CN107169934A - A kind of image mending method based on different redundant dictionaries - Google Patents
A kind of image mending method based on different redundant dictionaries Download PDFInfo
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- 238000000034 method Methods 0.000 title claims abstract description 55
- 238000012549 training Methods 0.000 claims abstract description 50
- 230000015556 catabolic process Effects 0.000 claims description 6
- 238000006731 degradation reaction Methods 0.000 claims description 6
- 230000003044 adaptive effect Effects 0.000 claims description 3
- 239000000654 additive Substances 0.000 claims description 3
- 230000000996 additive effect Effects 0.000 claims description 3
- 239000012141 concentrate Substances 0.000 claims description 2
- 230000007547 defect Effects 0.000 abstract description 4
- 238000012545 processing Methods 0.000 description 7
- 230000000694 effects Effects 0.000 description 5
- 238000005516 engineering process Methods 0.000 description 5
- 238000011084 recovery Methods 0.000 description 5
- 230000008859 change Effects 0.000 description 3
- 238000013461 design Methods 0.000 description 3
- 230000008439 repair process Effects 0.000 description 3
- 230000015572 biosynthetic process Effects 0.000 description 2
- 230000007850 degeneration Effects 0.000 description 2
- 238000009792 diffusion process Methods 0.000 description 2
- 239000011159 matrix material Substances 0.000 description 2
- 239000000203 mixture Substances 0.000 description 2
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- 230000003412 degenerative effect Effects 0.000 description 1
- 238000012217 deletion Methods 0.000 description 1
- 230000037430 deletion Effects 0.000 description 1
- 239000000945 filler Substances 0.000 description 1
- 230000004048 modification Effects 0.000 description 1
- 238000012986 modification Methods 0.000 description 1
- 238000010422 painting Methods 0.000 description 1
- 238000012913 prioritisation Methods 0.000 description 1
- 230000000717 retained effect Effects 0.000 description 1
- 230000011218 segmentation Effects 0.000 description 1
- 238000001308 synthesis method Methods 0.000 description 1
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- G06T5/77—
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- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
- G06T2207/00—Indexing scheme for image analysis or image enhancement
- G06T2207/20—Special algorithmic details
- G06T2207/20004—Adaptive image processing
Abstract
The invention discloses a kind of image mending method based on different redundant dictionaries, this method obtains redundancy DCT dictionaries first with discrete cosine transform, and Global Dictionary and self-adapting dictionary are obtained using the training of K SVD methods;It is then based on the above-mentioned three kinds different redundant dictionary difference pending images of rarefaction representation;The sparse coefficient that the part of defect can just be obtained by redundant dictionary and renewal in final image shows.Experiment compares the image mending method and traditional image mending method based on Total Variation based on different redundant dictionaries of proposition, as a result demonstrates the validity of proposition method.
Description
Technical field
The present invention relates to a kind of image mending method based on different redundant dictionaries, belong to technical field of image recovery.
Background technology
Image mending technology has many applications, common are the scratch got rid of on photo, to remove some in picture specific
Word in object and photo etc., others also have as the repairing of precious painting and calligraphy and historical relic works, it can be seen that image mending
Technology has very high practical significance.
Image mending Study on Problems has been achieved for certain progress so far, occurs in that many method for repairing and mending.Typically
Method is mainly summarized as two classes:The first kind is to be based on partial differential equation (partial differential equation, PDE)
Theoretical with variational algorithm, the mending course of this kind of method is that known region expands to zone of ignorance from image, that is, is schemed
The part lacked as in.Equations of The Second Kind method is then the technology synthesized based on sample texture, and this kind of method is from regional edge to be repaired
Edge starts segmentation figure as fritter, the image most matched with pending image fritter is found from the known portions of missing image small
Block, image mending is usually carried out using the member on correspondence position.It should be noted that natural image with texture layer except believing
Outside breath, also with structure sheaf information, the only texture layer of repairing figure picture can not obtain good repair efficiency, have ignored missing
The structure sheaf in region.
Publication number CN104680492A《Image repair method based on composition of sample uniformity》, this method calculates figure first
As on the edge of absent region each pixel prioritization functions value, choose the pixel wherein with greatest preference value,
Using the edge fritter comprising the pixel as object block to be repaired, found from image in known region and object block most
The image block matched somebody with somebody, pixel unknown in object block is repaired using the pixel value on correspondence position, filler pixels are then updated
Confidence level.Repeat the above steps until defect area is padded in image.But this method is when repairing bulk absent region,
Image detail information recovery effects are bad, additionally, due to the greediness of this method, and repairing result is readily incorporated incoherent object.
Chan et al. is in paper " Nontexture Inpainting by Curvature-Driven Diffusions "
In propose based on curvature spread (curvature-driven diffusions, CDD) nonlinear partial differential equation repair mould
Type solves the problems, such as image mending, while the problem of can solving the vision unconnectedness occurred when recovering at linear fracture object.
This method can be very good to recover structure sheaf information, such as marginal portion when handling less absent region.But in processing
Effect is not fine during large area, is readily incorporated fuzzy.
Chen et al. paper " in Sketch-Guided Texture-Based Image Inpainting ", using pair
The structural information and texture information of image deletion sites are repaired respectively, and wherein sketch model (sketch model) is used for weight
The structural information of structure missing image, then uses the texture synthesis method based on image block to go to the area lacked in composograph again
Domain.Image mending algorithm based on sample can handle the absent region of bulk, can preferably recover the line in region to be repaired
Reason information, but the greediness of the patch algorithm, may introduce incoherent object in processing procedure.
To sum up, existing image mending method, many limitations existed are mainly manifested in:(1) first kind is based on partially micro-
Equation and the theoretical restorative procedure of variational algorithm is divided to can be very good to recover the structure sheaf information of smaller absent region, but in processing
Easily cause when larger absent region fuzzy.(2) Equations of The Second Kind can handle relatively large based on the technology that sample texture is synthesized
Absent region, recover the texture information in region to be repaired, but the greediness of the patch algorithm, may in processing procedure
Introduce incoherent object.
The content of the invention
Goal of the invention:For problems of the prior art, the present invention provides a kind of figure based on different redundant dictionaries
As method for repairing and mending, method obtains redundancy DCT dictionaries first with discrete cosine transform, obtains global using the training of K-SVD methods
Dictionary and self-adapting dictionary;It is then based on the above-mentioned three kinds different redundant dictionary difference pending images of rarefaction representation;Final figure
The sparse coefficient that the part of defect can just be obtained by redundant dictionary and renewal as in shows, and realizes image mending.
Technical scheme:A kind of image mending method based on different redundant dictionaries, comprises the following steps:
Step 1, for Incomplete image, represented using following degradation model:
Y=Hx+ η
Wherein, x represents original picture rich in detail, and y then represents the image to be repaired of partial content missing, and η refers to that image is moved back
The additive noise that may be introduced during change, generally refers to the Gaussian noise of additivity, and the degeneration that H refers in image missing problem is calculated
Son.
Step 2, pending picture is defined asSize isTreat repairing figure picture and take piecemeal
The mode of processing, each image block can be expressed as yk=RkY, whereinImage is chosen in expression from missing image
The matrix operator of block, size isAllow image block y in order to make the marginal position between image block unaffected, during piecemealkMutually
Overlap.Note:HereRepresent size be N a scope, mean that picture, be not necessarily square, merely just in order to
Statement is convenient.
Step 3, redundant dictionary, including three kinds of DCT dictionaries, global training dictionary and self-adapting dictionary are trained, dictionary isWherein K is the number of atom, K > > B, it is ensured that redundancy.
Step 4, with reference to degradation model, each image block y is calculatedkBased on the rarefaction representation coefficient α on dictionary Dk。
Step 5, the sparse coefficient α tried to achieve is utilizedkEach image block is rebuild, x is designated ask=D αk, all images are rebuild successively
Block, makees average treatment in overlapping region, obtains the image x after final repairing.
As a preferred embodiment of the present invention, the training of redundant dictionary described in step 3.Wherein, the DCT dictionaries of redundancy are
Obtained by discrete cosine transform, and global training dictionary and self-adapting dictionary are to utilize K-SVD methods from training sample
What training was obtained.
The object function of K-SVD training methods is:
WhereinX=[x1,x2,...,xJ] it is training sample set, α=[α1,α2,...,αJ] it is training image
The set of rarefaction representation coefficient of the block under dictionary.
When training Global Dictionary, training sample set refers to from the image block largely clearly obtained in natural image;When
When training self-adapting dictionary, training sample is obtained from pending image.K-SVD training methods include sparse coding and word
Allusion quotation updates two stages, and calculating training sample according to known dictionary first concentrates sparse coefficient of each image fritter on dictionary
αk, then dictionary is updated by column using known dictionary and coefficient set α.Set dictionary updating number of times or reconstructed image block and
Residual error between training image blocks is as stop condition, and final training obtains redundant dictionary D.
As a preferred embodiment of the present invention, rarefaction representation system of each image block of calculating on dictionary D described in step 4
Number αk.Based on image block ykSparse coding problem can be expressed as:
Wherein, λ is regularization parameter, and p can take 0 or 1, and to the degree of rarefication of design factor, p is taken in context of methods
The number of nonzero element in=0, i.e. design factor.The degeneracy operator that H representative images are degenerated, degeneracy operator is in the patch formation model
Play an important role.It is above-mentioned onMinimization problem be a computationally intensive non-convex problem, can be using greedy calculation
Method obtains approximation, is solved herein using OMP algorithms.It is 0 norm, i.e. when p=0.
As a preferred embodiment of the present invention, image after repairing is solved described in step 5.First with the coefficient weight tried to achieve
Composition has as fritter
xk=D αk
All image blocks are rebuild successively, then the image x after repairing can be expressed as
Wherein, α refers to factor alpha of all image blocks under dictionarykSet, i.e. α=[α1,α2,...,αn].Above-mentioned public affairs
The implication of formula refers to each image block after recovery to be placed on original position, for part overlapped between image block, does
Average treatment, can so reduce error of the image block in each overlapping region, obtain preferably repairing result.
The present invention uses above technical scheme compared with prior art, with following technique effect:
The present invention obtains the DCT dictionaries of redundancy using discrete cosine transform, or obtains global word using the training of K-SVD methods
Allusion quotation and self-adapting dictionary, are then based in the pending image of the sparse expression of above-mentioned three kinds of different redundant dictionaries, final image
The part of defect can just be showed by redundant dictionary and the sparse coefficient updated.This method takes full advantage of natural image
It is openness, and compare the repairing result under different dictionaries, make use of the high efficiency of adaptive training dictionary, experimental result card
Understand the validity of proposition method.
Brief description of the drawings
Fig. 1 is the implementing procedure figure of the image mending method based on different redundant dictionaries of the embodiment of the present invention;
Fig. 2 is the signal of image mending problem.
Embodiment
With reference to specific embodiment, the present invention is furture elucidated, it should be understood that these embodiments are merely to illustrate the present invention
Rather than limitation the scope of the present invention, after the present invention has been read, various equivalences of the those skilled in the art to the present invention
The modification of form falls within the application appended claims limited range.
As shown in figure 1, being the implementing procedure figure of image mending method of the present invention based on different redundant dictionaries, specific steps
It is as follows:
Image mending problem is a lot, compares the image typically lacked for a width content, according to remaining in image
Part recovers the part lacked in image, and the problem vivid can be expressed as shown in Fig. 2.
Wherein, E is incomplete part in image, that is, part to be repaired, EcFor the part retained in image.This
Repairing problem can be described as according to EcRecover E process.Degenerative process shown in Fig. 2 can be represented with equation below:
Y=Hx+ η (1)
Wherein, x represents original picture rich in detail, and y then represents the image to be repaired of partial content missing, and η refers to that image is moved back
The additive noise that may be introduced during change, generally refers to the Gaussian noise of additivity.The degeneration that H refers in image missing problem is calculated
Son, now H for only comprising 0 and 1 two kind of element mask when, the pixel value of portion in image can be set to 0, cause image
Partial content is lacked.
1, according to the degradation model formula (1) of image mending problem, our target is to utilize the missing image y observed
Recover original picture rich in detail x.In order to express easily, it is by pending image definition hereSize isBut this method can handle the picture of arbitrary size.The mode for taking image piecemeal to handle, each image
BlockSize isAllow image block y in order to make the marginal position between image block unaffected, during piecemealkIt is heavy mutually
Folded, step-length is 1, although so processing can make the calculating quantitative change of whole recuperation big, the recovery effects that can have ensured.
2, dictionary training includes DCT dictionaries, global training dictionary and the self-adapting dictionary of redundancy.Wherein, the DCT of redundancy
Dictionary is obtained by discrete cosine transform, and global training dictionary and self-adapting dictionary are to utilize K-SVD methods from training
Training is obtained in sample.
The object function of K-SVD training methods is:
WhereinX=[x1,x2,...,xJ] it is training sample set, α=[α1,α2,...,αJ] it is training image
The set of block rarefaction representation coefficient under dictionary.
K-SVD training methods include two stages of sparse coding and dictionary updating, calculated train according to initial dictionary first
Sparse coefficient α of each image fritter on dictionary in sample setk, then word is updated by column using known dictionary and coefficient set α
Atom in allusion quotation.The residual error between the number of times or reconstructed image block and training image blocks of dictionary updating is set as stop condition,
Final training obtains redundant dictionary D.When training Global Dictionary, training sample set is from largely clearly obtaining in natural image
Image block, trained the image fritter more than 100000 8 × 8, obtained by K-SVD Algorithm for Training, iteration 180 times,
In each iteration, using OMP Algorithm for Solving sparse coefficients, the degree of rarefication of coefficient is set to 6.When training self-adapting dictionary,
Training sample is the image block obtained from pending image, is trained using K-SVD methods, 10 acquisitions of iteration.
3, each image block can be expressed as yk=RkY, whereinImage block is chosen in expression from missing image
Matrix operator.Dictionary, it is known that wherein K is the number of atom, K > > B.Then it is based on image block ykSparse coding
Problem can be expressed as:
Wherein, λ is regularization parameter, and p can take 0 or 1, and to the degree of rarefication of constraint factor, p=is taken in the method
The number of nonzero element in 0, i.e. design factor.The degeneracy operator that H representative images are degenerated, degeneracy operator rises in the patch formation model
Important effect.It is above-mentioned onMinimization problem be a computationally intensive non-convex problem, greedy algorithm can be used
To obtain approximation, this method is solved using OMP algorithms.
4, calculating obtains image block ykRarefaction representation coefficient α based on dictionary Dk, then each image block after recovering can be with
It is designated as:
xk=D αk (4)
5, all image blocks are rebuild successively, then the complete image x after recovering can be just expressed as:
Wherein, α refers to factor alpha of all image blocks under dictionarykSet, i.e. α=[α1,α2,...,αn].Formula (5)
Implication refer to be placed on the image block after recovery on original position, for part overlapped between image block, be averaged
Processing, can so reduce error of the image block in each overlapping region, obtain preferably repairing result.
Claims (4)
1. a kind of image mending method based on different redundant dictionaries, it is characterised in that comprise the following steps:
Step 1, for Incomplete image, represented using following degradation model:
Y=Hx+ η
Wherein, x represents original picture rich in detail, and y then represents the image to be repaired of partial content missing, and η refers to image degradation
The additive noise that may be introduced in journey, generally refers to the Gaussian noise of additivity, H refers to the degeneracy operator in image missing problem;
Step 2, pending picture is defined asSize isRepairing figure is treated as taking piecemeal to handle
Mode, each image block can be expressed as yk=RkY, whereinRepresent the square of the selection image block from missing image
Battle array operator, size isAllow image block y during piecemealkOverlap each other;
Step 3, redundant dictionary, including three kinds of DCT dictionaries, global training dictionary and self-adapting dictionary are trained, dictionary isWherein K is the number of atom, K > > B, it is ensured that redundancy;
Step 4, with reference to degradation model, each image block y is calculatedkBased on the rarefaction representation coefficient α on dictionary Dk;
Step 5, the sparse coefficient α tried to achieve is utilizedkEach image block is rebuild, x is designated ask=D αk, all image blocks are rebuild successively,
Average treatment is made in overlapping region, obtains the image x after final repairing.
2. the image mending method as claimed in claim 1 based on different redundant dictionaries, it is characterised in that superfluous described in step 3
The training of remaining dictionary;Wherein, the DCT dictionaries of redundancy are obtained by discrete cosine transform, and global training dictionary and adaptive
Answer dictionary to train from training sample using K-SVD methods to obtain;
The object function of K-SVD training methods is:
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WhereinX=[x1,x2,...,xJ] it is training sample set, α=[α1,α2,...,αJ] for training image blocks in word
The set of rarefaction representation coefficient under allusion quotation.
When training Global Dictionary, training sample set refers to the image block obtained from clearly natural image;It is adaptive when training
When answering dictionary, training sample is obtained from pending image;K-SVD training methods include sparse coding and dictionary updating two
In the individual stage, training sample is calculated according to known dictionary first and concentrates sparse coefficient α of each image fritter on dictionaryk, then
Dictionary is updated by column using known dictionary and coefficient set α;The number of times or reconstructed image block and training for setting dictionary updating are schemed
As the residual error between block is as stop condition, finally train obtaining redundant dictionary D.
3. the image mending method as claimed in claim 1 based on different redundant dictionaries, it is characterised in that described in step 4
Calculate rarefaction representation coefficient α of each image block on dictionary Dk;Based on image block ykSparse coding problem can be expressed as:
<mrow>
<msub>
<mi>&alpha;</mi>
<mi>k</mi>
</msub>
<mo>=</mo>
<mi>arg</mi>
<mi> </mi>
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</mrow>
Wherein, λ is regularization parameter, p=0, the degeneracy operator that H representative images are degenerated.
4. the image mending method as claimed in claim 1 based on different redundant dictionaries, it is characterised in that asked described in step 5
Image after solution repairing:First with the coefficient reconstructed image fritter tried to achieve, have
xk=D αk
All image blocks are rebuild successively, then the image x after repairing can be expressed as
Wherein, α refers to factor alpha of all image blocks under dictionarykSet, i.e. α=[α1,α2,…,αn]。
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CN109816600A (en) * | 2018-12-21 | 2019-05-28 | 西北工业大学 | Confocal microscopy image restored method based on rarefaction representation |
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Cited By (4)
Publication number | Priority date | Publication date | Assignee | Title |
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CN109816600A (en) * | 2018-12-21 | 2019-05-28 | 西北工业大学 | Confocal microscopy image restored method based on rarefaction representation |
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