WO1999064989A1

WO1999064989A1 - Image processor

Info

Publication number: WO1999064989A1
Application number: PCT/JP1999/003045
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: TW440802B; JPH11353472A

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 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.冃 Technology

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 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, there is a disadvantage that the image after enlargement or reduction 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. 10 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, when the sampling frequency is f, the sine function is (0 = ί (…. According to this equation (1), the interpolation by the sinc function is performed by the function sin {7T f (t-k T)} /; rf (t _ k T) It can be seen that this is realized by performing a so-called convolution operation, which shifts by kT in the time axis direction and multiplies the sample value.

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 by a convolution operation 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 this finite number of sections is subject to interpolation calculation, so that the amount of calculation is small and no truncation error is generated. Interpolation accuracy can be obtained, and distortion of an image obtained by image processing can be reduced.

Further, it is desirable that the pixel position calculation performed for each pixel of the image after the image processing be performed in a relative relationship to the pixel position of each pixel of the original image. In general, If an attempt is made to obtain the pixel value of each pixel of the image after image processing 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 it has conventionally been thought that there is no sampling function that satisfies such a condition. However, the present inventor's research has found a function satisfying the above conditions.

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)-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 + 1 2 t + 9) / 4 for one 3 / 2≤t <-1/2, and one l / 2≤t < l / 2 can be expressed as 1 2 t ² + 3/2, and l / 2≤t <3/2 as (4 t ² _ 12 t + 9) / 4. Since the above-described sampling function operation can be performed by the piecewise polynomial according to, the operation content is relatively simple and the amount of operation can be reduced. Also, instead of using the B-spline function to represent the sampling function as described above, 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, for one l≤t <— l / 2, (5 t ² +12 t + 7) / 4, and for one l / 2≤t <l / 2, (— 7 t ² +4 ) / in 4, l / 2≤t <for 1 (5 t ² - in 1 2 t + 7) / 4 , for l≤t rather ^{3/2 (3 t 2 - 8 t} + 5) / 4 in, for 3 / 2≤t ^ 2 is ^{(- t 2 + 4 t -} 4) / by using a sampling function is defined by 4, Ru can be performed above interpolation process.

Further, in the present invention, the pixel value calculating means for performing the pixel value interpolation operation includes an interpolation target pixel extracting means, a sampling function operation means, and a convolution operation means for performing the above-described interpolation operation. The interpolation target pixel extracting means extracts a plurality of pixels which are present in a predetermined range around the target pixel and which are to be subjected to the interpolation calculation. The sampling function calculation means calculates the value of the sampling function H (t) for each of the plurality of pixels extracted in this way, where t is the distance between the pixel of interest and the convolution calculation means. Calculates the pixel value of the pixel of interest by performing a convolution operation based on the values of each sampling function corresponding to that of the plurality of pixels obtained by the calculation and each pixel value of the plurality of pixels . In this way, the pixel value of the target pixel can be obtained simply by calculating the value of the sampling function corresponding to the plurality of extracted pixels and performing a convolution operation on the result. The required processing amount can be greatly reduced. Moreover, as described above, since a truncation error is eliminated by using a finite number of sampling functions, it is possible to prevent distortion of an image that has been subjected to image processing. 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 a range of constituent pixels of an original image extracted around a pixel of interest. FIG. 5 is an explanatory diagram of a sampling function used in the operation in the sampling function operation unit. FIG. 6 is an explanatory diagram of a distance calculation between the target pixel p and each interpolation target pixel performed by the sampling function operation unit.

FIG. 7 is a diagram showing a specific example of calculating the value of the sampling function at the pixel of interest corresponding to each interpolation target pixel,

FIG. 8 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. 9 is an explanatory diagram when the interval at which the value of the sampling function becomes 0 is changed according to the relative direction between each interpolation target pixel and the pixel of interest.

FIG. 10 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 the pixel data of each pixel constituting the original image. C The pixel data includes the pixel position and the pixel value of each pixel. The pixel position is address information of each pixel constituting the original image, and includes an X address along the horizontal direction and a Y address along the vertical direction. The X address and the Y address may be implicitly indicated by an array of pixel values or the like in addition to the case where the X address and the Y address are explicitly specified as part of the pixel data. In addition, the pixel value is a data that indicates the characteristics of each pixel, and for example, grayscale data, color data, luminance data, and the like of each pixel correspond thereto.

The pixel position calculation unit 20 calculates the scaling factor a when the image scaling factor a is specified. Then, the pixel positions of the pixels constituting the image obtained by the image processing are calculated based on the relative relationship with respect to the pixel positions of the pixels constituting the original image before the image processing. 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 process and the pixel value 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 constituent pixels of an original image in which pixel data is stored in the pixel data storage unit 10, and asterisks 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), the pixel located at the upper left is set as the enlargement center position), and the distance from each pixel position is changed to a times. In this way, each of the constituents of the original image is After changing the pixel position of the pixel, the pixel position calculation unit 20 determines each pixel position having the same pixel interval L as the original pixel interval L as indicated by a mark in FIG. It is set as each pixel position constituting the image. In Fig. 2 (c), the pixel positions that make up the image after image processing are set with reference to the upper left pixel as in the original image, but this reference position can be set arbitrarily and is not necessarily There is no need to match any pixel location in the 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 is configured to include an interpolation target pixel extraction unit 32, a sampling function calculation unit 34, and a convolution calculation unit 36.

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 (（ Those included in a predetermined range centered on the pixel of interest are selected from (誊).

Figure 4 shows the range of constituent pixels of the original image extracted around the pixel of interest _c . As shown in Figure 4, if one pixel of interest is p and its coordinates are (x, y), then The interpolation target pixel extraction unit 32 extracts pixels included in a range of two pixels before and after each pixel in the X direction and the Y direction around the pixel of interest p. Since the pixel interval of each pixel constituting the original image is set to a L by the pixel position calculating unit 20, the address in the X direction and the Y back from the pixel of interest p is from −2 a L. The constituent pixels of the original image included in the range of 2 a L are extracted. Therefore, the points in Figure 4 A total of 16 constituent pixels of the original image included in the rectangular area of the line 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 sampling function calculation unit 34 calculates the distance between each interpolation target pixel extracted by the interpolation target pixel extraction unit 32 and the pixel of interest p, and calculates the value of the sampling function based on the calculated distance. I do. The value of the sampling function is calculated for each of the 16 interpolation target pixels extracted by the interpolation target pixel extraction unit 32.

The convolution operation unit 36 multiplies the values of the 16 standardization functions calculated by the sampling function operation unit 34 by the pixel values of the corresponding pixels to be interpolated, and adds the results. Performs a convolution operation. 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 is a first data storage unit, a pixel position calculation unit 20 is a pixel position calculation unit, a pixel value calculation unit 30 is a pixel value calculation unit, and a pixel data storage unit. 40 corresponds to the second pixel data storage means. The interpolation target pixel extraction unit 32 corresponds to the interpolation target pixel extraction unit, the sampling function operation unit 34 corresponds to the sampling function operation unit, and the convolution operation unit 36 corresponds to the convolution operation unit.

Next, details of the interpolation processing performed by the above-described pixel value calculation unit 30 will be described. C FIG. 5 is an explanatory diagram of a sampling function used in the calculation in the sampling function calculation unit 34. The sampling function H (t) shown in Fig. 5 is a finite function focusing on differentiability.For example, it is differentiable only once in the entire region, and the sampling position t along the horizontal axis is It is a finite function with a finite non-zero value when +2. 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

Can be defined as Where the third-order B-spline function F (t) is

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

-2 t ² +3/2-l / 2≤t <l / 2

^{(4 t 2 - 12 t +} 9) / 4 1 / 2≤ t <

It is represented by

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

Thus, the above-mentioned function H (t) is a sampling function, which is differentiable only once in the whole range, and is a finite function converging to 0 at t = ± 2. Therefore, by performing superimposition based on the pixel value of each interpolation target pixel using this sampling function H (t), the pixel value of the pixel of interest existing between each pixel of the original image is obtained only once. Interpolation can be performed using a differentiable function.

FIG. 6 is an explanatory diagram of the distance calculation between the pixel of interest p and each pixel to be interpolated performed by the sampling function calculation unit 34. In FIG. 6, the pixel of interest p and some of the pixels to be interpolated are shown. Pi, indicates the pixel value of the pixel to be interpolated arranged at coordinates, Yj). For example, the coordinates of the pixel position of the pixel p to be interpolated are X = Xi + 2 + 0.5, and Y = Y.j _{+ 2} + 0.2.

When calculating the distance t1 between the pixel to be interpolated at the coordinates (Xi _{+ 2} , Yj ₊ .) And the pixel of interest p, the sampling function calculator 34 calculates the difference between the X coordinates of these two pixel positions. Δ The difference between X and Y coordinates ΔΥ is obtained, and the distance t 1 is calculated based on these values. In the case of the pixel to be interpolated at the coordinates (Xi _{+ 2} , Υο ₊ ι), ΔΧ = — 0.5, Δ 1. = -1.2, so the distance t 1 is

t 1 = (0.5) ² + (1.2) ² }

= 1.3

Becomes Note that the distance aL between the X and Y directions of the pixel to be interpolated was both normalized and set to 1.

Similarly, when calculating the distance t2 between the pixel to be interpolated at the coordinates (Xi _{+ 2} , Yj _{+ 2} ) and the pixel of interest p, the sampling function calculation unit 34 calculates the X seat Find the difference Δ 標 (= — 0.5) of the target and the difference ΔΥ (= — 0.2) of the Y coordinate. Based on these values, the distance t 2 is

t 2 {(― 0.5) ² + (-0.2) ² }

= 0.539

Becomes

Once the distance between each pixel to be interpolated and the pixel of interest p is determined, the sampling function calculator 34 calculates the value at the position of the pixel of interest p for the sampling function H (t) corresponding to each pixel to be interpolated. Is calculated. As shown in Fig. 7, the interpolation target pixel at the coordinates (Xi _{+ 2} , Yj ₊ i) described above is sampled by substituting the distance t = t1 (= 1.3) to the target pixel p. Calculate the function value H (1.3). Similarly, for the pixel to be interpolated at the coordinates (X _{1 +2} , Yj _{+ 2} ) described above, the distance t to the pixel of interest t = t 2 (= 0.539) is substituted into the value H for sampling. (0.539) is calculated. When the value at the position of the pixel of interest p is determined for the sampling function H (t) corresponding to each interpolation target pixel, the convolution operation unit 30 calculates the value of each of the obtained sampling functions as the pixel of each interpolation target pixel. The values Ρχ and γ are multiplied, and a convolution operation is performed by adding the result of the multiplication for all of the 16 interpolation target pixels to output a pixel value ある which is an interpolation value corresponding to the target pixel ρ. Similarly, the pixel values of all the pixels constituting the image after the image processing are calculated by the interpolation calculation.

As described above, since the image processing apparatus 1 of the present embodiment uses a finite number of functions that can be differentiated only once over the entire area as the sampling function, the pixel of each pixel constituting the image obtained by the image processing is used. The amount of calculation required to calculate the value by interpolation can be greatly reduced.

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. Since 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 a finite scale, 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 in the related art. By preventing the occurrence of aliasing, an interpolation result with a small 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 direction and the Y direction 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. 8 is a diagram showing an outline of a modification of the image enlarging process performed by the image processing apparatus 1 shown in FIG. FIG. 8 (a) partially shows constituent pixels of an original image in which pixel data is stored in the pixel data storage unit 10, and a symbol indicates each pixel. Let the pixel spacing be along each of the X and Y directions.

First, the interpolation 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 position where the dotted line in FIG. 8B intersects is the pixel position to be calculated, and the pixel position is 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 interpolation position calculation unit 20 (indicated by 〇 in FIG. 8 (c)) into each pixel constituting the original image. 'Calculate by interpolation processing using the pixel value of ((in Fig. 8 (c)). The pixel The interpolation processing itself performed by the 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 pixel of interest p, and a plurality of pixels included in the original image in each of the X direction and the Y direction centering on the pixel of interest P , 16 pixels included in the range of two pixels before and after are extracted as interpolation target pixels. The relationship shown in Fig. 4 is applied as it is to the relationship between the pixel of interest p and the 16 interpolation target pixels, and the pixel value of the pixel of interest p is calculated by a convolution operation using the sampling function shown in Fig. 5. 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.

Note that 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 is described as a specific example of the image processing. However, a case where the original image is reduced at a predetermined magnification can be similarly considered.

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 each of the above-described embodiments, the interval t O at which the value of the sampling function H (t) becomes 0 is set to the same value 1 (normalized as the interval in the X and Y directions of each pixel constituting the original image). ), But may be set to the interval 2 between each of the pixels adjacent in a diagonal direction of 45 °. In this case, the above sampling function can be used as it is by calculating H (t / 2). Alternatively, the above-described interval to ′ may be set to a value b that satisfies 1 <b <2. In this case, H (t By calculating / b), the above-mentioned sampling function can be used as it is.

Further, the interval t 0 at which the value of the sampling function H (t) becomes 0 may be changed according to the relative direction between each pixel constituting the original image and the interpolation target image. For example, as shown in FIG. 9, the interval t0 is set according to the direction connecting the pixel of interest p (〇) and each pixel to be interpolated (image). Specifically, when the angle between the direction connecting the pixel of interest p and each pixel to be interpolated and the horizontal or vertical direction is 0 (^ 45 °), the above-described interval t 0 is 1 / cos Θ Set to. In this case, by calculating H (t xcos Θ), _c can be used as a sampling function described above also, in the above embodiment, a sampling function with a B-spline function F (t) H (t) is defined, and the sampling function H (t) is calculated using a quadratic piecewise polynomial.

(-t ^2-4 t-4) / 4-2≤t <-3/2

(3 t ² + 8 t + 5) / 4 — 3 / 2≤ t <— 1

(5 t ² + 1 2 t + 7) / 4-1≤ t <-1/2

(-7 t ² + 4) / 4-1 / 2≤ t <1/2

^{(5 t 2 - 1 2 t} + 7) 1 / 2≤ t <1

^{(3 t 2 - 8 t +} 5) / 4 1≤ t <3/2

(-t ² + 4 t-4) / 4 ≤ t≤ 2

Can be equivalently expressed as 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. By using a sampling function having a finite number of values, only the pixel data corresponding to this 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 high interpolation accuracy and reduce distortion of an image obtained by image processing.

Claims

The scope of the claims

1. first pixel data storage means for storing first pixel data including pixel positions and pixel values of a plurality of pixels constituting an original image to be subjected to image processing;

When a predetermined magnification is designated, based on the magnification, a pixel position calculation means for calculating a pixel position of each pixel constituting the image obtained by the image processing; and each pixel of the image obtained by the image processing The pixel value of is finitely differentiable and finite based on the pixel position calculated by the pixel position calculation means and the first pixel data stored in the first pixel data storage means. A pixel value calculating unit that calculates by performing a convolution operation using a sampling function having a plurality of values, and a pixel value of each pixel calculated by the pixel value calculating unit, together with a pixel position of the pixel value. An image processing apparatus, comprising: second pixel data storage means for storing as pixel data.

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. The sampling function is defined as F (t), where the third-order B-spline function is

H (t) = — F (t + 1/2) / 4 + F (t) — F (t— 1/2) / 4

2. The image processing apparatus according to claim 1, wherein the image processing apparatus is defined by:

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

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

— For 1 / 2≤ t <1/2, one 2 t ² + 3/2,

l / 2 ^ for t rather 3/2 ^{(4 t 2 - 1 2 t} + 9) / 4 by being represented by the image processing apparatus of the fourth Claims claims, wherein.

6. The sampling function is:

— 2≤ t <— 3/2 is (one t ^2-4 t-4) / 4,

— (3 t ² + 8 t + 5) / 4 for 3/2 ^ t

For one l ^ t ku 1/2, (5 t ² + 12 t + 7) / 4, lb

— For 1/2 ^ t 1/2, (1 7 t ² +4) / 4,

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

For 1≤ t rather 3/2 - at ^{(3 t 2 8 t + 5} ) / 4,

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

7. The pixel value calculation means,

Using any one of a plurality of pixels constituting the image obtained by the image processing as a target pixel, extracting a plurality of pixels existing in a predetermined range around the target pixel from among the plurality of pixels constituting the original image Interpolation target pixel extraction means,

For each of the plurality of pixels extracted by the interpolation target pixel extracting unit, a distance between the pixel of interest and t is a sampling function calculating unit for calculating the sampling function H (t),

By performing a convolution operation based on the pixel values of a plurality of pixels extracted by the interpolation target pixel extraction unit and the value of the sampling function calculated by the sampling function operation unit, Convolution operation means for obtaining a pixel value of a pixel;

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

8. The pixel value calculating means includes:

For each of the plurality of pixels extracted by the interpolation target pixel extracting unit, a distance between the pixel of interest and t is a sampling function calculating unit that calculates the sampling function H (t),

By performing a convolution operation based on the respective pixel values of a plurality of pixels extracted by the interpolation target pixel extraction unit and the value of the sampling function calculated by the sampling function operation unit, Convolution operation means for obtaining a pixel value of the pixel of interest;

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