specified. Later, interpolation processing for obtaining the pixel value of each of these pixels is performed for each of the two variables that define the two-dimensional space by using a sampling function that is finitely differentiable and has a finite number of values. By using a sampling function having a finite number of values, only the pixel data corresponding to the finite number of sections is subjected to the interpolation calculation, so that the amount of calculation is small and no truncation error is generated. It is possible to obtain a high interpolation accuracy and reduce the distortion of the image obtained by the image processing.

The pixel position calculation performed for each pixel of the image after image processing is performed by calculating It is desirable to perform the processing in a relative relationship to the pixel position of each pixel. Generally, if the pixel value of each pixel of the image after image processing is to be obtained by interpolation using the pixel value of each pixel of the original image, the relative positional relationship of each pixel becomes important. That is, the pixel position of each pixel of the image after image processing is calculated based on the relative relationship to the pixel position of each pixel of the original image, and the subsequent interpolation processing becomes possible by using the calculation result.

As the above-mentioned sampling function, it is preferable to use a function that can be differentiated only once over the entire area of a finite range. Various signals existing in the natural world are considered to need to be differentiable because they change smoothly, but the number of differentiable times does not have to be infinite, but rather only once. Then, it is thought that natural phenomena can be sufficiently approximated.

As described above, there are many advantages to using a sampling function that is finitely differentiable and finite, but in the past it was thought that there was no sampling function that satisfied such conditions. However, the research by the present inventors has found a function satisfying the above conditions.

More specifically, the sampling function H (t) to which the present invention is applied is represented by one F (t + 1/2) / 4 + F (, where F (t) is a third-order B-spline function. t) It can be obtained by one F (t-1/2) / 4. This sampling function H (t) is a finite function that can be differentiated only once in the entire region and whose value converges to 0 at t = ± 2, and satisfies the above two conditions. By using such a function H (t) to perform an interpolation operation for obtaining a pixel value of a pixel corresponding to an intermediate position of each pixel, an interpolation operation with a small amount of operation and high accuracy can be performed. Therefore, the speed of the image processing can be increased, and the distortion of the image obtained by the image processing can be reduced.

The third-order B-spline function F (t) described above is (4 t ² + 12 t + 9) / 4 for — 3 / 2≤t <— 1/2, and — l / 2 ^ t / 2 can be expressed as 1 2 t ² + 3/2, and l / 2≤t <3/2 can be expressed as (4 t ² — 12 t + 9) / 4. Since the above-mentioned sampling function operation can be performed by a piecewise polynomial, the operation content is relatively simple and the operation amount is small. Can be done.

As described above, instead of using a B-spline function to represent a sampling function, it can be represented by a quadratic piecewise polynomial. Specifically, (1 t ^2-4 t-4) / 4 for one 2≤t <-3/2, and (3 t ² + 8 t + 5 for one 3 / 2≤ t <-1 ) / 4, (5 t ² + 12 t + 7) / 4 for 1 l≤t <1 1/2 and (-7 t ² + 4) for 1 1/2 ^ t <1/2 / at 4, 1/2 ≤ 1: clause for one - at ^{(5 t 2 12 t + 7} ) / 4, for 1 ^ t rather than 3/2 - in ^{(3 t 2 8 t + 5} ) / 4 , 3/2 t 2, the above-described interpolation processing can be performed by using the sampling function defined by (1 t ² +4 t −4) / 4.

Further, in the present invention, the pixel value calculating means for performing the interpolation calculation of the pixel value includes the interpolation target pixel extracting means, the first and second sampling function calculating means, the first and the second Two convolution means are provided. The interpolation target pixel extracting means extracts a plurality of pixels to be subjected to an interpolation operation existing in a predetermined range around the target pixel. First, the first sampling function operation means and the first convolution operation means perform a convolution operation on one of the two variables using the above-described sampling function. The convolution operation is performed on the other of the two variables by the convolution operation means 2 using the above-described sampling function, and the pixel value of the pixel of interest is finally obtained. In this way, the pixel value of the pixel of interest can be obtained simply by calculating the value of the sampling function separately for each of the two variables and performing a convolution operation on the result, and the amount of processing required for the interpolation process Can be greatly reduced. In addition, as described above, since a truncation error is eliminated by using a finite number of sampling functions, it is possible to prevent distortion of the processed image. BRIEF DESCRIPTION OF THE FIGURES

FIG. 1 is a diagram illustrating a configuration of an image processing apparatus according to an embodiment;

FIG. 2 is a diagram showing an outline of an image enlargement process performed by the image processing apparatus shown in FIG. 1,

FIG. 3 is a diagram showing a detailed configuration of the pixel value calculation unit, Fig. 4 is a diagram showing the range of constituent pixels of the original image extracted around the pixel of interest. Fig. 5 is a diagram showing the relationship between pixels arranged at regular intervals along the X direction and the interpolation position between them. ,

Fig. 6 is an explanatory diagram of the sampling function used in the operation in the sampling function operation unit. Fig. 7 is the relationship between the pixel value of each pixel arranged in the X direction and the X direction interpolation value at the interpolation position between them. Figure showing

FIG. 8 is a diagram showing a specific example of calculating an X-direction interpolation value,

FIG. 9 is a diagram showing the relationship between the X direction interpolation value corresponding to each pixel arranged along the Y direction and the pixel value of the pixel of interest.

FIG. 10 is a diagram showing an outline of a modification of the image enlarging process performed by the image processing device shown in FIG. 1,

FIG. 11 is an explanatory diagram of the sinc function. BEST MODE FOR CARRYING OUT THE INVENTION

Enlarging or reducing an image composed of a plurality of pixels means increasing or decreasing the number of constituent pixels according to a predetermined magnification while maintaining the contour shape of the original image. The feature of the present embodiment lies in that the process of increasing or decreasing is performed by an interpolation operation using a predetermined sampling function. Hereinafter, an image processing apparatus according to an embodiment will be described in detail with reference to the drawings.

FIG. 1 is a diagram showing a configuration of an image processing apparatus according to an embodiment to which the present invention is applied. The image processing apparatus 1 shown in FIG. 1 includes a pixel data storage unit 10, a pixel position calculation unit 20, a pixel value calculation unit 30, and a pixel data storage unit 40.

The pixel data storage unit 10 stores pixel data for each pixel constituting the original image. The pixel data includes a pixel position and a pixel value of each pixel. The pixel position is address information of each pixel constituting the original image, and includes an X address along a horizontal direction and a Y address along a vertical direction. The X address and the Y address may be indicated implicitly by an array of pixel values, in addition to the case where the X address and the Y address are explicitly specified as part of the pixel data. The pixel value is data indicating the characteristics of each pixel. For example, grayscale data, color data, luminance data, and the like of each pixel include this. Equivalent to.

The pixel position calculation unit 20 performs the image processing based on the relative magnification to the pixel position of each pixel constituting the original image before the image processing based on this magnification when the image magnification / reduction magnification a is designated. The pixel position of each pixel constituting the image obtained by the above is calculated. For example, (1) After virtually shifting the pixel position of each pixel constituting the original image so that the pixel interval becomes a times as large as the pixel interval, the image is adjusted so that the pixel interval becomes the same as the original pixel interval of the original image. When calculating the pixel position of each pixel that constitutes the image after processing, or (2) without changing the pixel position of each pixel that constitutes the original image, the pixel position of each pixel that constitutes the image after image processing It is possible to calculate each pixel position by changing the interval to 1 / a times.

The pixel value calculation unit 30 calculates a pixel value of each pixel forming the image after the image processing by performing a predetermined interpolation process based on the pixel value of each pixel forming the original image. The pixel data storage unit 40 stores the pixel value of each pixel calculated by the interpolation processing and the pixel position of each pixel as pixel data after image processing.

The image processing device 1 of the present embodiment has such a configuration, and the operation will be described next. As described above, since a specific procedure of calculating the pixel position performed prior to the interpolation processing can be implemented in a number of modifications, each case will be described separately.

(1) After virtually shifting the pixel position of each pixel constituting the original image so that the pixel interval becomes a times, the image processing is performed so that the pixel interval becomes the same as the original pixel interval of the original image. When calculating the pixel position of each pixel constituting the subsequent image

FIG. 2 is a diagram illustrating an outline of an image enlargement process performed by the image processing apparatus 1 illustrated in FIG. FIG. 2 (a) partially shows the constituent pixels of the original image in which the pixel data is stored in the pixel data storage unit 10, and the marks indicate each pixel. Let L be the pixel interval along each of the X and Y directions.

First, the pixel position calculation unit 20 performs a process of changing the pixel position of each pixel constituting the original image according to the specified scaling factor a. For example, when the magnification ratio a is greater than 1 (in the case of the enlargement process), as shown in FIG. 2 (b), the pixel position of each pixel constituting the original image is set to a predetermined enlargement center position (see FIG. 2 In (b), upper left The distance from each pixel position to the position of each pixel is a-times as large as-. In this way, after changing the pixel position of each pixel constituting the original image according to the scaling factor a, the pixel position calculation unit 20 returns to the original position as indicated by a triangle in FIG. 2 (c). Each pixel position having the same pixel interval as the pixel interval L is set as each pixel position constituting an image after image processing. In Fig. 2 (c), the pixel positions that make up the image after image processing are the force s set based on the upper left pixel as in the original image, and this reference position can be set arbitrarily. It is not necessary to match any pixel position in the original image.

The pixel value calculation unit 30 calculates the pixel value of each pixel constituting the image after the image processing by a predetermined interpolation process. In FIG. 2 (c), the pixel values of the pixels arranged at the pixel interval L are calculated by interpolation based on the pixel values of the pixels arranged at the pixel interval aL. The pixel position and pixel value of each pixel calculated by the interpolation processing in this manner are stored in the pixel data storage unit 40 as pixel data of each pixel constituting the image after the image processing.

Next, a detailed configuration of the pixel value calculation unit 30 included in the above-described image processing apparatus 1 will be described. FIG. 3 is a diagram showing a detailed configuration of the pixel value calculation unit 30. As shown in FIG. 3, the pixel value calculation unit 30 includes an interpolation target pixel extraction unit 32, an X-direction sampling function operation unit 34, an X-direction convolution operation unit 35, and a Y-direction sampling function operation unit 36. , And a Y-direction convolution operation unit 37.

The interpolation target pixel extraction unit 32 includes, from among a plurality of pixels constituting the original image, a pixel included in a predetermined range around a pixel whose pixel value is to be calculated by the interpolation processing (hereinafter, referred to as a “pixel of interest”). Is extracted and held. In this extraction process, one of the pixels (marked with 〇) constituting the image after image processing shown in FIG. 2 (c) is set as a target pixel, and a plurality of pixels (（ Among them, those included in a predetermined range centered on the pixel of interest are selected.

FIG. 4 is a diagram illustrating a range of constituent pixels of an original image extracted around a target pixel. As shown in FIG. 4, assuming that one pixel of interest is p and its coordinates are (X, y), the pixel-to-be-interpolated 32 extracts the pixel of interest in the X and Y directions around the pixel of interest p. For, the pixels included in the range of two pixels before and after are extracted. Pixel position Since the pixel interval of each pixel constituting the original image is set to a L by the position calculating unit 20, the address in the X direction and the Y back from the pixel of interest p is from 1 2a to + The constituent pixels of the original image included in the range of 2 a L are extracted. Therefore, a total of 16 constituent pixels of the original image included in the rectangular area indicated by the dotted line in FIG. 4 are extracted by the interpolation target pixel extracting unit 32. Hereinafter, each of the 16 pixels extracted in this manner is referred to as an “interpolation target pixel”.

The X-direction sampling function operation unit 34 calculates the distance along the X direction between each interpolation target pixel extracted by the interpolation target pixel extraction unit 32 and the pixel of interest p, and based on the calculated distance. Compute the value of the sampling function. The value of the sampling function is calculated for each of the 16 interpolation pixels extracted by the interpolation pixel extraction unit 32.

The X-direction convolution operation unit 35 multiplies the values of the 16 sampling functions calculated by the X-direction sampling function operation unit 34 by the pixel values of the corresponding interpolation target pixels, and calculates the result. The convolution operation along the X direction is performed by adding for each series with the same Y coordinate. The value obtained by this convolution operation is the interpolated value for each X direction, and as shown by “*” in FIG. 5, based on the pixel value of each interpolation target pixel along the X direction, Interpolated values corresponding to the four pixels A, B, C, and D having the same Y coordinate (hereinafter referred to as “X-direction interpolated values”) are calculated. The Y-direction sampling function calculation unit 36 calculates the distance along the Y direction between the pixel corresponding to the X-direction interpolation value calculated in this way and the pixel of interest p, and calculates the calculated distance. Based on, calculate the value of the sampling function corresponding to each X-direction interpolation value. In this way, the value of the sampling function is calculated for each of the four X-direction interpolated values calculated by the X-direction convolution operation unit 35.

The Y-direction convolution operation unit 37 multiplies each of the four sampling function values calculated by the Y-direction sampling function operation unit 36 by the corresponding X-direction interpolation value, and adds the result. In this way, convolution operation corresponding to four X-direction interpolation values is performed. The interpolation value obtained by this convolution operation is the pixel value of the pixel of interest p.

The above-described pixel data storage unit 10 serves as a first pixel data storage unit, the pixel position calculation unit 20 serves as a pixel position calculation unit, the pixel value calculation unit 30 serves as a pixel value calculation unit, and a pixel data storage unit. The evening storage unit 40 corresponds to each of the second pixel data storage units. Also, the interpolation target-. The pixel extraction unit 32 is used as the interpolation target pixel extraction unit, the X-direction sampling function operation unit 34 is used as the first sampling function operation unit, and the X-direction convolution operation unit 35 is used as the first convolution operation unit. In addition, the Y-direction sampling function calculator 36 corresponds to the second sampling function calculator, and the Y-direction convolution calculator 37 corresponds to the second convolution calculator. The X-direction interpolation value corresponds to the first interpolation value, and the pixel value of the pixel of interest p corresponds to the second interpolation value. Next, details of the interpolation processing performed by the above-described pixel value calculation unit 30 will be described. FIG. 6 is an explanatory diagram of the sampling functions used in the calculations in the X-direction sampling function calculation unit 34 and the Y-direction sampling function calculation unit 36. The sampling function H (t) shown in Fig. 6 is a finite function focusing on differentiability. For example, the function is differentiable only once in the entire region, and the sampling position t along the horizontal axis is It is a finite function having a finite value other than 0 when +2. In addition, since H (t) is a sampling function, it has the characteristic that it becomes 1 only at the sample point of t = 0, and becomes 0 at the sample points of t = ± l, ± 2.

It has been confirmed by the inventor's research that there exists a function H (t) that satisfies the above-described various conditions (sampling function, one-time differentiable, finite table). Specifically, such a sampling function H (t) is expressed as follows, where F (t) is the third-order B-spline function.

H (t) = _ F (t + 1/2) / 4 + F (t) -F (t-1 / 2) / 4.

Where the third-order B-spline function F (t) is

(4 t ² + 12 t + 9) / 4 -3 / 2≤ t <-1/2

1 2 t ² +3/2-1 / 2≤ t <1/2

^{(4 t 2 - 12 t +} 9) / 4 l / 2≤t <3/2

It is represented by

The sampling function H (t) described above is a quadratic piecewise polynomial, and uses a third-order B-spline function F (t). Function. Also, it becomes 0 at t = ± l, ± 2.

Thus, the function H (t) described above is a sampling function, and 1 It is a finite function that is differentiable only once and converges to 0 at t = ± 2. Therefore, by performing superposition based on the pixel value of each interpolation target pixel using this sampling function H (t), the pixel value of each pixel existing between each pixel of the original image is differentiated only once. Interpolation can be performed using possible functions.

As described above, the interpolation processing using the sampling function is performed by using the pixel values of a plurality of pixels discretely present in a two-dimensional space (XY plane) as shown in FIG. To extend the processing, as shown in Fig. 5, interpolation is first performed along the X direction, and the interpolation value for each Y coordinate that has the same X coordinate as the pixel of interest p to be finally obtained is obtained. (Interpolated value in the X direction) is calculated, and then the interpolation process is performed again in the Y direction using the interpolated value in the X direction to finally obtain the interpolated value P which is the pixel value of the pixel of interest P. .

FIG. 7 is a diagram showing a relationship between pixels to be interpolated arranged at regular intervals in the X direction and an interpolated value in the X direction between them. For example, an X direction interpolated value corresponding to pixel A shown in FIG. The relationship between each pixel value of four surrounding pixels to be interpolated having the same Y coordinate is shown. Y coordinate X coordinate Y _{j + 1} is _{_{X i + 1, Xi + 2}} , Xi + 3, it its pixel values of _{_{_{Xi +4 P i + 1, j}}} + 1, P i + 2, j + ₁ , P i _{+ 3} , _{j + 1} , P _{i +} 4 _{+ 1,} and the X direction interpolation value corresponding to the predetermined position Xa (distance a from Xi _{+ 2} ) between X coordinates Xi _{+ 2} and X _{i + 3} Consider the case of finding p _{j +1} .

In general, in order to obtain the interpolation value P _{j + 1} using the sampling function, the value of the sampling function at the interpolation position Xa for each of the surrounding pixels to be interpolated must be obtained, and the convolution operation is performed using this. By the interpolation value Ρ "10! Can be requested. The si ne function is a function that converges to 0 at the sample point of t = ± ∞, so if you try to find the interpolation value P _{j + 1} accurately, it will correspond to each pixel of each X coordinate up to X = ± ∞ Then, it was necessary to calculate the value of the sinc function at the interpolation position Xa, and use this to perform the convolution operation.

However, the sampling function H (t) used in the present embodiment converges to 0 at t = ± 2 sampling points, so that pixel data up to t = ± 2, that is, two pixels before and after the interpolation position, Just take it into account. Therefore, in order to obtain the X direction interpolation value Ρ ” ₊₁ shown in FIG. 7, each pixel value of the four pixels whose X coordinate is Xi _{+ 1} , Xi + 2, Xi ₊ 3, and Xi ₊ 4 P i ₊ l, j ₊ ls Pi + 2, j _{+ 1} , P i ₊ 3, j + KP i ₊ 4, j ₊₁ Only need to be considered-. be able to. In addition, the pixel values of the other pixels should be considered originally, but they are not neglected in consideration of the amount of calculation and accuracy, etc., and need not be considered theoretically. Does not occur.

FIG. 8 is a detailed explanatory diagram of the interpolation processing by the X-direction sampling function operation unit 34 and the X-direction convolution operation unit 35. The procedure of the interpolation processing, as shown in FIG. 8 (A) ~ (D) , the pixel value P _{i +1} of the four interpolation target _{_{pixel, j + 1, P i +}} 2, j + 1, P i + The peak height at t = 0 (center position) of the sampling function H (t) shown in Fig. 6 is matched to each of ₃ , j _{+ 1} and P _{i +} 4 _{+ 1} , and the interpolation position Xa Find the value of each sampling function at.

For example, it will be described in detail pixel value P _{i +} 1. _{J +1} of the interpolation target pixel at the pixel position X _{i + 1} shown in FIG. 8 (A). The distance between the interpolation position Xa and the pixel position Xi _{+ 1} is 1 + a when the distance between each pixel position is normalized to be 1. Therefore, when the center position of the sampling function H (t) is adjusted to the pixel position Xi _{+ 1} , the value of the sampling function at the interpolation position Xa is H (1 + a). Actually, in order to adjust the peak height at the center position of the sampling function H (t) so that it coincides with the pixel value P _{i + 1 + 1} , the above-mentioned H (1 + a) is converted to P _{i + 1} , _The value multiplied by _{j +} 1 H (1 + a) · _{Pi + 1} , _{j + 1} is the desired value. In the configuration shown in FIG. 3, H (1 + a) is calculated by the X-direction sampling function operation unit 34, and an operation of multiplying it by Pi _{+ 1 + 1} is performed by the X-direction convolution operation unit 35.

Similarly, as shown in FIGS. 8 (B) to (D), corresponding to the other three interpolation target pixels, each operation result H (a) -Pi _{+ 2} , _{j + at the} interpolation position Xa H (1−a) −Pi ₊ 3, _{j + 1}ヽ H (2−a) −Pi ₊ 4j ₊ ₁ is obtained.

The X-direction convolution operation unit 35 calculates the four operation results H (1 + a) · Pi ₊ i, _{j + 1} , H (a) _{.Pi + 2} , _{J + 1} , H (1-a) ■ P _{i + 3} , j tens "H (2-a) · Convolution operation is performed by adding P i _{+ 4} , _{j +1} to correspond to pixel A shown in Fig. 5. Outputs the X direction interpolation value P _{j +1} .

The same interpolation calculation is performed for each of the other pixels B to D shown in FIG. Then, the other three X-direction interpolation values P _{j +2} , P _{j +3} , and P _{J +4} are output from the X-direction convolution unit 3.5.

Next, by using the four X-direction interpolation values output from the X-direction convolution operation unit 35 in this way, interpolation processing along the Y direction is performed, and the interpolation value (pixel value) corresponding to the pixel of interest p Value) is required.

FIG. 9 is a diagram illustrating a relationship between four X-direction interpolated values arranged at regular intervals in the Y-direction and interpolated values therebetween. As described above, the sampling function H (t) used in the present embodiment converges to 0 at a sampling point of t = ± 2. What is necessary is just to consider an interpolation value. Accordingly, in order to obtain the interpolation value P shown in FIG. 9, the Y coordinate is Yj10i, Yj ₊ 2, Yj ₊ 3, Yj ₊ 4, and four pixels having the same X coordinate as the pixel of interest p Only the X-direction interpolation values P _{+ 1} , _{Pj + 2} , Pj ₊ 3, and Pj ₊ 4 that are the values need to be considered.

The distance between the interpolation position Yb and the pixel position corresponding to the X-direction interpolation value P _{j +1} is 1 + b when the distance between the pixel positions corresponding to each X-direction interpolation value is normalized to 1. Therefore, when the center position of the sampling function H (t) is adjusted to the pixel position corresponding to the X-direction interpolation value Ρ '' _{+ 1} , the value of the sampling function at the interpolation position Yb is H (1 + b) And Actually, to adjust the peak height of the center position of the sampling function H (t) so that it matches the X-direction interpolation value _{Pj + 1} , the above-mentioned H (1 + b) is multiplied by Ρ " _{+ 1} Value H (1 + b)-P j-, ι is the desired value. In the configuration shown in FIG. 3, H (1 + b) is calculated by the Y-direction sampling function operation unit 36, and an operation of multiplying it by Pj _{+ 1} is performed by the Y-direction convolution operation unit 37.

Similarly, corresponding to the other three X-direction interpolation values P _{j +2} , P _{j +3} , and P _{j +4} , each operation result H (b) at the interpolation position Yb. P _{j +2} , H (1—b) · Ρ ” ₊₃ , Η (2—b) · P _{j + 4} .

The Y-direction convolution operation unit 37 calculates the four operation results この (1 + b) _J P _{J +} i, H (b) · P j _{+ 2} , H (1-b)-P _{j +3} , H (2−b) · Ρ J ₊₄ to perform a convolution operation to obtain an interpolation value that is a pixel value corresponding to the pixel of interest p (X, y) shown in FIGS. 4 and 5. Outputs P. Similarly, the pixel values of all the pixels constituting the image after the image processing are calculated by the interpolation processing. As described above, the image processing apparatus 1 according to the present embodiment uses a finite number of functions that can be differentiated only once as a sampling function in the entire region. Therefore, each pixel constituting the image obtained by the image processing is used. It is possible to greatly reduce the amount of calculation required when calculating the pixel values of the above by interpolation processing.

In particular, when calculating the pixel value of each pixel after image processing, only the pixel values of a total of 16 pixels to be interpolated need to be considered, so that the amount of calculation can be reduced, and sampling can be performed. Since the function is represented by a simple quadratic piecewise polynomial, the value of the sampling function can be obtained by a simple multiply-accumulate operation, and the amount of operation can be further reduced from this point.

In addition, since the sampling function used in the present embodiment is of finite level, there is no truncation error that occurs when the number of pixels to be subjected to the interpolation operation is reduced to a finite number, and aliasing distortion occurs. Thus, the interpolation result with less error can be obtained. For this reason, it is possible to reduce distortion generated in the shape, color, and the like of an image obtained by image processing.

(2) When calculating the pixel position by changing the pixel interval of each pixel constituting the image after image processing to 1 / a times without changing the pixel position of each pixel constituting the original image

In the description of the above-described embodiment, the interval between the pixels constituting the original image is virtually widened according to the magnification of the image processing, and the image after the image processing is processed based on the pixel value of each pixel having the widened interval. Although the pixel values of the constituent pixels were obtained by interpolation processing, the pixel values of the constituent pixels of the image after image processing may be obtained without virtually widening the intervals between the constituent pixels of the original image. Good.

For example, when the original image is enlarged by a times, the number of pixels in the X and Y directions of the enlarged image becomes a times. To obtain a magnified image in which the number of pixels in each of the X and Y directions is a times larger by enlarging a certain original image by a times, first, the interval L between pixels constituting the original image is 1 / a The multiplied pixel positions may be obtained by calculation, and then the pixel values corresponding to these pixel positions may be obtained by interpolation processing.

Hereinafter, a description will be given of a modification in which the pixel value of each pixel constituting the image obtained by the image processing is calculated by the interpolation processing. FIG. 10 is a diagram showing an outline of a modified example of the image enlarging process performed by the image processing apparatus 1 shown in FIG. Fig. 10 (a) partially shows the constituent pixels of the original image in which the pixel data is stored in the pixel data storage unit 10, and reference symbols indicate each pixel. Let L be the pixel spacing along the X and Y directions.

First, the pixel position calculation unit 20 calculates the pixel position of each pixel constituting the image obtained by the image processing based on the pixel data of each pixel stored in the pixel data storage unit 10. The positions where the dotted lines in FIG. 10 (b) intersect are the pixel positions to be calculated, and the pixel positions are calculated such that the adjacent intervals in the X and Y directions are L / a.

Next, the pixel value calculation unit 30 calculates the pixel value of each pixel corresponding to the pixel position calculated by the pixel position calculation unit 20 (indicated by a triangle in FIG. 10 (c)) into each of the pixels constituting the original image. It is calculated by interpolation using the pixel value of the pixel (marked in Fig. 10 (c)). Note that the interpolation processing itself performed by the pixel value calculation unit 30 is basically the same as the interpolation processing outlined in FIG. 2, and is realized by the configuration shown in FIG. That is, any pixel for which a pixel value is to be obtained by an interpolation operation is defined as a target pixel p, and a plurality of pixels included in the original image in each of the X direction and the Y direction with the target pixel P as a center. Sixteen pixels included in the range of two pixels before and after from the inside are extracted as pixels to be interpolated. The relationship shown in Fig. 4 is directly applied to the relationship between the target pixel p and the 16 interpolation target pixels, and the pixel value of the target pixel p is calculated by a convolution operation using the sampling function shown in Fig. 6. Is done.

Thus, without changing the pixel interval of the original image, the pixel position of each pixel constituting the image obtained by the image processing is directly calculated, and the pixel value corresponding to this pixel position is calculated by the interpolation process. Accordingly, image processing at a predetermined magnification can be performed. Since this interpolation process is performed using a finite number of functions that can be differentiated only once in the entire area as a sampling function, the amount of computation required to calculate the pixel value of each pixel can be significantly reduced. In addition, since no truncation error occurs, it is possible to prevent an image obtained by the image processing from being distorted or changed in color.

The present invention is not limited to the above embodiment, and various modifications can be made within the scope of the present invention. For example, in the above-described embodiment, a case where the original image is enlarged at a predetermined magnification has been described as a specific example of the image processing. The same can be considered for a case of reduction by a magnification.

Further, in the above-described embodiment, the sampling function is a finite-level function that can be differentiated only once in the entire region. However, the number of differentiable times may be set to two or more. Further, as shown in FIG. 5, the sampling function of the present embodiment converges to 0 at t = ± 2, but may converge to 0 at t = ± 3 or more.

In the embodiment described above, the sampling function H (t) is defined using the third-order B-spline function F (t), but the sampling function H (t) is calculated using a quadratic piecewise polynomial.

(One t ^2-4 t-4)-2≤t <-3/2

(3 t ² + 8 t + 5) / 4-3 / 2≤t <-l

(5 t ² + 1 2 t + 7) / 4-1≤ t <-1/2

(-7 t ² +4) / 4-l / 2≤t <l / 2

^{(5 t 2 - 1 2 t} + 7) / 4 1 / 2≤ t <1

^{(3 t 2 - 8 t +} 5) / 4 1≤ t <3/2

(One t ² + 4 t-4) 3 / 2≤ t≤ 2

Can be equivalently expressed as

In the above-described embodiment, the interpolation processing is first performed along the X direction using the pixel values corresponding to each pixel of the original image arranged two-dimensionally, and thereafter, the interpolation processing is performed. Although the interpolation processing is performed along the Y direction using the X-direction interpolation value to finally obtain the interpolation value P corresponding to the target pixel P, the order in which the interpolation processing is performed may be changed. That is, first, interpolation processing is performed along the Y direction, and then interpolation processing is performed along the X direction using the Y direction interpolation value obtained by this interpolation processing, and finally corresponds to the pixel point p of interest. Alternatively, the interpolation value P to be calculated may be obtained. Industrial applicability

As described above, according to the present invention, when a predetermined magnification is designated, after calculating the pixel positions of a plurality of pixels constituting an image after image processing, the pixel value of each of these pixels is obtained. The interpolation process is performed by convolution using a sampling function that is finitely differentiable and has finite values. A sampling function with finite values By using, only the pixel data corresponding to this finite number of sections can be subjected to the interpolation calculation, so that the amount of calculation is small and no truncation error occurs, so that good interpolation accuracy can be obtained. In addition, distortion of an image obtained by image processing can be reduced.

Claims

The scope of the claims

1. For an original image composed of a plurality of pixels arranged at equal intervals in a two-dimensional space defined by two variables, first pixel data including pixel positions and pixel values of the plurality of pixels is stored. First pixel data storage means for performing

A pixel position calculating means for calculating a pixel position of each pixel constituting an image obtained by the image processing based on the predetermined magnification when a predetermined magnification of the image processing is designated;

The pixel value of each pixel of the image obtained by the image processing is calculated based on the pixel position calculated by the pixel position calculation means and the first pixel data stored in the first pixel data storage unit. A pixel value calculating means for calculating by separately performing a convolution operation using a sampling function having finitely differentiable and finite values for each of the two variables;

An image processing apparatus comprising: a second pixel data storage unit that stores, as second pixel data, a pixel value of each pixel calculated by the pixel value calculation unit together with a pixel position.

2. The pixel position calculating means calculates a pixel position of each pixel forming an image obtained by the image processing in a relative relationship with respect to a pixel position of each pixel forming the original image. The image processing device according to claim 1.

3. The image processing apparatus according to claim 1, wherein the sampling function is a function whose entire region can be differentiated only once.

4. When the sampling function is F (t) with the third-order B-spline function,

The image according to claim 1, wherein H (t) =-F (t + 1/2) / 4 + F (t) -F (t-1 / 2) / 4. Processing equipment.

5. The third-order B-spline function F (t) is

— For (3/2 ^ t) 1/2, (4 t ² + 12 t + 9) / 4, for — 1 / 2≤ t <1/2, for 1 2 t ² +3/2,

l / 2 ^ for t rather 3/2 ^{(4 t 2 - 12 t +} 9) / 4 by being represented by the image processing apparatus of the fourth Claims claims, wherein.

6. The sampling function is: For 1 2≤ t <— 3/2, (1 t ^2-4 t-4) / 4, for 1 3 / 2≤ t <— 1, (3 t ² + 8 t + 5) / 4,

For 1 1 ^ t 1 1/2, (5 t ² + 1 2 t + 7) / 4

— For l / 2≤t く 1/2, (one 7 t ² +4) / 4,

For l / 2≤t <l - at ^{(5 t 2 1 2 t +} 7) / 4,

For 1 t <3/2, (3 t ² — 8 t + 5) / 4,

2. The image processing apparatus according to claim 1, wherein 3 / 2≤t ^ 2 is defined by (1 t ² +4 t-) / 4.

7. The pixel value calculation means,

Any one of a plurality of pixels constituting the image obtained by the image processing is taken as a pixel of interest, and a plurality of pixels constituting the original image are selected from the plurality of pixels constituting the original image in a predetermined range around the focused pixel in the two-dimensional space. Interpolation target pixel extraction means for extracting a plurality of existing pixels;

For each of the plurality of pixels extracted by the interpolation target pixel extraction unit, the distance to the pixel of interest is t 1 along a direction corresponding to one of the two variables defining the two-dimensional space, and the sample is A first standardization function calculating means for calculating a generalization function H (t1),

A plurality of sequences along one of the two variables is obtained by performing a convolution operation along one of the two variables using the values of the plurality of sampling functions calculated by the first sampling function operation means. A first convolution operation means for obtaining a first interpolation value for each of the plurality of first interpolation values extracted by the first convolution operation means, each of which corresponds to the other of the two variables A second sampling function calculating means for calculating the sampling function H (t 2) along a direction with a distance to the pixel of interest as t 2,

By performing a convolution operation along the other of the two variables using the values of the plurality of sampling functions calculated by the second sampling function operation means, a second interpolation value corresponding to the target pixel is obtained. A second convolution operation means for obtaining

5. The image processing device according to claim 4, comprising:

8. The pixel value calculating means includes: Any one of a plurality of pixels constituting the image obtained by the image processing is regarded as a pixel of interest, and a predetermined area around the focused pixel in the two-dimensional space is selected from among the plurality of pixels constituting the original image. Interpolation target pixel extraction means for extracting a plurality of pixels existing in the range,

7. The image processing device according to claim 6, comprising: