CN113393402A - Method for restoring image background based on tensor ring decomposition - Google Patents

Method for restoring image background based on tensor ring decomposition Download PDF

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CN113393402A
CN113393402A CN202110709871.0A CN202110709871A CN113393402A CN 113393402 A CN113393402 A CN 113393402A CN 202110709871 A CN202110709871 A CN 202110709871A CN 113393402 A CN113393402 A CN 113393402A
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周郭许
余芷
张桂东
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Guangdong University of Technology
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Abstract

The invention discloses a method for restoring an image background based on tensor ring decomposition, which comprises the following steps: converting an original image to be processed into a gray-scale image, extracting the edge of the gray-scale image through an edge extraction algorithm, and then performing dot multiplication on the image with the extracted edge and the original image after the image is folded into a third-order tensor to obtain a color edge image; setting a polygonal area where a target object is located in a mouse selection mode; taking the polygonal area in the obtained image as an ROI, setting pixels in the ROI to be zero, and keeping the pixel values of the rest areas unchanged to obtain a graph with the target object removed; copying the most similar part of color edge information outside the ROI to the ROI of the image; establishing a mathematical model, and introducing an auxiliary variable tensor to solve the mathematical model to obtain a recovered image; the method can remove the loss of irregular holes in images such as electric wires in landscape and sky photos, other tourists in passerby photos and the like by using a tensor decomposition-based method, and the recovered images are more vivid.

Description

Method for restoring image background based on tensor ring decomposition
Technical Field
The invention relates to the field of digital image processing, in particular to a method for restoring an image background based on tensor ring decomposition.
Background
With the rapid development of digital image processing technology in China, tensor completion algorithm has gained wide attention and achievement in the fields of data mining, computer vision, signal processing and further neuroscience and the like. Tensor completion is the recovery of pixels that are not observed (i.e., lost) using observable pixels. Due to the multidimensional nature of tensors in describing complex datasets, tensor completion algorithms are very effective in processing randomly missing images. However, when irregular holes are lost, for example, wires in landscape and sky photographs and other tourists in passerby photographs are removed, the effect of recovery by using the original tensor completion algorithm is often unsatisfactory. Therefore, there is a need for improvement on the prior art to fill in an image from which a target object is removed.
Disclosure of Invention
The invention aims to provide a method for restoring an image background based on tensor ring decomposition, which aims to remove a target object in an image and restore and fill a background area based on tensor ring decomposition.
In order to realize the task, the invention adopts the following technical scheme:
a method of restoring image context based on tensor ring decomposition, comprising:
converting an original image to be processed into a gray-scale image, extracting the edge of the gray-scale image through an edge extraction algorithm, and then performing dot multiplication on the image with the extracted edge and the original image after the image is folded into a third-order tensor to obtain a color edge image;
setting a polygonal area where a target object is located in a mouse selection mode; in the selection process, coordinate values of the position of the cursor are obtained, edge polygon coordinates of the target object are obtained, and a polygon area of the edge of the target object is formed; then, the polygonal area is converted into a region mask, and the polygonal area in the obtained image is used as an ROI; then, after the images are folded into third-order tensors, taking an inverse number, multiplying the inverse number by the original image point, setting the pixels in the ROI of the images to be zero, and keeping the pixel values of the rest areas unchanged to obtain a graph with the target object removed;
copying the most similar part of color edge information outside the ROI to the ROI of the image;
establishing a mathematical model as follows:
Figure BDA0003133142370000021
s.t.：χΩ＝TΩ
wherein, T is represented as an original image, omega is an observation index, chi is an image which is to be restored and lacks ROI area pixel values, k represents tensor circularly expanded according to tensor of each modality, N is a tensor order, d is a step length, chik，d>Representing the tensor loop expansion of χ, Ω1Indicating the color edge information index copied to the ROI,
Figure BDA0003133142370000022
denotes x and omega1The dot product of (a) is,
Figure BDA0003133142370000023
represents T and omega1Dot product of (1); chi shapeΩ＝TΩFor constraint, indicating that pixel points outside the ROI area are kept unchanged, and only updating the pixel points in the ROI area; lambda and alphakThe value of lambda is (0,1) and alpha is adjustable parameterkThe value rule is as follows:
Figure BDA0003133142370000024
and introducing an auxiliary variable tensor to solve the mathematical model to obtain a recovered image.
Further, copying the most similar part of the color edge information outside the ROI to the ROI of the image includes:
searching the edge of the ROI area on the graph with the target object removed, and setting the filling priority of edge pixel points;
selecting the pixel point with the highest priority, and obtaining a pixel block to be filled according to the pixel point;
using a least squares sum algorithm, finding pixel blocks most similar to the pixel blocks in the remaining part of the color edge map except the ROI;
filling the ROI area part with the found pixel block with the highest similarity, and judging whether filling is finished; and if the filling is completed, obtaining a filling graph.
Further, the auxiliary variable tensor is M, and is expressed as follows:
Figure BDA0003133142370000025
s.t.：χ＝M(k),k＝1,...,N
χΩ＝TΩ
the lagrangian function is defined according to the above equation as follows:
Figure BDA0003133142370000031
s.t.：χΩ＝TΩ
gamma is a lagrange multiplier and is a linear multiplier,<χ-M(k),γ(k)>expressed as inner product, rho is parameter, and the value range is (0.001, 100).
Further, solving the mathematical model comprises:
solving for M(K)Solving for M(K)Can be equated to the following equation:
Figure BDA0003133142370000032
thus, it is possible to provide
Figure BDA0003133142370000033
foldkRepresenting the complete updating of the unfolded matrices into a tensor, Dτ(.) represents a thresholded singular value decomposition operation, Y ═ Y<χ-M(k),γ(k)>，Yk，d>Representing a tensor cycle expansion of Y;
solving for gamma(K)Through type gamma(k)＝γ(k)+ρ(χ-M(k))；
Solving X, under the condition that other variables are fixed, obtaining the optimal X by solving the following equation, and extracting and combining the terms only containing X into the following formula according to the defined Lagrangian function:
Figure BDA0003133142370000034
s.t.：χΩ＝TΩ
a terminal device comprising a memory, a processor and a computer program stored in said memory and executable on said processor, the processor implementing the steps of the method for restoring an image background based on tensor ring decomposition when executing the computer program.
A computer-readable storage medium, in which a computer program is stored which, when being executed by a processor, carries out the steps of the method of restoring an image background based on tensor ring decomposition.
Compared with the prior art, the invention has the following technical characteristics:
1. the present invention introduces a tensor decomposition-based approach to recover an image with the target object removed. In the prior art, previous studies on complementing images based on tensor decomposition can only be applied to recovering images with random loss and streak loss. In the invention, the method based on tensor decomposition can be used for removing the loss of irregular holes in images such as electric wires in landscape sky photographs, other tourists in passerby photographs and the like.
2. The method can autonomously select similar edge information to be copied to the ROI, and can ensure that the restored image is more vivid.
3. The method for restoring the image background based on tensor ring decomposition is similar to the cutout of computer software PS and has the function of restoring the background, and compared with the computer software PS, after a belt is selected to remove a target object, the image restoration can be automatically completed by the algorithm.
Drawings
FIG. 1 is an original drawing in the embodiment;
FIG. 2 is an image with a target object removed in the embodiment;
FIG. 3 is an edge view in an embodiment;
FIG. 4 is an edge diagram of an image with colors with a target object removed in the embodiment;
FIG. 5 is a color information map of other regions copied to the ROI in the embodiment;
FIG. 6 is an observation image in the embodiment of FIG. 5;
FIG. 7 is an image populated with tensor resolution in an embodiment;
FIG. 8 is a schematic flow diagram of the method of the present invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention clearer and clearer, the present invention is further described below with reference to the accompanying drawings and examples.
Referring to fig. 8, the present invention provides a method for restoring image background based on tensor ring decomposition, which includes the following steps:
step S0, extracting an edge of the image to be processed, including:
converting an original image to be processed into a gray-scale image, extracting the edge of the gray-scale image through an edge extraction algorithm, and then performing dot multiplication on the image with the extracted edge and the original image after the image with the extracted edge is folded into a third-order tensor to obtain a color edge image.
As shown in fig. 3 and 4. The tensor decomposition-based completion image algorithm is mainly used for randomly lost images, and the existing tensor decomposition-based filling algorithm is used for completing lost images of big holes, so that the lost images are mostly fuzzy and unclear, the outline edge of a lost area cannot be recovered by using the existing method, and the recovered images are more vivid by adding edge information with colors; in this embodiment, fig. 1 needs to be converted into a gray scale map. Then, the canndy edge operator is used to extract the edge of the gray scale image as shown in fig. 3, and finally, the gray scale image 3 is overlapped into a third-order tensor and then is subjected to point multiplication with the original image, which is referred to fig. 4. The image after the operation is the outline information with color, so that the restored image effect is more vivid.
Step S1, setting a polygon area of the position of the target object by means of mouse selection; in the selection process, coordinate values of the position of the cursor are obtained, edge polygon coordinates of the target object are obtained, and a polygon area of the edge of the target object is formed; then, the polygonal area is converted into a region mask, the image is a binary image, and the polygonal area in the obtained image is used as an ROI; then, after the images are folded into third-order tensors, taking an inverse number, multiplying the inverse number by the original image point, setting the pixels in the ROI of the images to be zero, and keeping the pixel values of the rest areas unchanged to obtain a graph with the target object removed; the effect of this step process is shown in fig. 2.
In this embodiment, the ROI region where the target object is located is extracted, the cursor position coordinate of the mouse may be captured through a ginput function in matlab, and the region mask may be converted through a poly2mask function or the like. The image obtained by the function is a binary image, the pixel of the target area is 1, and the pixels of other areas are 0. The images are stacked into three-order tensors, and the three-order tensors are multiplied by the original image to obtain the image 2.
Before restoring the image, the image needs to be preprocessed, that is, a region of a target object to be removed in the image is determined, and the region is called as an ROI (region of interest); the pixel value of the ROI area in the image is set to 0, and the pixel value of the area outside the ROI area is not changed.
Step S2, copying similar edge information to ROI
After the processing in steps S0 and S1, the color edge map of the image and the map from which the target object is removed are obtained, and the closest part of the color edge information other than the ROI is copied to the ROI of the image. As shown in fig. 5.
Using the color edge map (fig. 4), on the basis of the map (fig. 2) from which the target object is removed, filling the hole with redundant information of the remaining part of the clipped picture, including:
2.1 searching the edge of the ROI area on the graph with the target object removed, and setting the filling priority of edge pixel points;
2.2 selecting the pixel point with the highest priority, and obtaining the pixel block to be filled according to the pixel point;
2.3 using the least squares sum algorithm, finding pixel blocks most similar to the pixel blocks in the rest of the color edge map except the ROI;
2.4 filling the ROI area part with the pixel block with the highest similarity, and judging whether the filling is finished; if the filling is completed, a filling graph is obtained, as shown in FIG. 5, and if not, 2.1 is returned.
Step S3, a mathematical model is established as follows:
Figure BDA0003133142370000061
s.t.：χΩ＝TΩ
where T is the original image, and as shown in fig. 1, Ω is an observation index (three-order tensor, 0 is a missing part in the image, and 1 is the other part), and the observation index is a binary image of the original image; chi shapeΩ＝TΩFor constraint, the pixel points outside the ROI area are kept unchanged, and only the pixel points in the ROI area are updated. Omega1Indicating the color edge information index copied to the ROI, referring to those color edge information within the ROI area in fig. 5; as shown in fig. 6, i.e., a point in the target region where the pixel is 0, the copied color edge information distances in the ROIs representing the images before and after restoration are as similar as possible. k represents the cyclic expansion of the tensor according to each mode, the values are (1,3), N is the tensor order, d is the step length, and xk，d>The expression is to carry out tensor cycle expansion on chi, and the matrix size after expansion is ItIt+1...Ik×Ik+1...It-1，ItRepresenting the size of a dimension, the number of the dimensions
Figure BDA0003133142370000062
Figure BDA0003133142370000063
Representing a set of real numbers, | | · | non-calculation*Defined as the sum of the singular values of the matrix,
Figure BDA0003133142370000064
defined as the sum of squares of the elements, λ and αkThe value of lambda is (0,1) and alpha is adjustable parameterkThe value rule is as follows:
Figure BDA0003133142370000065
χ is the image to be restored which lacks the pixel value of the ROI regionΩ1Denotes x and omega1The dot product of (a) is,
Figure BDA0003133142370000066
represents T and omega1Dot product of (1); in the formula
Figure BDA0003133142370000067
This part represents the minimization of the rank,
Figure BDA0003133142370000068
is a penalty term.
In the initial tensor completion algorithm, the minimization of rank is solved, but the solving of rank is an NP-hard problem, the minimization of rank is approximately replaced by the minimization of nuclear norm for solving tensor, and then the original modal expansion of tensor is replaced by tensor cyclic expansion; design introduction of punishment items is carried out in the scheme.
Step S4, solving the mathematical model in the step 3 to obtain a recovered image; for the convenience of solution, an auxiliary variable tensor M is introduced:
Figure BDA0003133142370000071
s.t.：χ＝M(k),k＝1,...,N
χΩ＝TΩ
where k denotes the cyclic expansion of the tensor for each modality, N is the order, here 3, and the image is a third order tensor because it is necessary to cycle for each modalityTo expand, three auxiliary variables are needed to solve.
Figure BDA0003133142370000072
For matrix representation after tensor expansion of M, M(k)Denoted as the kth auxiliary tensor.
The lagrangian function is defined according to the above equation as follows:
Figure BDA0003133142370000073
s.t.：χΩ＝TΩ
gamma is Lagrange multiplier, and the parameters in the upper parentheses in the scheme represent the order of tensor cycle expansion;<χ-M(k),γ(k)>the method is based on a constraint term, expressed as an inner product, rho is a parameter, the value is generally (0.001, 100), and the best value is obtained according to a test in the experimental process.
The step S4 further includes:
step S41: solving for M(K)Solving for M(K)Can be equated to the following equation:
Figure BDA0003133142370000074
the term containing only M is extracted and recombined into the above formula according to the calculation mode.
Thus, it is possible to provide
Figure BDA0003133142370000075
foldkRepresenting the complete updating of the unfolded matrices into a tensor, Dτ(.) represents a thresholded singular value decomposition operation, τ is a parameter,
Figure BDA0003133142370000076
Y＝<χ-M(k),γ(k)>，Y<k，d>the representation is a tensor loop expansion of Y.
Step S42: solving forγ(K)Through type gamma(k)＝γ(k)+ρ(X-M(k)) Iteratively updating; updating each step to be a current value plus the value of a following expression; k has a value of 1 to n, where n is 3.
Step S43: solving χ, under the condition that other variables are fixed, obtaining the optimal χ by solving the following equation, and extracting and combining the terms only containing χ into the following formula according to the defined Lagrangian function:
Figure BDA0003133142370000081
s.t.：χΩ＝TΩ
the following can be obtained:
Figure BDA0003133142370000082
in the above formula, i1,...,iNAnd representing pixel points of the image, wherein the first item represents the update of all pixel points in the target area, the second item represents the update of all pixel points outside the target area, the third item represents the update in the omega 1 area, the result in the first item is covered at the moment, and the X obtained through iteration is the finally recovered image.
In one embodiment of the present invention, the parameter configuration is as follows:
Figure BDA0003133142370000083
ρ＝0.1，λ＝0.1
the final restored image obtained by the set of parameters is shown in fig. 7, and as can be seen from the result, the algorithm can make the restored image effect vivid.
The above embodiments are only used to illustrate the technical solutions of the present application, and not to limit the same; although the present application has been described in detail with reference to the foregoing embodiments, it should be understood by those of ordinary skill in the art that: the technical solutions described in the foregoing embodiments may still be modified, or some technical features may be equivalently replaced; such modifications and substitutions do not substantially depart from the spirit and scope of the embodiments of the present application and are intended to be included within the scope of the present application.

Claims (6)

1. A method for restoring image background based on tensor ring decomposition, comprising:
converting an original image to be processed into a gray-scale image, extracting the edge of the gray-scale image through an edge extraction algorithm, and then performing dot multiplication on the image with the extracted edge and the original image after the image is folded into a third-order tensor to obtain a color edge image;
setting a polygonal area where a target object is located in a mouse selection mode; in the selection process, coordinate values of the position of the cursor are obtained, edge polygon coordinates of the target object are obtained, and a polygon area of the edge of the target object is formed; then, the polygonal area is converted into an area mask, the polygonal area in the obtained image is used as an ROI, then the image is overlapped into a third-order tensor, an inverse number is taken and multiplied by an original image point, pixels in the ROI of the image are set to be zero, pixel values of the rest areas are unchanged, and the image with the target object removed is obtained;
copying the most similar part of color edge information outside the ROI to the ROI of the image;
establishing a mathematical model as follows:
Figure FDA0003133142360000011
s.t.：χΩ＝TΩ
wherein, T is represented as an original image, omega is an observation index, chi is an image which is to be restored and lacks ROI area pixel values, k is represented as tensor circularly expanded according to each modal tensor, N is an order, d is represented as step length, chik，d>Representing the tensor loop expansion of χ, Ω1Representing the color edge information index, χ, copied to the ROIΩ1Denotes x and omega1The dot product of (a) is,
Figure FDA0003133142360000012
represents T and omega1Dot product of (1); chi shapeΩ＝TΩFor constraint, indicating that pixel points outside the ROI area are kept unchanged, and only updating the pixel points in the ROI area; the value of lambda is (0,1), alphak＞0；
And introducing an auxiliary variable tensor to solve the mathematical model to obtain a recovered image.
2. The method for restoring image background based on tensor ring decomposition as recited in claim 1, wherein copying the most similar part of color edge information outside the ROI to the ROI of the image comprises:
searching the edge of the ROI area on the graph with the target object removed, and setting the filling priority of edge pixel points;
selecting the pixel point with the highest priority, and obtaining a pixel block to be filled according to the pixel point;
using a least squares sum algorithm, finding pixel blocks most similar to the pixel blocks in the remaining part of the color edge map except the ROI;
filling the ROI area part with the found pixel block with the highest similarity, and judging whether filling is finished; and if the filling is completed, obtaining a filling graph.
3. The method for restoring image background based on tensor ring decomposition as recited in claim 1, wherein the auxiliary variable tensor is expressed as M as follows:
Figure FDA0003133142360000021
s.t.：χ＝M(k),k＝1,...,N
χΩ＝TΩ
the lagrangian function is defined according to the above equation as follows:
Figure FDA0003133142360000022
s.t.：χΩ＝TΩ
gamma is a lagrange multiplier and is a linear multiplier,<χ-M(k),γ(k)>expressed as inner product, rho is parameter, and the value is (0.001, 100).
4. The method for restoring an image background based on tensor ring decomposition as recited in claim 1, wherein solving the mathematical model comprises:
solving for M(K)Solving for M(K)Can be equated to the following equation:
Figure FDA0003133142360000023
thus, it is possible to provide
Figure FDA0003133142360000024
foldkRepresenting the complete updating of the unfolded matrices into a tensor, Dτ(.) represents a thresholded singular value decomposition operation, Y ═ Y<χ-M(k),γ(k)>，Y<k，d>Representing a tensor cycle expansion of Y;
solving for gamma(K)Through type gamma(k)＝γ(k)+ρ(χ-M(k))；
Solving χ, under the condition that other variables are fixed, obtaining the optimal χ by solving the following equation, and extracting and combining the terms only containing χ into the following formula according to the defined Lagrangian function:
Figure FDA0003133142360000031
s.t.：χΩ＝TΩ。
5. a terminal device comprising a memory, a processor and a computer program stored in said memory and executable on said processor, characterized in that the processor, when executing the computer program, carries out the steps of the method of restoring an image background based on tensor ring decomposition.
6. A computer-readable storage medium, in which a computer program is stored which, when being executed by a processor, carries out the steps of the method of restoring an image background based on tensor ring decomposition.
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