CN106251324B - A kind of Target Segmentation method based on the sparse shape representation of implicit nuclear space - Google Patents

A kind of Target Segmentation method based on the sparse shape representation of implicit nuclear space Download PDF

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CN106251324B
CN106251324B CN201610302391.1A CN201610302391A CN106251324B CN 106251324 B CN106251324 B CN 106251324B CN 201610302391 A CN201610302391 A CN 201610302391A CN 106251324 B CN106251324 B CN 106251324B
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姚劲草
于慧敏
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Zhejiang University ZJU
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    • G06V10/40—Extraction of image or video features
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    • G06—COMPUTING; CALCULATING OR COUNTING
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    • G06T2207/20076—Probabilistic image processing
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    • G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
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    • G06—COMPUTING; CALCULATING OR COUNTING
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Abstract

The sparse shape representation Target Segmentation method based on implicit nuclear space that the invention discloses a kind of carries out core principal Component Extraction to original prior shape training set first；It extracts result according to KPCA and establishes implicit nuclear shape space and construct and imply the sparse shape representation model of nuclear space；Construct the dual constraint item based on sparse coefficient and the bottom variation driving energy function based on probability shape；Objective function is solved using alternative iteration method；The variation energy function based on probability shape is supervised using implicit nuclear space shape rarefaction representation result to develop, and realizes image segmentation using evolution curve derived from energy function.The present invention overcomes Target Segmentation ability in the existing rarefaction representation dividing method based on shape neighbour is poor, the low problem of segmentation accuracy rate, to solve the problems, such as bad in original-shape domain progress rarefaction representation segmentation effect.

Description

A kind of Target Segmentation method based on the sparse shape representation of implicit nuclear space
Technical field
The present invention relates to image segmentations and shape representation field, more particularly to one kind is based on implicit nuclear space shape sparse table The Target Segmentation method shown.
Background technique
The expression and segmentation of target shape are one of the core missions in image procossing and computer vision.Current existing side Method can totally be divided into the shape segmentations method based on edge and the shape segmentations method based on region, these methods pass through fixed mostly An adopted variation energy function based on image, and the energy function is minimized to drive the evolution of pattern curve, to energy After function convergence, target area finally is marked using a curve based on energy function.This method is for target shape There is preferable segmentation effect than more complete situation, still, when target has defect, blocks or and background similar with target When noise adhesion, simple energy function of the solution based on image can not obtain satisfied segmentation result.With image processing techniques Development, the development trend of shape segmentations is had become in conjunction with the dividing method of priori knowledge.Target original-shape has been wrapped Different specific methods has been proposed in situation about being contained in prior shape library, many scholars, but in practical applications, often not Target original-shape can be obtained as priori knowledge, and some shapes similar with target (shape neighbour) can only be obtained, at this In the case of kind, how to establish a model restored using the shape neighbour of target target be blocked or the part polluted in recent years To have become the hot spot of research.
In view of searching for shape neighbour and using the combination of shape neighbour in priori shape library come approximate representation target Treatment process is consistent with the thought of rarefaction representation, and recent some scholars start to explore shape rarefaction representation technology.For example, based on dilute Dredge the Target Segmentation method of (SSC) of combination of shapes, V1 Target Segmentation method based on sparse coding etc..These methods are in original shape Shape space introduces rarefaction representation to realize Target Segmentation, they are using priori knowledge as a training shapes collection, for be split Target shape, in original-shape space search shape neighbour and sparse combination is constructed approximately to indicate target shape.These In place of method comes with some shortcomings, firstly, shape neighbour is searched in original-shape space when target has pollution and defect Effect is poor, while it is also possible to obtaining the neighbour of mistake to influence segmentation effect, secondly these methods usually assume that differentiation The sparse linear combination of shape and reference figuration be equivalent, and actual conditions are really not so；Therefore, it is necessary to one kind to be avoided that The rarefaction representation dividing method of shape neighbour noise, block, the factors such as background interference, target defect under the influence of Target Segmentation energy Power is poor, the Target Segmentation method of the low problem of segmentation accuracy rate.
Summary of the invention
(1) technical problems to be solved are to provide a kind of image partition method for being related to implying nuclear space rarefaction representation, should Method overcomes the bad problem of existing shape neighbor sparse representation segmentation fruit.
(2) technical solution
The purpose of the present invention is achieved through the following technical solutions:
Sparse shape representation Target Segmentation method provided by the invention based on implicit nuclear space, comprising the following steps:
S1: KPCA processing is carried out to training shapes collection；
S2: being based on KPCA processing result, establishes implicit nuclear shape space；
S3: the high-rise sparse representation model based on implicit nuclear shape space is established；
S4: establishing the bottom layer driving energy function based on probability shape, while establishing pair of bottom energy and high-rise energy It is coupled to connect item；
S5: initialization sparse coefficient and bottom probability shape model；
S6: antithesis is calculated using sparse coefficient and connects item；
S7: bottom energy function is optimized；
S8: bottom probability shape is mapped in high-rise sparse representation model, and sparse representation model is optimized and is obtained Obtain sparse coefficient；
S9: judge to export whether result meets required precision: if so, simultaneously according to the target shape of energy function output segmentation Terminate algorithm；If it is not, then return step S6.
Further, the implicit nuclear shape space in the step S2 is the convex implicit shape space ζ based on sparse combination, institute State shape space expression formula are as follows:
Wherein, matrixFor KPCA processing result, V are KPCA feature vector,For sparse coefficient；
qNIndicate n-th training sample；Indicate real number space；N indicates training set sample number；
ηPTo imply the arbitrary shape in shape space, (Ms)iFor i-th of element in sparse combination Ms.
Further, the sparse representation model in the step S3 is the sparse representation model of Hilbert space, the mould Type expression formula are as follows:
Wherein, γ is weighting coefficient, and φ is destination probability shape.
EH(s) implicit nuclear sparse expression total energy function is indicated；αTIndicate that KPCA maps weighting coefficient；K indicates kernel function.
Further, the antithesis in the step S4 connects item expression formula are as follows:
Wherein, EDItem is connected for antithesis；Q=[q1,q2,qi…,qN] ∈ I, qiFor binaryzation probability shape sample, N is shared A shape, I are original-shape space；It is normalization sparse coefficient.
Further, the bottom probability shape model, expression formula are as follows:
EI(x)=∫ ro(x)φ(x)dx+∫rb(x)(1-φ(x))dx；
Wherein, EIFor probability shape model；roIt is destination probability distribution, rbIt is background probability distribution, φ (x) is that target is general Rate shape.
Further, the bottom energy function merges antithesis connection item and probability shape model according to following formula:
EL(x)=EI(x)+βED(x)；
Wherein, ELFor bottom energy function；β is weighting coefficient.
(3) beneficial effect
Compared with the prior art and product, the present invention has the following advantages:
It is related to the image partition method of implicit nuclear space rarefaction representation the present invention provides a kind of, including to original priori shape Shape training set carries out core principal component (KPCA) and extracts；The implicit nuclear shape space of result foundation is extracted according to the KPCA and is constructed hidden Containing the sparse shape representation model of nuclear space；Construct the dual constraint item based on sparse coefficient and the bottom variation based on probability shape Driving energy function；Objective function is solved using alternative iteration method；Base is supervised using implicit nuclear space shape rarefaction representation result Develop in the variation energy function of probability shape, and realizes image segmentation using evolution curve derived from energy function.
The present invention overcomes existing based on the rarefaction representation dividing method of shape neighbour in noise, blocks, background interference, mesh Target Segmentation ability is poor under the influence of marking the factors such as defect, the low problem of segmentation accuracy rate, to solve to carry out in original-shape domain The bad problem of rarefaction representation segmentation effect；Target Segmentation problem is converted to training set shape in implicit nuclear space by this method Rarefaction representation problem, compared with traditional Target Segmentation, imply the sparse shape representation model of nuclear space to those large area carry on the back Scape adhesion, target part, which is blocked, can provide more reliable prior shape neighbor information and more preferable with the case where target part defect Segmentation result.
Bottom-up information is mapped to nuclear space and carries out rarefaction representation by this method simultaneously, and the result of rarefaction representation is recycled to supervise Bottom energy function carries out Target Segmentation, and this method can be realized simultaneously the identification and segmentation of target, rather than as traditional Method needs first to carry out preliminary classification or positioning to target, searches again for target shape neighbour.The present invention is using the double-deck energy function The case where target shape has part and global change relative to training set can be effectively treated in model, while supporting multi-class full-page proof This training set provides a kind of new model for multi-class Target Segmentation and rarefaction representation.
Detailed description of the invention
Fig. 1 is the Target Segmentation method flow diagram of the invention based on implicit nuclear shape space rarefaction representation.
Specific embodiment
Understand for the ease of those of ordinary skill in the art and implement the present invention, with reference to the accompanying drawing and specific embodiment The present invention is described in further detail.
Embodiment 1
As shown, the present embodiment provides a kind of sparse shape representation Target Segmentation method based on implicit nuclear space, packet Include following steps:
S1: KPCA processing is carried out to training shapes collection；
S2: being based on KPCA processing result, establishes implicit nuclear shape space；
S3: the high-rise sparse representation model based on implicit nuclear shape space is established；
S4: establishing the bottom layer driving energy function based on probability shape, while establishing pair of bottom energy and high-rise energy It is coupled to connect item；
S5: initialization sparse coefficient and bottom probability shape model；
S6: antithesis is calculated using sparse coefficient and connects item；
Antithesis connection item provided in this embodiment can be calculated in initial phase using initialization sparse coefficient, in iteration rank Section can return to sparse coefficient using last iteration and calculate)；
S7: bottom energy function is optimized；
S8: bottom probability shape is mapped in high-rise sparse representation model, and sparse representation model is optimized and is obtained Obtain sparse coefficient；
S9: judge to export whether result meets required precision: if so, simultaneously according to the target shape of energy function output segmentation Terminate algorithm；If it is not, then return step S6.
Implicit nuclear shape space in the step S2 is the convex implicit shape space ζ based on sparse combination, the shape Spatial expression are as follows:
Wherein, matrixFor KPCA processing result, V are KPCA feature vector,For sparse coefficient；
qNIndicate n-th training sample；Indicate real number space；N indicates training set sample number；
ηPTo imply the arbitrary shape in shape space, (Ms)iFor i-th of element in sparse combination Ms.
Sparse representation model in the step S3 is the sparse representation model of Hilbert space, the model expression Are as follows:
Wherein, γ is weighting coefficient, and φ is destination probability shape.
EH(s) implicit nuclear sparse expression total energy function is indicated；αTIndicate that KPCA maps weighting coefficient；K indicates kernel function.
Antithesis in the step S4 connects item expression formula are as follows:
Wherein, EDItem is connected for antithesis；Q=[q1,q2,qi…,qN] ∈ I, qiFor binaryzation probability shape sample, N is shared A shape, I are original-shape space；It is normalization sparse coefficient.
The bottom probability shape model, expression formula are as follows:
EI(x)=∫ ro(x)φ(x)dx+∫rb(x)(1-φ(x))dx；
Wherein, EIFor probability shape model；roIt is destination probability distribution, rbIt is background probability distribution, φ (x) is that target is general Rate shape.
The bottom energy function merges antithesis connection item and probability shape model according to following formula:
EL(x)=EI(x)+βED(x)；
Wherein, ELFor bottom energy function；β is weighting coefficient.
Embodiment 2
The present embodiment establishes bi-layer segmentation mould while constructing implicit nuclear shape space and implicit nuclear space rarefaction representation Type frame；Specific step is as follows for the bi-layer segmentation model framework:
A it) obtains image data and KPCA processing is carried out to training shapes collection；
B it) is based on KPCA processing result, establishes implicit nuclear shape space；
C the high-rise rarefaction representation based on implicit nuclear shape space) is established；
D driving energy function of the bottom based on probability shape) is established, while establishing the antithesis of bottom energy and high-rise energy Connect item；
E sparse coefficient) is initialized, bottom probability shape is initialized；
F) antithesis connection item is calculated as the constraint of bottom function using sparse coefficient；
G) bottom energy function is optimized；The bottom energy function is solved using conventional gradients descent method, Middle conventional gradients descent method is classical mature equation calculation method.
H) bottom probability shape is mapped in high-rise sparse representation model, and sparse representation model optimize and is obtained Obtain sparse coefficient；
I) judge to export whether result meets required precision: if so, output target shape, terminates algorithm；If it is not, then returning Step F.
Wherein, step A) in training set carry out KPCA processing include, establish input training shapes collection:
Q=[q1, q2..., qN]∈I；
Wherein, qiFor binaryzation probability shape sample, N number of shape is shared, I is original-shape space；
Define Nonlinear Mapping
Wherein, F is Hilbert space, then according to kernel method principle, there are equations Wherein k () is kernel function,Indicate mapping function.
According to core principle component analysis principle, demand solution characteristic equation λ V=CV, wherein V is feature vector, and λ is characterized value, C For cross-correlation matrix.Since Matrix C can not directly acquire, usual structural matrix K, wherein matrix element Pass through characteristics of decomposition equationAvailable KPCA parameter alpha=[α1,…,αn], whereinThen core Spatial signature vectors are represented byFor arbitrarily inputting shape q, defineThen Nuclear space mapping can be expressed as
Step B) in construct implicit nuclear shape space include structural matrixWhereinConstruct sparse coefficientImplicit shape space ζ is constructed simultaneously such as Under:
Wherein, ηPTo imply the arbitrary shape in shape space, (Ms)iFor i-th of element in sparse combination Ms；This reality The implicit shape space ζ for applying example construction is convex set, and reason is as follows:
Given parameters γ ∈ [0,1], for any two shape There is following equation establishment:
IfDue toThenIt can thus be concluded thatMeet Convex set definition, therefore ζ is a convex set.
Wherein, step C) in high-rise sparse representation model, including tectonic model energy letter are established in implicit shape space ζ Number EHIt is as follows:
Wherein, γ is weighting coefficient,It indicates to be based on rarefaction representation energy function；Indicate the nuclear mapping of destination probability shape.It can not be straight although parent Spatial Dimension is unknown It connects and establishes sparse representation model, but it can be proved that in the sparse representation theory proposed by the present invention based on implicit nuclear shape space It is equivalent to the rarefaction representation of protokaryon space reflection shape.Reason is as follows:
According to such as giving a definition:
According to the Mercer theorem of kernel method,Then
It include two subitems in the first sport of above-mentioned formulaWithObviously such as Fruit training set is given, and first subitem will be completely fixed, and the minimum of energy function will depend entirely on second subitemThis obvious subitem is equivalent to use under sparse constraintIt indicatesIt is equivalent in original Beginning nuclear space carries out rarefaction representation.
Therefore, the rarefaction representation proposed by the present invention based on implicit nuclear shape space can be used as original nuclear space sparse table The alternative model shown.
Step D) in propose establish antithesis item EDIt is as follows:
Wherein, Q is binaryzation training set,It is normalization sparse coefficient；
The probability shape model expression that the bottom layer image energy function of the present embodiment uses is as follows:
EI(x)=∫ ro(x)φ(x)dx+∫rb(x)(1-φ(x))dx；
Wherein, roIt is destination probability distribution, rbIt is background probability distribution, φ (x) is destination probability shape.
Merging two energy functions is EL；
EL(x)=EI(x)+βED(x)；EL(x)=EI(x)+βED(x) weighting coefficient is indicated；
Step E) in, initializationInitialization bottom shape is average shape
Step F) it obtainsCalculate antithesis item ED, and result is fed back to energy function ELIn.
Step G) utilize conventional gradients descent method to ELIt optimizes and obtains new probability shape φ (x)；
Step H) bring φ (x) into EH(s), and using conventional gradients descent method and Soft thresholding to EH(s) it optimizes and obtains Obtain s newly；
Step J) in class between residual error is defined as:
Wherein, Θτ() expression formula are as follows:
Wherein, e (s, x) indicates residual error function,Indicate that threshold function table, x indicate each pixel Probability value, τ are probability threshold value.When residual error e (s, x) is smaller or requires lower than the residual error of setting, segmentation is completed.
Above embodiments are only one embodiment of the present invention, and the description thereof is more specific and detailed, but cannot therefore and It is interpreted as limitations on the scope of the patent of the present invention.Its specific structure and size can be adjusted correspondingly according to actual needs.It answers When, it is noted that for those of ordinary skill in the art, without departing from the inventive concept of the premise, can also make Several modifications and improvements, these are all within the scope of protection of the present invention.

Claims (5)

1. a kind of sparse shape representation Target Segmentation method based on implicit nuclear space, which comprises the following steps:
S1: KPCA processing is carried out to training shapes collection；
S2: being based on KPCA processing result, establishes implicit nuclear shape space；
S3: the high-rise sparse representation model based on implicit nuclear shape space is established；
S4: establishing the bottom layer driving energy function based on probability shape, while establishing bottom energy with high-rise energy to coupled Connect item；
S5: initialization sparse coefficient and bottom probability shape model；
S6: antithesis is calculated using sparse coefficient and connects item；
S7: bottom energy function is optimized；
S8: bottom probability shape is mapped in high-rise sparse representation model, and it is dilute to optimize acquisition to sparse representation model Sparse coefficient；
S9: judge to export whether result meets required precision: if so, according to the target shape of energy function output segmentation and end Algorithm；If it is not, then return step S6；
Wherein, the implicit nuclear shape space in the step S2 is the convex implicit shape space ζ based on sparse combination, the shape Spatial expression are as follows:
Wherein, matrixAt KPCA Reason as a result, V be KPCA feature vector,For sparse coefficient；
qNIndicate n-th training sample；Indicate real number space；N indicates training set sample number；
ηPTo imply the arbitrary shape in shape space, (Ms)iFor i-th of element in sparse combination Ms.
2. the sparse shape representation Target Segmentation method according to claim 1 based on implicit nuclear space, which is characterized in that Sparse representation model in the step S3 is the sparse representation model of Hilbert space, the model expression are as follows:
Wherein, γ is weighting coefficient, and φ is destination probability shape；
EH(s) implicit nuclear sparse expression total energy function is indicated；αTIndicate that KPCA maps weighting coefficient；K indicates kernel function.
3. the sparse shape representation Target Segmentation method according to claim 1 based on implicit nuclear space, which is characterized in that Antithesis in the step S4 connects item expression formula are as follows:
Wherein, EDItem is connected for antithesis；Q=[q1,q2,…,qN] ∈ I, qiFor binaryzation probability shape sample, N number of shape is shared, I is original-shape space；It is normalization sparse coefficient.
4. the sparse shape representation Target Segmentation method according to claim 3 based on implicit nuclear space, which is characterized in that The bottom probability shape model, expression formula are as follows:
EI(x)=∫ ro(x)φ(x)dx+∫rb(x)(1-φ(x))dx；
Wherein, EIFor probability shape model；roIt is destination probability distribution, rbIt is background probability distribution, φ (x) is destination probability shape Shape.
5. the sparse shape representation Target Segmentation method according to claim 4 based on implicit nuclear space, which is characterized in that The bottom energy function merges antithesis connection item and probability shape model according to following formula:
EL(x)=EI(x)+βED(x)；
Wherein, ELFor bottom energy function；β is weighting coefficient.
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