CN106846279A - A kind of adapting to image method for repairing and mending and its system based on interpolation by continued-fractions technology - Google Patents

Abstract

The invention relates to an adaptive image repair method and system based on continuous fraction interpolation technology, which solves the defects of poor repair effect and low efficiency compared with the prior art. The present invention comprises the following steps: initializing image feature analysis; repairing the damaged point of the scratched image by using the unary continued fraction interpolation technique; re-repairing the scratched image by using the binary continued fraction interpolation technique, and using the initial repaired image A as In the information image, the position of each damaged point is determined by the mask image, and the pixel information of each damaged point is obtained by updating the pixel information around the damaged point by binary continued fraction interpolation to obtain the final repaired image B. The invention improves the quality and efficiency of image repair, can modify scratches of any type, and is suitable for all image processing.

Description

An adaptive image repair method and system based on continued fraction interpolation technology

technical field

The invention relates to the technical field of image processing, in particular to an adaptive image repair method and system based on continued fraction interpolation technology.

Background technique

Image restoration is to repair the damaged part of the image in a certain way to make it a complete image. Image restoration has a wide range of applications in image processing, film industry and other industries, such as the removal of scratches in photos and old movies, the removal of text and occlusions in images, etc. are all related to image restoration. Therefore, image inpainting has great application prospects and is a research hotspot in computer vision and computer graphics.

At this stage, many researchers have proposed different image inpainting methods, and have achieved some success, but these methods lack versatility, incomplete inpainting, and blurred boundaries at the same time. Among them, methods based on partial differential equations and methods based on texture synthesis are currently the most common inpainting methods. The image repair method based on partial differential equations iterates the information around the repaired area into the area to be repaired along the direction of the isoluminance line of the pixel points in the image until the image is completely filled. This method based on partial differential equations has a certain repair effect, but it lacks stability, especially when dealing with texture images with large backgrounds, it cannot get good results. Texture synthesis method is another restoration method, which uses Markov random field model in texture synthesis for the first time. Practice has proved that the method based on texture synthesis often cannot solve the boundary blur problem, so it cannot be practically applied.

For example, as shown in FIG. 3 , FIG. 3 is an image to be patched.

1. Repair using the methods of literature [1] and literature [2], ([1] Xing Huo, Jieqing Tan, and MinHu. An automatic video scratch removal based on Thiele type continuedfraction, Multimedia Tools and Applications, vol.71, no.2, pp.451-467, 2014. [2] Xing Huo, Jieqing Tan. A novel non-linear method of automatic video scratch removal, Proceedings-4th International Conference on Digital Home, pp.39-45, 2012.) By using the method of unary continued fraction repair (that is, the latest method of image repair using unary continued fraction, the specific algorithm is detailed in literature [1][2], where literature [1] is a part of literature [2]. An improved method) after processing, as shown in Figure 5, this method can only basically restore the image of the scratched part.

2. After processing by using the method of bivariate continued fraction patching in literature [3], the result is shown in Figure 6, ([3] XingHuo, Jieqing Tan. Bivariate rational interpolant in image inpainting, Journal of Information and Computational Science, vol. 2, no.3, pp.487-492, 2005. Literature [3] is the latest image repair method using binary continued fraction), this method can be compared with the method of unary continued fraction repair Good scratch repair, but the overall image repair effect is not good, the image is blurry.

It can be found that, aiming at the limitations of various repairing technologies at present, how to design an efficient and simple repairing method has become an urgent technical problem to be solved under the existing hardware conditions.

Contents of the invention

The purpose of the present invention is to solve the defects of poor repair effect and low efficiency in the prior art, and provide an adaptive image repair method and system based on continuous fraction interpolation technology to solve the above problems.

In order to achieve the above object, the technical scheme of the present invention is as follows:

An adaptive image patching method based on continued fraction interpolation technology, comprising the following steps:

Initialize the image feature analysis, analyze the input scratch image, and judge whether the scratch image is a grayscale image or a color image; Execute in grayscale image;

Use unary continued fraction interpolation technology to repair the damaged point of the scratch image, obtain the position of each point to be repaired in the corresponding scratch image through the input mask image, and then target the information matrix of the scratch image Detect these points to be repaired line by line, adaptively select the surrounding known pixels as sampling points for each point to be repaired, and reconstruct the pixels of each point to be repaired by combining these sampling points with unary continued fraction rational interpolation information to get the initial patched image A;

Use the binary continued fraction interpolation technique to repair the scratched image, take the initial repaired image A as the information image, use the mask image to determine the position of each damaged point, and use the pixel information around the damaged point to use binary continuous The pixel information of each damaged point is updated by fractional interpolation, and the final repaired image B is obtained.

The repairing of the damaged point of the scratched image by using the unary continued fraction interpolation technique comprises the following steps:

Determination of the damaged point of the scratched image, inputting the mask image of the scratched image, overlapping the masked image with the scratched image, and obtaining the points to be repaired of the scratched image;

Adaptively select interpolation sampling points, read the damaged information matrix of the scratch image, adaptively select the 4 known pixels closest to the point to be repaired (x, y), and form these 4 known pixels for interpolation Sampling point;

The calculation of the pixel value of the damaged point is to calculate the pixel value of the damaged point by combining 4 known pixel points with the unary continued fraction interpolation function, which includes the following steps:

Define the unary continued fraction interpolation format as:

Among them, b _i =φ[x ₀ ,x ₁ ,…, _xi ;y](i=0,…,m) is the function f(x,y) at points x ₀ ,x ₁ ,…, _xi The deficit quotient, m is the length of the input image, which satisfies the following:

φ[x _i ; y]=f(x _i ; y), i=0,1,2,...,m,

The pixel value R ₁ (x, y) of the point to be repaired is calculated by using the information of 4 known pixel points around the point to be repaired (x, y) combined with the unary continued fraction interpolation function;

in,

b ₀ = φ[x ₀ ; y] = f(x ₀ ; y),

In the above formula, f(x ₀ ; y), f(x ₁ ; y), f(x ₂ ; y), f(x ₃ ; y) are 4 known pixel points (x ₀ , y), ( x ₁ , y), (x ₂ , y), (x ₃ , y) pixel values, R ₁ (x, y) is the calculated pixel value of the point to be repaired (x, y);

Each point to be repaired in the scratch image is detected sequentially from left to right and from top to bottom, and the step of adaptively selecting the interpolation sampling point and the calculation step of the pixel value of the damaged point are performed to obtain the initial repair image A.

The re-patching of the scratched image by using the binary continued fraction interpolation technique comprises the following steps:

The determination of binary interpolation sampling points, read the initial patched image A and use it as an information matrix, overlap the mask image with the initial patched image A, and obtain the position of the point to be patched in the initial patched image A. The 16 known pixel information around the repair point (x, y) constitute the interpolation pixel;

Search for the point to be repaired (x, y) to find 16 adjacent pixel points around it, and select in order according to the coordinate position of the point to be repaired:

Use the above 16 pixel points as binary interpolation sampling points;

The update of the pixel value of the damaged point is to calculate the pixel value of the damaged point by combining the binary interpolation sampling point with the binary continued fraction interpolation function, and update and replace the pixel value of the point in the original repaired image A, which includes the following steps:

Define the binary continued fraction interpolation format as:

Among them, i=0,1,...,m, m, n are the length and width of the input image respectively;

in, It is Newton–Thiele type mixed difference quotient;

Constructed binary vector rational functions Satisfy:

The 16 pixels around the point to be patched (x, y) are used as binary interpolation sampling points, that is Calculate the pixel value R ₂ (x, y) of the point to be repaired by combining the binary vector rational function;

R ₂ (x, y) = B ₀ (y) + 2B ₁ (y) + 2B ₂ (y) - 2B ₃ (y),

Among them, x ₀ ′=x-2, x ₁ ′=x-1, x ₂ ′=x+1, x ₃ ′=x+2, y ₀ ′=y+2, y ₁ ′=y+1, y ₂ '=y-1, y ₃ '=y-2,

in,

φ _NT [x ₀ ′,…, _xi ′; y ₀ ′,…,y _j ′], i=0,1,2,3,j=0,1,2,3, Newton–Thiele type mixture Difference quotient, x ₀ ′=x-2, x ₁ ′=x-1, x ₂ ′=x+1, x ₃ ′=x+2, y ₀ ′=y+2, y ₁ ′=y+1 , y ₂ '=y-1, y ₃ '=y-2,

In the above formula, φ _NT [ _xi ′; y _j ′] satisfies: φ _NT [ _xi ′; y _j ′]=f( _xi ′, y _j ′), where f( _xi ′, y _j ′) , is the pixel value of the corresponding known pixel point ( _xi ′, y _j ′);

Replace the pixel value R ₂ (x, y) with the pixel value R ₁ (x, y) of the point in the initial repaired image A, and the updated pixel value of the point (x, y) to be repaired is R ₂ (x, y );

From left to right and from top to bottom, each point to be repaired in the initial repair image A is determined by binary interpolation sampling points and updated by the pixel value of the damaged point, and the final repair is obtained. Image B.

The self-adaptive selection of interpolation sampling points comprises the following steps:

Targeting the damage information matrix of the scratch image for line-by-line detection;

If the point to be repaired (x, y) is found, search for the adjacent undamaged pixels around the damaged point from near to far on both sides of the same line of the point to be repaired (x, y), and search for the undamaged pixels as a sampling point;

When the number of undamaged pixels reaches 4, the search is stopped, and a total of 4 effective sampling points are obtained on both sides of the point to be repaired (x, y).

A system of an adaptive image repair method based on continued fraction interpolation technology, comprising: an initialization image input module for determining the type of an input image, a unitary continued fraction interpolation repair module for obtaining an initial repair image A, and a A binary continued fraction interpolation re-patching module for obtaining the final patched image B;

The output end of the initialized image input module is connected to the input end of the unary continued fraction interpolation patching module, and the output end of the unary continuous fraction interpolation patching module is connected to the input end of the binary continued fraction interpolation patching module.

Beneficial effect

An adaptive image repair method and system based on continued fraction interpolation technology of the present invention improves the quality and efficiency of image repair compared with the prior art, can modify any type of scratches, and is suitable for all image processing .

Through the combined use of the mask map, the patching position can be quickly determined and the patching time can be saved. At the same time, the interested part of the image block can be flexibly patched according to the user's requirements. The repaired image of the invention has good effect, rich texture details, greatly improved modification efficiency and strong practical applicability.

Description of drawings

Fig. 1 is a method sequence diagram of the present invention;

Fig. 2 is a schematic diagram of the system structure of the present invention;

Fig. 3 is the picture to be repaired in the prior art;

FIG. 4 is a mask diagram corresponding to FIG. 3;

Figure 5 is the effect diagram after repairing Figure 3 using the method of literature [1][2];

Fig. 6 is the effect diagram after repairing Fig. 3 by using the method of literature [3];

Fig. 7 is an effect diagram after using the method of the present invention to repair.

detailed description

In order to have a further understanding and understanding of the structural features of the present invention and the achieved effects, the preferred embodiments and accompanying drawings are used for a detailed description, as follows:

As shown in Fig. 1, a kind of self-adaptive image repairing method based on continuous fraction interpolation technique described in the present invention can obtain the initial patched image through unary continued fraction interpolation, and then use binary continued fraction interpolation to correct the initial The patched image is patched again to get the final patched effect. In the present invention, the combination of the two methods will not bring about the problem of a huge amount of calculation, because the calculation amount of the simple unary continued fraction interpolation repair is much smaller than that of the simple binary continued fraction interpolation repair, so the unary continuous fraction The fractional interpolation repair method is used as the main repair technology, and the binary continued fraction interpolation repair method is used as the secondary repair technology, which is only used to update the pixel value of the damaged point, thereby reducing the overall calculation amount.

It includes the following steps:

The first step is to initialize image feature analysis. The input scratch image is analyzed to determine whether the scratch image is a grayscale image or a color image. If it is a color image, the color image is executed in the manner of a grayscale image along the three color channels of R, G, and B respectively, and the second step is performed; if it is a gray image, the second step is directly performed.

The second step is to repair the damaged point of the scratched image by using the unary continued fraction interpolation technique.

Obtain the position of each point to be repaired in the corresponding scratch image through the input mask image, and then use the information matrix of the scratch image as the target to detect these points to be repaired line by line, and adapt to each point to be repaired The surrounding known pixel points are selected as sampling points, and the pixel information of each point to be repaired is reconstructed from these sampling points combined with unary continued fraction rational interpolation, and the initial repaired image A is obtained.

As shown in Figure 3 and Figure 4, the mask image is the scratch image of the image to be repaired, and the scratches in the image to be repaired can be accurately located by using the mask image. At the same time, the cooperative repair of the mask image breaks through the traditional repair only for the damaged image, and can also be applied to the repair of a certain part of the image of interest, not necessarily a scratch image, such as the removal of occluders, image Reconstruction of some details, etc. In addition, the mask map can also shield certain areas on the image so that they will not be repaired, thereby improving the repair efficiency. At the same time, for some special-shaped image repairs, the mask map can be better repaired. Use selected images, graphics or objects to block the image to be processed (all or part) to control the area or process of image processing. The specific image or object used for overlay is called a mask or stencil.

The specific steps are as follows:

(1) Determination of the damaged point of the scratch image. Input the mask image of the scratch image, overlap the mask image with the scratch image, and obtain the points to be repaired of the scratch image. The mask image is usually a binary image, and the size of the image is the size of the scratch image. The pixel value of the uninteresting part is 0, which is reflected in black, while the pixel value of the interesting or occluded or scratched position is 1. Appears in white.

(2) Adaptive selection of interpolation sampling points.

Read the damage information matrix of the scratch image, adaptively select the 4 known pixels (non-damaged effective information points) closest to the point to be repaired (x, y), and form these 4 known pixels Interpolate sample points. Generally speaking, the greater the number of interpolation sampling points, the more the advantages of the continued fraction can be reflected, but the efficiency of the algorithm will be low due to the use of more than 4 pixels for interpolation, and the interpolation effect is also similar to that of 4 pixels. Interpolation. In addition, the interpolation of 2 or 3 pixels does not reflect the advantages of continued fraction interpolation, and the interpolation effect is not good. Therefore, it is most appropriate to use 4 pixels for interpolation.

A. Taking the damage information matrix of the scratch image as the target to perform line-by-line detection;

B. If the point to be repaired (x, y) is found, search for the adjacent undamaged pixels around the damaged point from near to far on both sides of the point to be repaired (x, y), and search for the undamaged pixels The pixel is used as a sampling point;

C. When the number of undamaged pixel points reaches 4, the search is stopped, and a total of 4 effective sampling points are obtained on both sides of the point (x, y) to be repaired.

Compared with the traditional interpolation window, the self-adaptive method is more flexible in the selection of unary continuous fraction interpolation sampling points, because there may be several adjacent points to be repaired in each row or column that are unknown. The traditional interpolation window will inevitably cause the calculation of the pixel value of the damaged point to be incorrect or the deviation is too large, and the adaptive method is to use the search method of the left and right nearest neighbors in the same line to find the available sampling points according to the actual position of the point to be repaired. The sampling point is added as an interpolation point, and once the number of searched sampling points reaches the requirement, the search is stopped, and these sampling points are used for interpolation to calculate the pixel value of the repair point.

The invention combines the self-adaptive method and the continuous fraction theory and applies it to image processing, which is the first in the field of image processing. Combining the self-adaptive method with the continued fraction theory is used in image repair, which is mainly reflected in the selection of sampling points for unary continued fraction interpolation using the self-adaptive method. The selection of traditional one-element continuous fraction interpolation sampling points is arbitrary, and usually several known pixels near the damaged point are selected as sampling points (such as the method in literature [1][2]) or along the coordinates of the damaged point In the forward direction of , several known pixel points are sequentially selected as sampling points. Due to this arbitrariness, the repair algorithm is unstable, and even the pixel value of the damaged point obtained by each interpolation is different. When the self-adaptive method is used to select the sampling point, it takes the damaged point as the center and selects the sampling point in a symmetrical way from near to far. Similar to pointer processing, first find the nearest point to the damaged point. Two pixels on the left and right (here, the order of the two pixels on the left and right is not distinguished), judge whether they are known pixels, if both are known pixels, then use these two pixels as sampling points, if One of them is a known pixel point, then add this pixel point as a sampling point, if neither of them is a known pixel point, then the pointer moves to the next closest point to the damaged point (the second closest point is the middle distance from the damaged point A pixel point on the left or right of the position of a pixel point), the same method is used to judge whether the pixel point is a known pixel point, and to process it. By analogy, the same operation, when the number of searched sampling points reaches the requirement, the search is stopped, and these sampling points are used for interpolation to calculate the pixel value of the patched point.

(3) Calculation of the pixel value of the damaged point. The pixel value of the damaged point is calculated by combining 4 known pixel points with a continuous fraction interpolation function, which includes the following steps:

A. Define the unary continued fraction interpolation format as:

Among them, b _i =φ[x ₀ ,x ₁ ,…, _xi ;y](i=0,…,m) is the function f(x,y) at points x ₀ ,x ₁ ,…, _xi The deficit quotient, m is the length of the input image, which satisfies the following:

φ[x _i ; y]=f(x _i ; y), i=0,1,2,...,m,

B. Calculate the pixel value R ₁ (x, y) of the point to be repaired by using the information of 4 known pixel points around the point to be repaired (x, y) in combination with the unary continued fraction interpolation function;

in,

b ₀ = φ[x ₀ ; y] = f(x ₀ ; y),

In the above formula, f(x ₀ ; y), f(x ₁ ; y), f(x ₂ ; y), f(x ₃ ; y) are 4 known pixel points (x ₀ , y), ( x ₁ , y), (x ₂ , y), (x ₃ , y) pixel values, R ₁ (x, y) is the calculated pixel value of the point to be repaired (x, y);

(4) Detect each point to be repaired in the scratch image according to the direction sequence from left to right and from top to bottom, all carry out the step of adaptively selecting the interpolation sampling point and the calculation step of the pixel value of the damaged point, when all the points to be repaired After all points are calculated, the initial inpainted image A is obtained.

The third step is to use binary continued fraction interpolation technology to repair the scratched image. The initial repair image A is used as the information image, and the position of each damaged point is determined by the mask map. Here, the mask image is used again to confirm the location of the damaged point, because the damaged point cannot be seen in the initial repair image A, so the mask image must be used to determine the location information of the damaged point. The pixel information of each damaged point is updated by binary continued fraction interpolation from the pixel information around the damaged point, and the final repaired image B is obtained.

The binary continued fraction interpolation technique for repairing the scratched image is the same as the existing interpolation method in terms of the interpolation function and the selection of the interpolation window. The difference is that the objects of the interpolation function and the interpolation window are different. The object of action of the prior art is the original damaged image, while the object of the present invention is the initial repair image obtained in the previous step. The reason why the initial repair map is used is to improve the efficiency of repair. Since the second step has been repaired by the unary continued fraction, some damaged points may have obtained the correct pixel values. If the original damaged image is repaired by the binary continued fraction again, repeated operations are bound to be carried out. It is unnecessary, and it will also reduce the efficiency of the overall algorithm. Therefore, in this step, when using the binary continued fraction interpolation technique to repair the scratched image, we only regard the point to be repaired as the damaged point, while the other damaged points in the original damaged image are not regarded as the damaged point, but These points are regarded as known pixel points, and the pixel values taken by them are corresponding to the pixel values of these points in the initial repair image, and then the pixel values of the points to be repaired are calculated by using the existing interpolation function and interpolation window. The reason why this step is processed in this way is to consider the correlation between the image pixels, the closer the pixels to the point to be repaired are, the greater the similarity between them is, therefore, all other pixels around the point to be repaired are taken as already It is bound to get closer to the original pixel value to process the known pixels. From this step, it can also be found that since all other pixels except the point to be repaired are regarded as known pixels, it becomes difficult to determine the next point to be repaired. At this time, it is necessary to cooperate with the mask map Using , the position of each damaged point is determined by the mask map.

It includes the following steps:

(1) Determination of binary interpolation sampling points. Read the initial patched image A and use it as an information matrix, overlap the mask image with the initial patched image A, and obtain the position of the point to be patched in the initial patched image A, by surrounding the point (x, y) to be patched The 16 known pixel information constitute interpolation pixel points;

Search for the repair point (x, y) to find 16 adjacent pixel points around it, and select in order according to the coordinate position of the point to be repaired:

The above 16 pixel points are used as sampling points for binary interpolation.

Here, the damage information is updated on the basis of the initial repair image A, so instead of using a 3*3 interpolation window (that is, 9 pixels), a 4*4 interpolation window (that is, 16 pixels) is used to processing, because the 3*3 interpolation window and the 4*4 interpolation window have similar effects here, and at the same time, the image blocks are more efficient when divided into 3*3 image blocks than into 4*4 image blocks. more, and the more image blocks, the more times the algorithm will be executed. Therefore, from the perspective of efficiency, it is more appropriate to use 16 pixels as sampling points. For more than 16 pixels, the speed of the continued fraction operation is slow, and the efficiency of the whole algorithm is low, so it is not suitable for use.

(2) Update the pixel value of the damaged point. Calculate the pixel value of the damaged point by combining the binary interpolation sampling point with the binary continued fraction interpolation function, and update and replace the pixel value of the point in the original repair image A, which includes the following steps:

A. Define the binary continued fraction interpolation format as:

Among them, i=0,1,...,m, m, n are the length and width of the input image respectively;

in, It is Newton–Thiele type mixed difference quotient;

Constructed binary vector rational functions Satisfy:

B. Use 16 pixels around the point to be repaired (x, y) as binary interpolation sampling points, that is Calculate the pixel value R ₂ (x, y) of the point to be repaired by combining the binary vector rational function;

R ₂ (x, y) = B ₀ (y) + 2B ₁ (y) + 2B ₂ (y) - 2B ₃ (y),

Among them, x ₀ ′=x-2, x ₁ ′=x-1, x ₂ ′=x+1, x ₃ ′=x+2, y ₀ ′=y+2, y ₁ ′=y+1, y ₂ '=y-1, y ₃ '=y-2,

in,

φ _NT [x ₀ ′,…, _xi ′; y ₀ ′,…,y _j ′], i=0,1,2,3,j=0,1,2,3, Newton–Thiele type mixture bad business,

x ₀ ′=x-2, x ₁ ′=x-1, x ₂ ′=x+1, x ₃ ′=x+2, y ₀ ′=y+2, y ₁ ′=y+1, y ₂ '=y-1,y ₃ '=y-2,

In the above formula, φ _NT [ _xi ′; y _j ′] satisfies: φ _NT [ _xi ′; y _j ′]=f( _xi ′, y _j ′), where f( _xi ′, y _j ′) , is the pixel value of the corresponding known pixel point ( _xi ′, y _j ′);

C. Replace the pixel value R ₂ (x, y) with the pixel value R ₁ (x, y) of the point in the initial repaired image A, and update the pixel value of the point (x, y) to be repaired with R ₂ (x ,y).

(3) According to the order from left to right and from top to bottom, each point to be repaired in the initial repaired image A is subjected to the determination step of binary interpolation sampling point and the update step of the pixel value of the damaged point, and the final result is obtained The inpainted image of B.

As shown in Figure 2, a system of an adaptive image repair method based on continued fraction interpolation technology is also provided here, which includes: an initialization image input module for determining the type of input image, for obtaining an initial repair image The one-element continued fraction interpolation repairing module of A and the binary continued fraction interpolation re-patching module for obtaining the final repaired image B.

The output end of the initialized image input module is connected to the input end of the unary continued fraction interpolation patching module, and the output end of the unary continuous fraction interpolation patching module is connected to the input end of the binary continued fraction interpolation patching module.

Figure 3 shows the picture to be repaired, and Figure 4 shows the mask image used for repairing. After using the unary continued fraction repair method (see literature [1][2] for details of the algorithm), as shown in Figure 5, the damaged part of the picture has been partially modified, but there are still some damaged points that have not been repaired. After using the binary continued fraction patching method (see the literature [3] for the specific algorithm), as shown in Figure 6, the overall visual effect and quality of the picture have been improved. As shown in Figure 7, after the method of the present invention is used for repairing, the details of the obviously scratched part are restored better, and the overall visual effect is better, which is greater than the method of literature [1][2][3] optimization and enhancement.

In order to reflect that the efficiency of the present invention is higher than that of the other three methods, the comparison of the running time of these four methods is shown in Table 1.

Table 1 The running time comparison table of the inventive method and the document [1] [2] [3] method

In order to show that the effect of the present invention is better, compared with the other three methods, there is a better promotion, and the theoretical parameter for evaluating image quality, that is, the peak signal-to-noise ratio will be used as an evaluation index, which is shown in Table 2 Comparison of peak signal-to-noise ratios of images inpainted by these four methods.

Table 2 uses the comparison table of the peak signal-to-noise ratio of the inventive method and the literature [1] [2] [3] method

Comparing from an objective point of view, it can be found that according to the formula Here m×n is the size of the matrix, max=255, f(i,j) is the original image, For the repaired image, use this formula to calculate the value of the peak signal-to-noise ratio PSNR. The larger the peak signal-to-noise ratio, the closer the patched image is to the original image, that is, the better the visual effect of the patched image and the higher the resolution.

As shown in Table 2, the results of the peak signal-to-noise ratio after the above method is used to repair the picture to be repaired, it can be found that the peak signal-to-noise ratio after the repair of the present invention is obviously higher than the result of the prior art method, and the image resolution and quality higher.

As shown in table 1, the picture to be repaired uses the result of the running time of above method patching, runs the prior art method and the method of the present invention on the computer of same operating environment, and records the running time of algorithm, can find that the present invention The efficiency is higher than that of the binary continued fraction repair method (that is, the method of literature [3]). Since the unary continued fraction is processed in the one-dimensional coordinate direction, the binary continued fraction processed simultaneously with the two-dimensional coordinate direction Continuing fractions are more efficient. Therefore, from an overall perspective, compared with the prior art, the present invention not only has better computing efficiency, but also has higher quality of repaired pictures.

The basic principles, main features and advantages of the present invention have been shown and described above. Those skilled in the art should understand that the present invention is not limited by the above-mentioned embodiments. What are described in the above-mentioned embodiments and the description are only the principles of the present invention. Variations and improvements, which fall within the scope of the claimed invention. The scope of protection required by the present invention is defined by the appended claims and their equivalents.

Claims (5)

1. an adaptive image patching method based on continued fraction interpolation technology, is characterized in that, comprises the following steps: 11) Initialize the image feature analysis, analyze the input scratch image, and judge whether the scratch image is a grayscale image or a color image; if it is a color image, then the color image is followed by three color channels of R, G, and B Execute according to the grayscale image respectively; 12) Use unary continued fraction interpolation technology to repair the damaged point of the scratch image, obtain the position of each point to be repaired in the corresponding scratch image through the input mask map, and then use the information matrix of the scratch image Detect these points to be repaired line by line for the target, adaptively select surrounding known pixel points as sampling points for each point to be repaired, and reconstruct each point to be repaired by combining these sampling points with unary continued fraction rational interpolation The pixel information of , get the initial repair image A; 13) Use the binary continued fraction interpolation technique to repair the scratched image, use the initial repaired image A as the information image, determine the position of each damaged point by the mask image, and use binary information from the pixel information around the damaged point The pixel information of each damaged point is updated by element continued fraction interpolation, and the final repaired image B is obtained. 2. a kind of adaptive image repairing method based on continued fraction interpolation technique according to claim 1, is characterized in that, described utilizes unary continued fraction interpolation technique to carry out the mending of scratched image damage point and comprises the following steps: 21) Determination of the damaged point of the scratched image, inputting the mask image of the scratched image, overlapping the masked image with the scratched image, and obtaining the points to be repaired of the scratched image; 22) Adaptively select interpolation sampling points, read the damage information matrix of the scratch image, adaptively select the 4 known pixels nearest to the point to be repaired (x, y), and convert these 4 known pixels Constitute interpolation sampling points; 23) Calculation of the pixel value of the damaged point, the pixel value of the damaged point is calculated by 4 known pixel points in conjunction with the unary continued fraction interpolation function, which includes the following steps: 231) define the unary continued fraction interpolation format as: ${\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; b</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; +</span>\frac{\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}}{{\mathrm{<span\; class="notranslate">\; b</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}}<span\; class="notranslate">\; +</span>\frac{\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}}{{\mathrm{<span\; class="notranslate">\; b</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; ...</span>}<span\; class="notranslate">\; +</span>\frac{\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}}{{\mathrm{<span\; class="notranslate">\; b</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}}}<span\; class="notranslate">\; ,</span>$ Among them, b _i =φ[x ₀ ,x ₁ ,…, _xi ;y](i=0,…,m) is the function f(x,y) at points x ₀ ,x ₁ ,…, _xi The deficit quotient, m is the length of the input image, which satisfies the following: φ[x _i ; y]=f(x _i ; y), i=0,1,2,...,m, $\mathrm{<span\; class="notranslate">\; \&phi;</span>}<span\; class="notranslate">\; \&lsqb;</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; p</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; q</span>}}<span\; class="notranslate">\; ;</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; \&rsqb;</span><span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; q</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; p</span>}}}{\mathrm{<span\; class="notranslate">\; \&phi;</span>}<span\; class="notranslate">\; \&lsqb;</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; q</span>}}<span\; class="notranslate">\; ;</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; \&rsqb;</span><span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; \&phi;</span>}<span\; class="notranslate">\; \&lsqb;</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; p</span>}}<span\; class="notranslate">\; ;</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; \&rsqb;</span>}<span\; class="notranslate">\; ,</span>$ $\mathrm{<span\; class="notranslate">\; \&phi;</span>}<span\; class="notranslate">\; \&lsqb;</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; ...</span>}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; l</span>}}<span\; class="notranslate">\; ;</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; \&rsqb;</span><span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; l</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}}{\mathrm{<span\; class="notranslate">\; \&phi;</span>}<span\; class="notranslate">\; \&lsqb;</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; ...</span>}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; l</span>}}<span\; class="notranslate">\; ;</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; \&rsqb;</span><span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; \&phi;</span>}<span\; class="notranslate">\; \&lsqb;</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; ...</span>}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}<span\; class="notranslate">\; ;</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; \&rsqb;</span>}<span\; class="notranslate">\; ;</span>$ 232) Calculate the pixel value R ₁ (x, y) of the point to be repaired by using the information of 4 known pixel points around the point to be repaired (x, y) combined with the unary continued fraction interpolation function; ${\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; T</span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; b</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; +</span>\frac{\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}}{{\mathrm{<span\; class="notranslate">\; b</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}}<span\; class="notranslate">\; +</span>\frac{\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}}{{\mathrm{<span\; class="notranslate">\; b</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}}<span\; class="notranslate">\; +</span>\frac{\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}}{{\mathrm{<span\; class="notranslate">\; b</span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}}<span\; class="notranslate">\; ,</span>$ in, b ₀ = φ[x ₀ ; y] = f(x ₀ ; y), ${\mathrm{<span\; class="notranslate">\; b</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; \&phi;</span>}<span\; class="notranslate">\; \&lsqb;</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; ;</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; \&rsqb;</span><span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}}{\mathrm{<span\; class="notranslate">\; \&phi;</span>}<span\; class="notranslate">\; \&lsqb;</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; ;</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; \&rsqb;</span><span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; \&phi;</span>}<span\; class="notranslate">\; \&lsqb;</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; ;</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; \&rsqb;</span>}<span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}}{\mathrm{<span\; class="notranslate">\; f</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; ;</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; f</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; ;</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; ,</span>$ ${\mathrm{<span\; class="notranslate">\; b</span>}}_{\mathrm{<span\; class="notranslate">\; 12</span>}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; \&phi;</span>}<span\; class="notranslate">\; \&lsqb;</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; ;</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; \&rsqb;</span><span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}}{\mathrm{<span\; class="notranslate">\; \&phi;</span>}<span\; class="notranslate">\; \&lsqb;</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; ;</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; \&rsqb;</span><span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; \&phi;</span>}<span\; class="notranslate">\; \&lsqb;</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; ;</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; \&rsqb;</span>}<span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}}{\mathrm{<span\; class="notranslate">\; f</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; ;</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; f</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; ;</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; ,</span>$ ${\mathrm{<span\; class="notranslate">\; b</span>}}_{\mathrm{<span\; class="notranslate">\; 13</span>}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; \&phi;</span>}<span\; class="notranslate">\; \&lsqb;</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}<span\; class="notranslate">\; ;</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; \&rsqb;</span><span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}}{\mathrm{<span\; class="notranslate">\; \&phi;</span>}<span\; class="notranslate">\; \&lsqb;</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}<span\; class="notranslate">\; ;</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; \&rsqb;</span><span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; \&phi;</span>}<span\; class="notranslate">\; \&lsqb;</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; ;</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; \&rsqb;</span>}<span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}}{\mathrm{<span\; class="notranslate">\; f</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}<span\; class="notranslate">\; ;</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; f</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; ;</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; ,</span>$ ${\mathrm{<span\; class="notranslate">\; b</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; \&phi;</span>}<span\; class="notranslate">\; \&lsqb;</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; ;</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; \&rsqb;</span><span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}}{\mathrm{<span\; class="notranslate">\; \&phi;</span>}<span\; class="notranslate">\; \&lsqb;</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; ;</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; \&rsqb;</span><span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; \&phi;</span>}<span\; class="notranslate">\; \&lsqb;</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; ;</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; \&rsqb;</span>}<span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}}{{\mathrm{<span\; class="notranslate">\; b</span>}}_{\mathrm{<span\; class="notranslate">\; 12</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; b</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}}<span\; class="notranslate">\; ,</span>$ ${\mathrm{<span\; class="notranslate">\; b</span>}}_{\mathrm{<span\; class="notranslate">\; twenty\; two</span>}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; \&phi;</span>}<span\; class="notranslate">\; \&lsqb;</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}<span\; class="notranslate">\; ;</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; \&rsqb;</span><span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}}{\mathrm{<span\; class="notranslate">\; \&phi;</span>}<span\; class="notranslate">\; \&lsqb;</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}<span\; class="notranslate">\; ;</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; \&rsqb;</span><span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; \&phi;</span>}<span\; class="notranslate">\; \&lsqb;</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; ;</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; \&rsqb;</span>}<span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}}{{\mathrm{<span\; class="notranslate">\; b</span>}}_{\mathrm{<span\; class="notranslate">\; 13</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; b</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}}<span\; class="notranslate">\; ,</span>$ ${\mathrm{<span\; class="notranslate">\; b</span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; \&phi;</span>}<span\; class="notranslate">\; \&lsqb;</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}<span\; class="notranslate">\; ;</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; \&rsqb;</span><span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}}{\mathrm{<span\; class="notranslate">\; \&phi;</span>}<span\; class="notranslate">\; \&lsqb;</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}<span\; class="notranslate">\; ;</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; \&rsqb;</span><span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; \&phi;</span>}<span\; class="notranslate">\; \&lsqb;</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; ;</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; \&rsqb;</span>}<span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}}{{\mathrm{<span\; class="notranslate">\; b</span>}}_{\mathrm{<span\; class="notranslate">\; twenty\; two</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; b</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}}<span\; class="notranslate">\; ;</span>$ In the above formula, f(x ₀ ; y), f(x ₁ ; y), f(x ₂ ; y), f(x ₃ ; y) are 4 known pixel points (x ₀ , y), ( x ₁ , y), (x ₂ , y), (x ₃ , y) pixel values, R ₁ (x, y) is the calculated pixel value of the point to be repaired (x, y); 24) According to the order from left to right and from top to bottom, each point to be repaired in the scratch image is sequentially detected, and the step of adaptively selecting the interpolation sampling point and the calculation step of the pixel value of the damaged point are performed to obtain the initial repair image A . 3. A kind of adaptive image repairing method based on continued fraction interpolation technique according to claim 1, is characterized in that, described utilizing binary continued fraction interpolation technique to carry out the repairing of scratched image again comprises the following steps: 31) Determination of binary interpolation sampling points, read the initial patched image A and use it as an information matrix, overlap the mask image with the initial patched image A, and obtain the position of the point to be patched in the initial patched image A, Interpolation pixel points are composed of 16 known pixel information around the point to be repaired (x, y); Search for the point to be repaired (x, y) to find 16 adjacent pixel points around it, and select in order according to the coordinate position of the point to be repaired: (x-2,y+2)(x-2,y+1)(x-2,y-1)(x-2,y-2) (x-1,y+2)(x-1,y+1)(x-1,y-1)(x-1,y-2) (x+1,y+2)(x+1,y+1)(x+1,y-1)(x+1,y-2), (x+2,y+2)(x+2,y+1)(x+2,y-1)(x+2,y-2) Use the above 16 pixel points as binary interpolation sampling points; 32) The update of the pixel value of the damaged point, the pixel value of the damaged point is calculated by the binary interpolation sampling point combined with the binary continued fraction interpolation function, and the pixel value of the point in the original repaired image A is replaced by updating, which includes the following step: 321) defines the binary continued fraction interpolation format as: ${\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; no</span>}}^{\mathrm{<span\; class="notranslate">\; N</span>}\mathrm{<span\; class="notranslate">\; T</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; A</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; )</span>{\mathrm{<span\; class="notranslate">\; A</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; ...</span>}<span\; class="notranslate">\; +</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; ...</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; )</span>{\mathrm{<span\; class="notranslate">\; A</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ,</span>$ Among them, i=0,1,...,m, m, n are the length and width of the input image respectively; in, It is Newton–Thiele type mixed difference quotient; ${\mathrm{<span\; class="notranslate">\; \&phi;</span>}}_{\mathrm{<span\; class="notranslate">\; N</span>}\mathrm{<span\; class="notranslate">\; T</span>}}<span\; class="notranslate">\; \&lsqb;</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; ;</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}<span\; class="notranslate">\; \&rsqb;</span><span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; f</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ,</span><span\; class="notranslate">\; \&ForAll;</span><span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; \&Element;</span>{\mathrm{<span\; class="notranslate">\; \&Pi;</span>}}_{\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}}^{\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; no</span>}}<span\; class="notranslate">\; ,</span>$ ${\mathrm{<span\; class="notranslate">\; \&phi;</span>}}_{\mathrm{<span\; class="notranslate">\; N</span>}\mathrm{<span\; class="notranslate">\; T</span>}}<span\; class="notranslate">\; \&lsqb;</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}<span\; class="notranslate">\; ;</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}<span\; class="notranslate">\; \&rsqb;</span><span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; \&phi;</span>}}_{\mathrm{<span\; class="notranslate">\; N</span>}\mathrm{<span\; class="notranslate">\; T</span>}}<span\; class="notranslate">\; \&lsqb;</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}<span\; class="notranslate">\; ;</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}<span\; class="notranslate">\; \&rsqb;</span><span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; \&phi;</span>}}_{\mathrm{<span\; class="notranslate">\; N</span>}\mathrm{<span\; class="notranslate">\; T</span>}}<span\; class="notranslate">\; \&lsqb;</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; ;</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}<span\; class="notranslate">\; \&rsqb;</span>}{{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}}<span\; class="notranslate">\; ,</span>$ ${\mathrm{<span\; class="notranslate">\; \&phi;</span>}}_{\mathrm{<span\; class="notranslate">\; N</span>}\mathrm{<span\; class="notranslate">\; T</span>}}<span\; class="notranslate">\; \&lsqb;</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; p</span>}}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; ...</span>}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; q</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}<span\; class="notranslate">\; ;</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}<span\; class="notranslate">\; \&rsqb;</span><span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; \&phi;</span>}}_{\mathrm{<span\; class="notranslate">\; N</span>}\mathrm{<span\; class="notranslate">\; T</span>}}<span\; class="notranslate">\; \&lsqb;</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; p</span>}}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; ...</span>}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; q</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}<span\; class="notranslate">\; ;</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}<span\; class="notranslate">\; \&rsqb;</span><span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; \&phi;</span>}}_{\mathrm{<span\; class="notranslate">\; N</span>}\mathrm{<span\; class="notranslate">\; T</span>}}<span\; class="notranslate">\; \&lsqb;</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; p</span>}}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; ...</span>}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; q</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; ;</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}<span\; class="notranslate">\; \&rsqb;</span>}{{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}}<span\; class="notranslate">\; ,</span>$ ${\mathrm{<span\; class="notranslate">\; \&phi;</span>}}_{\mathrm{<span\; class="notranslate">\; N</span>}\mathrm{<span\; class="notranslate">\; T</span>}}<span\; class="notranslate">\; \&lsqb;</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; p</span>}}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; ...</span>}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; q</span>}}<span\; class="notranslate">\; ;</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; l</span>}}<span\; class="notranslate">\; \&rsqb;</span><span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; l</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}}{{\mathrm{<span\; class="notranslate">\; \&phi;</span>}}_{\mathrm{<span\; class="notranslate">\; N</span>}\mathrm{<span\; class="notranslate">\; T</span>}}<span\; class="notranslate">\; \&lsqb;</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; p</span>}}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; ...</span>}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; q</span>}}<span\; class="notranslate">\; ;</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; l</span>}}<span\; class="notranslate">\; \&rsqb;</span><span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; \&phi;</span>}}_{\mathrm{<span\; class="notranslate">\; N</span>}\mathrm{<span\; class="notranslate">\; T</span>}}<span\; class="notranslate">\; \&lsqb;</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; p</span>}}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; ...</span>}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; q</span>}}<span\; class="notranslate">\; ;</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}<span\; class="notranslate">\; \&rsqb;</span>}<span\; class="notranslate">\; ,</span>$ ${\mathrm{<span\; class="notranslate">\; \&phi;</span>}}_{\mathrm{<span\; class="notranslate">\; N</span>}\mathrm{<span\; class="notranslate">\; T</span>}}<span\; class="notranslate">\; \&lsqb;</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; p</span>}}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; ...</span>}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; q</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; r</span>}}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; ...</span>}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; the\; s</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; l</span>}}<span\; class="notranslate">\; \&rsqb;</span><span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; l</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}}{{\mathrm{<span\; class="notranslate">\; \&phi;</span>}}_{\mathrm{<span\; class="notranslate">\; N</span>}\mathrm{<span\; class="notranslate">\; T</span>}}<span\; class="notranslate">\; \&lsqb;</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; p</span>}}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; ...</span>}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; q</span>}}<span\; class="notranslate">\; ;</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; r</span>}}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; ...</span>}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; the\; s</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; l</span>}}<span\; class="notranslate">\; \&rsqb;</span><span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; \&phi;</span>}}_{\mathrm{<span\; class="notranslate">\; N</span>}\mathrm{<span\; class="notranslate">\; T</span>}}<span\; class="notranslate">\; \&lsqb;</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; p</span>}}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; ...</span>}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; q</span>}}<span\; class="notranslate">\; ;</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; r</span>}}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; ...</span>}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; the\; s</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}<span\; class="notranslate">\; \&rsqb;</span>}<span\; class="notranslate">\; ;</span>$ Constructed binary vector rational functions Satisfy: ${\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; no</span>}}^{\mathrm{<span\; class="notranslate">\; N</span>}\mathrm{<span\; class="notranslate">\; T</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; f</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 0</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; ...</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; ;</span>\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 0</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; ...</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; no</span>}<span\; class="notranslate">\; ;</span>$ 322) Use 16 pixels around the point to be repaired (x, y) as binary interpolation sampling points, namely Calculate the pixel value R ₂ (x, y) of the point to be repaired by combining the binary vector rational function; R ₂ (x, y) = B ₀ (y) + 2B ₁ (y) + 2B ₂ (y) - 2B ₃ (y), Among them, x′ ₀ =x-2, x′ ₁ =x-1, x′ ₂ =x+1, x′ ₃ =x+2, y′ ₀ =y+2, y′ ₁ =y+1, y' ₂ =y-1, y' ₃ =y-2, in, φ _NT [x′ ₀ ,…,x′ _i ; y′ ₀ ,…,y′ _j ], i=0,1,2,3, j=0,1,2,3, Newton–Thiele type mixture bad business, x' ₀ =x-2,x' ₁ =x-1,x' ₂ =x+1,x' ₃ =x+2,y' ₀ =y+2,y' ₁ =y+1,y' ₂ = y-1, y' ₃ = y-2, ${\mathrm{<span\; class="notranslate">\; \&phi;</span>}}_{\mathrm{<span\; class="notranslate">\; N</span>}\mathrm{<span\; class="notranslate">\; T</span>}}<span\; class="notranslate">\; \&lsqb;</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; ;</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; \&rsqb;</span><span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; \&phi;</span>}}_{\mathrm{<span\; class="notranslate">\; N</span>}\mathrm{<span\; class="notranslate">\; T</span>}}<span\; class="notranslate">\; \&lsqb;</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; ;</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; \&rsqb;</span><span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; \&phi;</span>}}_{\mathrm{<span\; class="notranslate">\; N</span>}\mathrm{<span\; class="notranslate">\; T</span>}}<span\; class="notranslate">\; \&lsqb;</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; ;</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; \&rsqb;</span>}{{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}^{<span\; class="notranslate">\; \&prime;</span>}}<span\; class="notranslate">\; ,</span>$ ${\mathrm{<span\; class="notranslate">\; \&phi;</span>}}_{\mathrm{<span\; class="notranslate">\; N</span>}\mathrm{<span\; class="notranslate">\; T</span>}}<span\; class="notranslate">\; \&lsqb;</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; p</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; ...</span>}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; q</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; ;</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; \&rsqb;</span><span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; \&phi;</span>}}_{\mathrm{<span\; class="notranslate">\; N</span>}\mathrm{<span\; class="notranslate">\; T</span>}}<span\; class="notranslate">\; \&lsqb;</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; p</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; ...</span>}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; q</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; ;</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; \&rsqb;</span><span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; \&phi;</span>}}_{\mathrm{<span\; class="notranslate">\; N</span>}\mathrm{<span\; class="notranslate">\; T</span>}}<span\; class="notranslate">\; \&lsqb;</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; p</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; ...</span>}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; q</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; ;</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; \&rsqb;</span>}{{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}^{<span\; class="notranslate">\; \&prime;</span>}}<span\; class="notranslate">\; ,</span>$ ${\mathrm{<span\; class="notranslate">\; \&phi;</span>}}_{\mathrm{<span\; class="notranslate">\; N</span>}\mathrm{<span\; class="notranslate">\; T</span>}}<span\; class="notranslate">\; \&lsqb;</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; p</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; ...</span>}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; q</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; ;</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; l</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; \&rsqb;</span><span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; l</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}^{<span\; class="notranslate">\; \&prime;</span>}}{{\mathrm{<span\; class="notranslate">\; \&phi;</span>}}_{\mathrm{<span\; class="notranslate">\; N</span>}\mathrm{<span\; class="notranslate">\; T</span>}}<span\; class="notranslate">\; \&lsqb;</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; p</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; ...</span>}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; q</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; ;</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; l</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; \&rsqb;</span><span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; \&phi;</span>}}_{\mathrm{<span\; class="notranslate">\; N</span>}\mathrm{<span\; class="notranslate">\; T</span>}}<span\; class="notranslate">\; \&lsqb;</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; p</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; ...</span>}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; q</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; ;</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; \&rsqb;</span>}<span\; class="notranslate">\; ,</span>$ ${\mathrm{<span\; class="notranslate">\; \&phi;</span>}}_{\mathrm{<span\; class="notranslate">\; N</span>}\mathrm{<span\; class="notranslate">\; T</span>}}<span\; class="notranslate">\; \&lsqb;</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; p</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; ...</span>}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; q</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; r</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; ...</span>}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; the\; s</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; l</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; \&rsqb;</span><span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; l</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}^{<span\; class="notranslate">\; \&prime;</span>}}{{\mathrm{<span\; class="notranslate">\; \&phi;</span>}}_{\mathrm{<span\; class="notranslate">\; N</span>}\mathrm{<span\; class="notranslate">\; T</span>}}<span\; class="notranslate">\; \&lsqb;</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; p</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; ...</span>}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; q</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; r</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; ...</span>}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; the\; s</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; l</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; \&rsqb;</span><span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; \&phi;</span>}}_{\mathrm{<span\; class="notranslate">\; N</span>}\mathrm{<span\; class="notranslate">\; T</span>}}<span\; class="notranslate">\; \&lsqb;</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; p</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; ...</span>}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; q</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; r</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; ...</span>}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; the\; s</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}}^{<span\; class="notranslate">\; \&prime;</span>}<span\; class="notranslate">\; \&rsqb;</span>}<span\; class="notranslate">\; ,</span>$ In the above formula, φ _NT [x′ _i ; y′ _j ] satisfies: φ _NT [x′ _i ; y′ _j ]=f(x′ _i ,y′ _j ), where f(x′ _i ,y′ _j ) , is the pixel value of the corresponding known pixel point (x′ _i , y′ _j ); 323) Replace the pixel value R ₂ (x, y) with the pixel value R ₁ (x, y) of the point in the initial patched image A, and update the pixel value of the point (x, y) to be patched with R ₂ (x ,y); 33) From left to right and from top to bottom, each point to be repaired in the initial repaired image A is subjected to the determination step of the binary interpolation sampling point and the update step of the pixel value of the damaged point to obtain the final The inpainted image of B. 4. a kind of adaptive image repair method based on continued fraction interpolation technique according to claim 2, is characterized in that, described adaptive selection interpolation sampling point comprises the following steps: 41) Taking the damage information matrix of the scratch image as the target to perform line-by-line detection; 42) If the point to be repaired (x, y) is found, search for the adjacent undamaged pixel points around the damaged point from near to far on both sides of the same line of the point to be repaired (x, y), and search for the undamaged pixels The pixel is used as a sampling point; 43) When the number of undamaged pixel points reaches 4, stop searching, and obtain 4 effective sampling points on both sides of the same row of the point to be repaired (x, y). 5. The system of a kind of adaptive image patching method based on continuous fraction interpolation technique according to claim 1, it is characterized in that comprising: an initialization image input module for determining the type of input image, for obtaining initial A unitary continued fraction interpolation patching module for patching image A and a binary continued fraction interpolation patching module for obtaining the final patched image B; The output end of the initialized image input module is connected to the input end of the unary continued fraction interpolation repair module, and the output end of the unary continued fraction interpolation repair module is connected to the input end of the binary continued fraction interpolation repair module.