CN105894519A - Robustness image segmentation algorithm based on low rank recovery - Google Patents

Abstract

The invention belongs to the field of image processing technology, and discloses a robustness image segmentation algorithm based on low rank recovery. The invention is characterized by obtaining a feature space image using a low rank space decomposition and segmenting the feature space image through an image segmentation method based on min-cut/max-flow; and by including the steps of: dividing an image to be processed into overlapping image blocks and converting the image blocks into a column vector matrix according to positions of the overlapping blocks; processing the column vector matrix of the image blocks using a low rank matrix recovery method to obtain a feature space image; and segmenting the feature space image through the image segmentation method based on min-cut/max-flow. The invention extracts more image edge information through low rank space recovery in such a manner that the image tag is more accurate and the segmentation quality of the image is improved. The invention overcomes the impact of noise points on the segmentation quality.

Description

A kind of robustness image segmentation algorithm recovered based on low-rank

Technical field

The present invention relates to technical field of image processing, particularly to a kind of robustness recovered based on low-rank Image segmentation algorithm.

Background technology

Image segmentation is the basis of image procossing and computer vision.Image segmentation is to be divided into by image the most not Overlapping region, it is achieved the separation of the target and background of image, the follow-up reconstruction to image and knowledge Not.In the plurality of application scenes of computer vision, it is follow-up that the quality of image segmentation have impact on image Process.Image segmentation quality is closely related with the accuracy at its edge.Increasing novel image divides The dividing method cut is suggested, and applies the various aspects with computer vision field.

The dividing method of image is a lot, numerous.Method based on edge mainly uses gradient operator to examine The edge of altimetric image；Dividing method based on region mainly finds suitable seed or suitably grows Criterion forms region, thus realizes image segmentation；Dividing method based on threshold value is by rational target Function obtains optimal segmenting threshold, distinguishes the target and background of image, it is achieved the segmentation of image.These pass The partitioning algorithm of system has certain disadvantages, it is impossible to meet the requirement to image segmentation quality.

During image tagged is split, owing to by effect of noise, marked erroneous, shadow can be made Ring the accuracy of labelling, so that energy function does not minimizes, have impact on the segmentation quality of image, Even can cover some features of image, directly affect the subsequent treatment effect of image.

Summary of the invention

The present invention provides a kind of robustness image segmentation algorithm recovered based on low-rank, solves prior art The quality of middle influence of noise image segmentation and the technical problem of the subsequent processes of image.

For solving above-mentioned technical problem, the invention provides a kind of robustness image recovered based on low-rank Partitioning algorithm, it is characterised in that: use low-rank spatial decomposition obtain feature space image, by based on The figure of minimal cut/max-flow cuts method, splits feature space image；Comprise the following steps:

Pending image division is become overlapped image block, will figure according to position during overlap partition As block changes into column vector matrix；

Use low-rank matrix restoration methods to process the column vector matrix of image block, obtain feature space image；

Cut method by figure based on minimal cut/max-flow, split feature space image.

Further, the process of the column vector matrix that low-rank matrix restoration methods processes image block includes:

Column vector matrix to image block, uses low-rank matrix space to solve, obtains the block of low-rank matrix Matrix；

According to position when taking block, the block matrix of low-rank matrix is rebuild, obtains feature space figure Picture.

Further, the described figure method of cutting based on minimal cut/max-flow includes:

Feature space image is mapped as figure, and seeks its energy function；

When the value of energy function minimizes, figure based on minimal cut/max-flow cuts method and just obtains figure A minimal cut, i.e. split image.

Further, when dividing image block, according to a fixed-direction, divide image block；

Wherein, when being divided into edge and being divided into a whole image block not, just use rollback method, On the basis of edge, reversely take block.

Further, to the image block L of pending image, (i j), uses K arest neighbors node algorithm to ask Nearest node；And represent by column vector, all of column vector is formed matrix X.

Further, described column vector formation matrix X is converted to low-rank matrix and carries out low-rank space Solve, obtain block matrix L_k；

According to position when taking block, (i j), carries out split to low-rank matrix, obtains characteristic image L.

Further, the described figure method of cutting based on minimal cut/max-flow includes:

Characteristic image L is mapped as figure, and seeks its energy function；

When the value of energy function minimizes, just obtain a minimal cut of figure, i.e. split image.

The one or more technical schemes provided in the embodiment of the present application, at least have the following technical effect that Or advantage:

The robustness image segmentation algorithm recovered based on low-rank provided in the embodiment of the present application, by low Order matrix recovers, and obtains the characteristic image of input picture.Characteristic image is split, it is to avoid make an uproar The impact on segmentation of the sound point.Make the segmentation containing noise image to input more accurate, finally obtain Obtain higher-quality segmentation image.

Accompanying drawing explanation

The overlap partition figure that Fig. 1 provides for the embodiment of the present invention；

The weight matrix figure that Fig. 2 provides for the embodiment of the present invention；

The subjective figure of the different dividing methods that Fig. 3 provides for the embodiment of the present invention；

The curve chart of the Precision-Recall of the different dividing methods that Fig. 4 provides for the embodiment of the present invention；

Fig. 5 for the embodiment of the present invention provide in the case of different noises, the curve of F-measure Figure.

Detailed description of the invention

The embodiment of the present application, by providing a kind of robustness image segmentation algorithm recovered based on low-rank, solves Quality and the technology of the subsequent processes of image that certainly in prior art, influence of noise image is split are asked Topic；Reach to avoid influence of noise, promote the technique effect of image segmentation quality.

For solving above-mentioned technical problem, the general thought of the embodiment of the present application offer technical scheme is as follows:

A kind of robustness image segmentation algorithm recovered based on low-rank, it is characterised in that: use low-rank empty Between decompose and obtain feature space image, cut method by figure based on minimal cut/max-flow, segmentation feature is empty Between image；Comprise the following steps:

Pending image division is become overlapped image block, will figure according to position during overlap partition As block changes into column vector matrix；

Use low-rank matrix restoration methods to process the column vector matrix of image block, obtain feature space image；

Cut method by figure based on minimal cut/max-flow, split feature space image.

By foregoing it can be seen that the robustness image segmentation algorithm recovered based on low-rank, solve During computer vision system obtains image, deposited by ambient noise, illumination and image The impact of storage, the quality causing major part image is relatively low, the problem that have impact on the segmentation quality of image. Low-rank spatial decomposition is utilized to obtain feature space image, it is thus achieved that more edge detail information；Then, The dividing method cut by figure based on minimal cut/max-flow, is split feature space image, obtains Obtain image segmentation result most preferably.

In order to be better understood from technique scheme, below in conjunction with Figure of description and concrete reality Technique scheme is described in detail by mode of executing, it should be understood that the embodiment of the present invention and embodiment In specific features be the detailed description to technical scheme rather than to present techniques side The restriction of case, in the case of not conflicting, the technical characteristic in the embodiment of the present application and embodiment can To be mutually combined.

See Fig. 1, a kind of robustness image segmentation recovered based on low-rank that the embodiment of the present invention provides Algorithm, it is characterised in that: use low-rank spatial decomposition to obtain feature space image, by based on minimum Cut/figure of max-flow cuts method, splits feature space image；Comprise the following steps:

Pending image division is become overlapped image block, will figure according to position during overlap partition As block changes into column vector matrix；

Use low-rank matrix restoration methods to process the column vector matrix of image block, obtain feature space image；

Cut method by figure based on minimal cut/max-flow, split feature space image.

To specifically introduce described method below.

The noise image of input is divided overlapped image block.Dividing mode according to from left to right, Order from top to bottom divides image block.When the edge of image division to image, it is divided into one not Whole piece, then just use rollback method to divide, i.e. when being divided into the right hand edge of image, with right hand edge On the basis of, take block to the left；When being divided into the edge, base of image, on the basis of edge, base, to On take block.

Assuming that the noise image inputted is z, size is M × N.Wherein M and N represents image respectively Length and width.It is d × d that image is taked overlap partition, piecemeal size.Overlapping block is

{Lⁿ(i,j)|1≤i≤M,1≤j≤N}

Wherein, (i j) represents the position coordinates of image block.To each image block L, (i j) uses k nearest Neighbors algorithm seeks its nearest node.And it is represented by column vector.All of column vector is formed square Battle array, represents with X.Matrix X contains the feature of destroyed image.

In step 2, for the column vector matrix X of image, it is converted into low-rank matrix and recovers problem, as Shown in formula (1).

$\begin{array}{ccc}\underset{L,E}{min}\left|\right|L|{|}_{*}+\mathrm{\λ}|\left|F\right|{|}_1& s.t.& X=L+E\end{array}---\left(1\right)$

Here, λ is weighting function.E is noise.The nuclear norm of L* representing matrix.I.e. matrix is all Singular value sum.||E||₁It it is the norm of matrix E.

Low-rank matrix X is carried out the low rank space solve, it is possible to use method of Lagrange multipliers.Such as formula (2) shown in.

$L(L,F,Y,\mathrm{\μ})=\left|\right|L|{|}_{*}+\mathrm{\λ}|\left|E\right|{|}_1+tr\[Y^T(X-L-F)\]+\frac{\mathrm{\μ}}{2}\left|\right|X-L-F|{|}_F^2---\left(2\right)$

Wherein, μ is positive scalar, and Y is Lagrange multiplier vector.

Formula (2) solves and can be decomposed into two subproblems: one is for fixing E, optimizes L；

Two is for fixing L, optimizes E.Optimize shown in formula such as formula (3) and formula (4).

$\begin{array}{c}L=\underset{L}{\arg }\left|\right|L|{|}_{*}+tr\[Y^T(X-L-E)\]+\frac{\mathrm{\μ}}{2}||X-L-E|{|}_F^2\\ =\underset{L}{\arg }\frac{1}{\mathrm{\μ}}\left|\right|L|{|}_{*}+\frac{1}{2}||L-(\frac{1}{\mathrm{\μ}}Y+X-E)|{|}_F^2\end{array}---\left(3\right)$

$\begin{array}{c}E=\underset{E}{\arg }\left|\right|E|{|}_1+tr\[Y^T(X-L-E)\]+\frac{\mathrm{\μ}}{2}||X-L-E|{|}_F^2\\ =\underset{E}{\arg }\frac{\mathrm{\λ}}{\mathrm{\μ}}\left|\right|E|{|}_1+\frac{1}{2}||E-(\frac{1}{\mathrm{\μ}}Y+X-L)|{|}_F^2\end{array}---\left(4\right)$

To low-rank matrix L and λ, when being optimized with formula (3) and formula (4), can make using the following method: First, Y=Y is initialized₀, E=E₀；When formula (2) is not restrained, update L according to formula (3)_k+1； According to formula (5), update E_k+1；According to formula Y_k+1=Y_k+μ(X-L_k+1-E_k+1), update Y； Then, make k ← k+1, until loop ends, export L_k, E_k。

In step 3, according to position when taking block, (i j), carries out split to low-rank matrix, obtains split Image x；When split, lap is arranged overlapping number of times, is weight matrix over_flag, Size is M × N, as shown in the figure.Can be in the hope of low-rank matrix L, i.e. characteristic image.Such as formula (5) Shown in.

L=x/over_flag (5)

In step 4, low-rank matrix L is mapped as figure G=(V, E).Need to add end points s and t, scheme G Cut set summit V is divided into two mutually disjoint subsets S and T, and s ∈ S, t ∈ T.Definition one Binary set Y=(the y of individual n dimension₁,y₂,…,y_p,…,y_||p||).Define its value: if v_i∈ S, then y_p=0, represent background；If v_i∈ T, then y_p=1, represent target；Vector y is with regard to correspondence image Segmentation result.Each binary set can a cut set of unique corresponding diagram G.According to figure G=(V, E), structure energy function E (y).As shown in formula (6).

$E\left(y\right)=\underset{\{p,q\}\∈N}{\Σ}{V}_{\{p,q\}(y_p,y_q)}+\mathrm{\λ}\underset{p\∈P}{\Σ}{D}_p\left(y_p\right)---\left(6\right)$

Wherein, Y={y_p| p ∈ L} is a labelling of figure G.D_p() is a penalty function.V_{p,q}{x_p,x_q} It is smooth item, the biggest to the discontinuous punishment between similar gray-scale pixels.P is based on prospect or background Seed points estimates the rectangular histogram obtained.P is summit, y_pIt it is mark value.

Formula (6) is solved, it is possible to use the method based on augmenting path that Boykov proposes. The method constantly grows into one tree by label, until can not find the augmenting path about feasible flow is Only.By two summit S and T, set up two search tree S and T.S is with source point as root, and T is to converge Point is root.In tree S, all father node points are all undersaturated to the limit of child's node, and node is divided into " main Dynamic " and " passively ".Active node can obtain new growth offspring by tree and make search tree " growing ", passive node can not grow.

Using after solving energy function (6), its value is vector Y=(y₁,y₂,…,y_p,…,y_||p||) institute right The minima of the minimal cut set correspondence energy function of the cost of the cut set answered, i.e. G, when energy function Hour, segmentation is optimum.Now, vector Y=(y₁,y₂,…,y_p,…,y_||p||) value obtain one Individual cut y, it is simply that required segmentation image.

The beneficial effect comprise that: recovered by low-rank matrix, obtain the feature of input picture Image.Characteristic image is split, it is to avoid the noise spot impact on segmentation.Make input Segmentation containing noise image is more accurate, the higher-quality segmentation image of final acquisition.

In order to make the purpose of the present invention, technical scheme and advantage clearer, below in conjunction with one Concrete example, is further elaborated to the present invention.Should be appreciated that tool described herein Body embodiment only in order to explain the present invention, is not intended to limit the present invention.

This experiment is with MATLAB R2013a as experiment porch,

Using data set is Berkeley partitioned data set and benchmark 300 (Berkeley Segmentation Data Set and Benchmarks 300,BSDS300).Choose 481 × 321 in Berkeley data base The standard testing image of pixel size is tested.Choose image in data base as test image, Meanwhile, by the image image as a comparison demarcated artificial in data base, the quality of segmentation quality is evaluated. Control methods choose in list of references [1] based on Optimal Boundary and the interactive mode of the target image in region Figure segmentation method (Graph Cuts) and list of references [2] image based on edge extracting and layering segmentation Method carries out splitting that (method individually selecting optimal threshold to split each image in literary composition is optimal Graphical rule, Optimal Image Scale, OIS).

Choose a test image, according to the method in step 1, be image block by test image division. For position (i, j) on each image block L (i, j) use k arest neighbors node algorithm seek its nearest node.? To column vector matrix X.According to formula (1), recover to express by low-rank matrix by low-rank matrix X.According to public affairs Formula (2) solves to (4), obtains low-rank matrix L_k.According to formula (5), according to when taking block position (i, j), Low-rank matrix is carried out split, obtains characteristic image L.Characteristic image L is mapped as figure G.According to public affairs Formula (6), structure energy function E (y).Use the method based on augmenting path that Boykov proposes, to public affairs Formula (6) solves.Vector Y=(y₁,y₂,…,y_p,…,y_||p||) value obtain one cut y, it is simply that required The segmentation image wanted.

Experiment presented below, illustrates the effectiveness of this method.

We take the appraisal procedure of general pattern, choose the recall ratio (Recall) of segmentation image, look into standard Rate (Precision) and F-measure, as objective evaluation index, quantify partitioning algorithm and manual segmentation figure The diversity of picture.Contrast algorithm is Graph Cuts in list of references [1], the OIS in list of references [2] Dividing method.Randomly select multiple images to test.To the image chosen, add varying strength Gaussian noise.Contrast algorithm is used to split.When splitting with context of methods, take optimum weight Folded block, splits containing noisy image.Being 0 for noise average, variance is the Gauss of 0.1 The image of noise, different dividing method subjectivity figures, the subjective figure of its edge extracting, as shown in Figure 3. The curve chart of the Precision-Recall of different dividing methods, as shown in Figure 4.At different noises In the case of, the curve chart of F-measure, as shown in Figure 5.

As can be seen from Figure 3, the image to interpolation noise, from subjective comparison, partitioning algorithm herein is more The result that adjunction person of modern times's work point cuts.The finest to the segmentation result of image.As for the first width figure Picture, Graph Cuts creates over-segmentation to aircraft, the part not being target image is also split. For the second width image, OIS creates segmentation deficiency to the segmentation of goose, not by the overall segmentation of goose Out.For the 3rd width image, therefore, the profile in three kinds of method all can completelys extraction target houses. But what context of methods was the most complete is extracted the profile in target house, also to being extracted more house Detail section.Therefore, the principal of dividing method has obtained good segmentation herein, and extracts More details.The overall segmentation effect making image is more preferable.

From fig. 4, it can be seen that be 0 for average, variance is the image of the Gaussian noise of 0.1, different The Precision-Recall value of dividing method different.Segmentation herein either from Recall, See on Precision, all preferable than other method.

From fig. 5, it can be seen that along with the continuous increase of noise, the F-measure of three kinds of dividing methods Value all can along with reduction, but, it is slow that the F-measure of dividing method herein reduces.I.e. exist Under equal noise situations, higher than the F-measure value of other dividing method.Due to F-measure Represent the comprehensive evaluation result of Precision and Recall, in the case of ensure that Recall, The value of Precision is the highest.Therefore, demonstrate from F-measure angle, dividing method herein Than other method segmentation effect on the best.

It should be noted last that, above detailed description of the invention is only in order to illustrate technical scheme And unrestricted, although the present invention being described in detail with reference to example, the ordinary skill people of this area Member should be appreciated that and can modify technical scheme or equivalent, without deviating from The spirit and scope of technical solution of the present invention, it all should be contained in the middle of scope of the presently claimed invention.

Claims (7)

1. the robustness image segmentation algorithm recovered based on low-rank, it is characterised in that: use low-rank Spatial decomposition obtains feature space image, cuts method by figure based on minimal cut/max-flow, splits feature Spatial image；Comprise the following steps:

Pending image division is become overlapped image block, will figure according to position during overlap partition As block changes into column vector matrix；

Use low-rank matrix restoration methods to process the column vector matrix of image block, obtain feature space image；

Cut method by figure based on minimal cut/max-flow, split feature space image.

2. the robustness image segmentation algorithm recovered based on low-rank as claimed in claim 1, its feature Being, the process of the column vector matrix that low-rank matrix restoration methods processes image block includes:

Column vector matrix to image block, uses low-rank matrix space to solve, obtains the block of low-rank matrix Matrix；

According to position when taking block, the block matrix of low-rank matrix is rebuild, obtains feature space figure Picture.

3. the robustness image segmentation algorithm recovered based on low-rank as claimed in claim 2, its feature Being, the described figure method of cutting based on minimal cut/max-flow includes:

Feature space image is mapped as figure, and seeks its energy function；

When the value of energy function minimizes, figure based on minimal cut/max-flow cuts method and just obtains figure A minimal cut, i.e. split image.

4. the robustness image segmentation calculation recovered based on low-rank as described in any one of claims 1 to 3 Method, it is characterised in that:

When dividing image block, according to a fixed-direction, divide image block；

Wherein, when being divided into edge and being divided into a whole image block not, just use rollback method, On the basis of edge, reversely take block.

5. the robustness image segmentation algorithm recovered based on low-rank as claimed in claim 4, its feature It is: to the image block L of pending image, (i j), uses K arest neighbors node algorithm to seek nearest node； And represent by column vector, all of column vector is formed matrix X.

6. the robustness image segmentation algorithm recovered based on low-rank as claimed in claim 5, its feature It is:

Described column vector formation matrix X is converted to low-rank matrix and carries out low-rank space and solve, obtains Block matrix L_k；

According to position when taking block, (i j), carries out split to low-rank matrix, obtains characteristic image L.

7. the robustness image segmentation algorithm recovered based on low-rank as claimed in claim 6, its feature Being, the described figure method of cutting based on minimal cut/max-flow includes:

Characteristic image L is mapped as figure, and seeks its energy function；

When the value of energy function minimizes, just obtain a minimal cut of figure, i.e. split image.