CN104091332A - Method for optimizing multilayer image segmentation of multiclass color texture images based on variation model - Google Patents

Abstract

The invention discloses a method for optimizing double-layer image segmentation of multiclass color texture images based on a variation model. The method comprises the steps of establishing a multiclass variation active contour model, obtaining an energy function of the multiclass variation active contour model, carrying out disperse expression on the energy function of the multiclass variation active contour model, establishing a multilayer image segmentation model, solving the energy function of the multiclass variation active contour model after disperse expression to obtain a globally near optimal solution, and carrying out multi-layer image segmentation minimality optimization on multiclass disperse variation active contour energy in an iteration mode to achieve stable segmentation.

Description

Multiclass color texture image multilayer figure based on Variation Model cuts optimization dividing method

Technical field

The invention belongs to technical field of image processing, be specifically related to a kind of multiclass color texture image dividing method based on variation movable contour model.

Background technology

At present, image partition method based on Variation Model has been subject to paying close attention to widely, because it can provide the curve of smooth sealing, and can be widely used in vision in conjunction with prior imformation obtains the non-homogeneous object boundary of expecting follows the tracks of, target detection, scene is understood, industrial detection, CBIR, and the field such as medical image analysis.Owing to comprising the target area of multiple non-homogeneous in image, although, there are a lot of scholars to propose the dividing method of multiclass, but they are all to adopt constant density to describe, and adopt mutual mode target-marking region or sub-goal region, cause the result of cutting apart to depend on to a great extent prior imformation, and for Video segmentation task, mutual partitioning scheme is frowzily superfluous, time-consumingly, or even be difficult to be competent at.Therefore be, still challenging with open studying a question based on Variation Model without supervision multiclass color texture image dividing method.

Image partition method based on Variation Model is mainly divided into two classes: the method based on limit and the method based on region.Method based on limit is mainly to utilize the partial gradient of image to attract active contour to evolve towards the edge direction of image.Although, these methods based on limit can obtain good segmentation result under specific applied environment, and still, they are more responsive to the placement location of initial point and profile, and for different initial positions, may obtain different interesting target segmentation results.In addition, these class methods are easily subject to the interference of noise, under the constraint that there is no global information, still rest in a way for correctly catching of border, various target area in color texture image, and it is difficult to obtain satisfied boundary segmentation result.Its hypothesis of method based on region is homogeneity in the statistics density of each intra-zone, relies on overall information to carry out the evolution of boot activity profile, the method based on limit relatively, and it is insensitive to the initial profile of placing, and has stronger noise resisting ability.But the method based on region is in the time cutting apart natural image complicated and changeable, easily there is false target area in the result of finally cutting apart, and the object edge of catching is smooth not, if the method based on limit is combined with the method based on region, it can obtain good segmentation result.Adopt K-Means to carry out the statistical computation of multiple constant cluster centres but demarcate region corresponding to color for every kind, may cause the feature distribution of multiple target areas to describe unstable.The more important thing is, for color texture image complicated and changeable, adopt the constant cluster centre of this multistage hypothesis, it is difficult in Description Image, to have non-linear and successional changing features.

Summary of the invention

The object of this invention is to provide a kind of multiclass color texture image multilayer figure based on Variation Model and cut optimization dividing method, by edge item, area item, geodesic active contour item, and the description of continuity probability density combines, the minimal cut that multiclass variation movable contour model is converted into multilayer figure and cuts model, can effectively overcome above-mentioned relevant issues.

The technical solution adopted in the present invention is that a kind of multiclass color texture image multilayer figure based on Variation Model cuts optimization dividing method, specifically implements according to following steps:

Step 1, set up the continuous variation movable contour model of multiclass, obtain multiclass variation movable contour model energy function;

Step 2, utilize Cauchy-Crofton theory to carry out discrete expression to the multiclass variation movable contour model energy function obtaining in step 1, obtain the class variation movable contour model energy function that discretize is expressed;

Step 3, set up multilayer figure and cut model, the multiclass variation movable contour model energy function that the discretize in step 2 is expressed solves, and obtains Approximate Global Optimal Solution;

The mode of step 4, employing iteration is carried out the optimization of multilayer figure minimal cut to the discrete variation active contour energy of multiclass, realizes stable cutting apart.

Feature of the present invention is also,

Setting up the continuous variation movable contour model of multiclass specifically implements according to following steps:

Step 1.1, for a width color texture image, be designated as u ₀, the image area of its correspondence is designated as: Ω: R ²→ R, the cut zone border subset that Ω is corresponding is C, it is by color texture image u ₀be divided into the subregion Ω that several are not connected _j, and meet: and wherein N (Ω) represents all disconnected cut zone numbers, and j represents the subscript of cut zone, i.e. region Ω _jinside constant c _jdescribe;

Step 1.2, employing multivariate Gaussian distribution are to each Ω _jportray in region, sets up the continuous movable contour model energy function of initial multiclass:

Wherein, K _phoseit is total category regions number;

it is edge item;

K region, uses Gaussian distribution Θ _k={ α _k, u _k, ∑ _kwherein u is described _kk region Ω _kmean vector, ∑ _kcorresponding covariance matrix, it is the weight in k class region; The dimension of D representative feature;

For effective number of regions K _phoseand relevant statistical parameter Θ _k={ α _k, u _k, ∑ _kinitialization, utilize GMM to carry out probability density distribution modeling to image;

Step 1.3, geodesic active contour is expanded in the edge item constraint of the continuous variation movable contour model of multiclass, obtain multiclass variation movable contour model;

Be specially: by geodesic active contour model expand to the edge item in formula (1) obtain multiclass variation movable contour model energy function:

Wherein, for k region Ω _k, use Gaussian distribution Θ _k={ α _k, u _k, ∑ _kcarry out probability density description, wherein u _kk region Ω _kmean vector, ∑ _kcorresponding covariance matrix, it is the weight in k class region.

Utilize Cauchy-Crofton theory to carry out discrete expression to the multiclass variation movable contour model energy function obtaining in step 1, specifically implement according to following steps:

Step 2.1, by image u ₀be expressed as two-dimentional trrellis diagram

M={m (i, j) | i ∈ 1,2 ..., W}, j ∈ 1,2 ..., and H}}, W and H distinguish the wide and high of representative image, introduce auxiliary function , it meets formula below,

For two-dimentional table images M, suppose that corresponding to the class label of m position be ψ (m), the label figure that M is corresponding be defined as ψ (m) | ψ (m) ∈ 1,2 ..., K _phose∩ m ∈ M};

Step 2.2, by the area item in multiclass variation movable contour model energy function, the discrete E1 that turns to, is specially:

If $p_{k,m}=\frac{1}{{\left(\sqrt{2\mathrm{\π}}\right)}^{(D+4)/2}{\left|{\mathrm{\Σ}}_k\right|}^{1/2}}\exp [-\frac{1}{2}{(u_0\left(m\right)-u_k)}^T{\mathrm{\Σ}}_k^{-1}(u_0\left(m\right)-u_k)],$ It has described color texture feature to the probability similarity degree that is under the jurisdiction of k class region, probability similarity is got to negative logarithm, i.e. E ₁abbreviation is

Step 2.3, for the edge item of multiclass variation energy function, the cutting cost of Euclid's boundary length is converted into the cutting cost of network flow graph, concrete Proof Equivalence and discretize represent, specifically implement according to following steps:

Step 2.3.1, for the boundary curve C of the continuous active contour of multiclass, utilize Cauchy-Crofton formula to carry out the length of curve of approximation all straight lines on two dimensional surface are expressed as { (ρ, θ) | xcos (θ)+ysin (θ)=ρ }, Euclid's length of boundary curve C | C| _ebe expressed as:

${\left|C\right|}_E=\frac{1}{2}\underset{-\∞}{\overset{+\∞}{\∫}}\underset{0}{\overset{\mathrm{\π}}{\∫}}{n}_c(\mathrm{\ρ},\mathrm{\θ})\mathrm{d\ρd\θ}$

N _c(ρ, θ) represents straight line xcos (θ)+ysin (the θ)=ρ total degree crossing with boundary curve C on two dimensional surface, and wherein (ρ, θ) is corresponding to a parallel family of straight lines;

Step 2.3.2, for Q=n _gwhen neighborhood, space plane neighborhood system corresponding to two-dimentional trrellis diagram is expressed as N _q={ e _k| 0≤k≤n _g, the angle between two vectors of arest neighbors is made as utilize Cauchy-Crofton formula approximate treatment length of curve | C| _e, Euclid's length is utilized discrete the turning to of lattice point in Q field:

${\left|C\right|}_E=\underset{k=1}{\overset{n_0}{\mathrm{\Σ}}}{n}_c\left(k\right)\frac{{\mathrm{\δ}}^2\·{\mathrm{\Δ\θ}}_k}{2\·\left|e_k\right|}$

Here, | e _k| be illustrated in the length of direction vector in two-dimentional trrellis diagram, suppose that family of straight lines corresponding to equidirectional vector has identical weight | C| _efurther abbreviation is

${\left|C\right|}_E=\underset{k=1}{\overset{n_0}{\mathrm{\Σ}}}{n}_c\left(k\right)\·{\mathrm{\ω}}_k$

The network flow graph G=(V, E, W) of step 2.3.3, two dimension, wherein V is the vertex set of trrellis diagram, and E is the set on border, and W is the non-negative weight set corresponding to limit collection E; In V, comprise two special end points S, T, according to cutting criterion, boundary curve C cuts S and T open, and corresponding cost is expressed as | C| _g,

Here (m, n) presentation graphs cuts the limit that G is cut open by boundary curve C in Q neighborhood, and the limit weight of its correspondence is w _{m, n}, and | C| _grepresent the cutting cost of boundary curve C; Due to | C| _ewith | C| _gall represent the cutting cost of boundary curve C, the in the situation that of two dimensional surface discretize, their approximately equals | C| _e≈ | C| _g

Step 2.3.4, cut the boundary curve C of multiple cut zone that G is corresponding and corresponding discrete the turning to of Q neighborhood label according to figure

Here N, _q(m) represent the Q field point set that m is ordered, utilize above-mentioned formula by the edge item energy function E of multiclass variation movable contour model energy function in step 1 ₂discrete turning to:

The discretize of the multiclass variation movable contour model energy of step 2.4, interpolation anti-noise constant is expressed as:

The multiclass variation movable contour model energy that discretize in step 2 is expressed solves, and specifically implements according to following steps:

Step 3.1, a multilayer figure G=of structure (V, E, W), its corresponding two-dimentional trrellis diagram M of every one deck, each the some m above it is corresponding to color texture image u ₀a pixel, multilayer figure G is just corresponding to a three-dimensional trrellis diagram, it is defined as { (l, m) ∈ R ²× R|l ∈ 1,2 ..., K _phose-1}, m ∈ M}; Be shown v for any one lattice point (l, m) on multilayer figure _{l, m}, the limit e (v between adjacent two layers figure _{l, m}, v _{l+1, m}) represent t-link, be positioned at the limit e (v in same layer trrellis diagram _{l, m}, v _{l, n}) expression n-link; In the process of structure multilayer figure G, vertex set V is expressed as discrete multiclass energy function area item energy E ₁with edge item energy E ₂, with the summit in vertex set V, be expressed as t-link limit collection E _dwith n-link limit collection E _s;

Step 3.2, for area item limit collection E _dit is expressed as:

E _D＝∪{E _m|m∈M}，

$E_m=e(s,v_{1,m}){\∪}_{l=1}^{K_{\mathrm{Phose}}-2}e(v_{l,m},v_{l+1,m})\∪e(v_{K_{\mathrm{phose}}-1,m},t)$

In multilayer figure G, weight corresponding to data item limit is made as w (e (v _{l, m}, v _{l+1, m})), the weights of its correspondence are:

${\mathrm{\α}}_{l+1}\·-\log \left(p_{l+1,m}\right)=$

$-{\mathrm{\α}}_{l+1}\·\log \left(\frac{1}{{\left(\sqrt{2\mathrm{\π}}\right)}^{(D+4)/2}{\left|{\mathrm{\Σ}}_k\right|}^{1/2}}\exp \right[-\frac{1}{2}{(u_0\left(m\right)-u_{l+1})}^T{{\mathrm{\Σ}}_{l+1}}^{-1}(u_0\left(m\right)-u_{l+1})\left]\right)$

It is for the region similarity cluster of textural characteristics;

Step 3.3, item limit, edge collection E _sbe expressed as: E _s={ e (v _{l, m}, v _{l, n}) | l ∈ 1,2 ..., K _phose-1), m, n ∈ M ∩ n ∈ N _q(m) }

Limit e (v _{l, m}, v _{l, n}) corresponding weight is

Step 3.4, utilize the multiclass variation movable contour model energy function that discretize that max-flow/minimal cut obtains step 2 is expressed to solve.

Adopt the mode of iteration to optimize the discrete variation active contour energy of multiclass is carried out to the optimization of multilayer figure minimal cut and specifically implement according to following steps:

Step 4.1, after t iteration cut apart, between adjacent twice iteration, the not variability of label area is it is calculated as follows:

Here, | total pixel count of M| representative image, not variability be made as 0, the not variability of the overall label area of image in adjacent twice iteration cutting procedure has been described;

Step 4.2, the probability density otherness of the different label areas of class is described by KL divergence distance, when t iteration, image M is corresponding class probability density interval is made as every class label area utilizes a multivariate Gauss Gaussian ^(t)(k) distribute and describe, the statistic of its correspondence is Θ ^(t) _k={ α ^(t) _k, u ^(t) _k, ∑ ^(t) _k, utilize KL divergence to calculate, establishing k class is D to the KL divergence distance of n class ^(t)(k, n), is calculated as:

$D^{\left(t\right)}(k,n)=\mathrm{KL}\left({\mathrm{Gaussian}}^{\left(t\right)}\left(k\right)\right|\left|{\mathrm{Gaussian}}^{\left(t\right)}\left(n\right)\right)$

$=\frac{1}{2}[\log \frac{\left|{\mathrm{\Σ}}_n^{\left(t\right)}\right|}{\left|{\mathrm{\Σ}}_k^{\left(t\right)}\right|}+\mathrm{tr}\left({\mathrm{\Σ}}_n^{\left(t\right)-1}{\mathrm{\Σ}}_k^{\left(t\right)}\right)+{({\mathrm{\μ}}_k^{\left(t\right)}-{\mathrm{\μ}}_n^{\left(t\right)})}^T{\mathrm{\Σ}}_n^{\left(t\right)-1}({\mathrm{\μ}}_k^{\left(t\right)}-{\mathrm{\μ}}_n^{\left(t\right)})]$

For the probability density interval of whole image M utilize any class in class arrives other the minimum KL divergence distance value sum of class represents,

$E_{\mathrm{KL}}^{\left(t\right)}=\underset{k=1}{\overset{K_{\mathrm{Phose}}^{\left(t\right)}}{\mathrm{\Σ}}}\underset{k\∈\{1,...,K_{\mathrm{Phose}}^{\left(t\right)}\}\∩\{k\≠n\}}{{\mathrm{\α}}_k^{\left(t\right)}\·\mathrm{Min}}{D}^{\left(t\right)}(k,n)$

Step 4.3, for image M the t time with the t-1 time between corresponding probability density rate of change be made as it utilizes the normalization probability density interval difference of adjacent twice iteration to calculate:

${\mathrm{\ΔE}}_{\mathrm{KL}}^{\left(t\right)}=\exp (-\frac{|E_{\mathrm{KL}}^{\left(t\right)}-E_{\mathrm{KL}}^{(t-1)}|}{E_{\mathrm{KL}}^{\left(t\right)}})$

And overall label variations and probability density variation utilize step 4.1 and the formula in step 4.2 to carry out the crossing process of co-controlling iteration, Intersection is differentiated as follows:

$E_L^{\left(t\right)}\≥{\mathrm{\β}}_1\mathrm{and\Δ}{E}_{\mathrm{KL}}^{\left(t\right)}\≥{\mathrm{\β}}_2$

Wherein β ₁with β ₂be convergence controlling elements, be respectively used to label and probability density to differentiate, and realize the termination of iteration cutting procedure.

The invention has the beneficial effects as follows: the edge item of (1) multiclass variation active contour has been introduced the geodesic active contour of rim detection ability, therefore, this method has stronger edge detection ability, there is stronger anti-noise jamming and shade ability, can catch and there is darker matrix limit and convex limit.(2) adopted the probability density similarity information between global information and the regional area of label area, the edge smoother in multiclass segmentation tag region, can adaptive termination cutting procedure, and cutting procedure speed of convergence is very fast.(3) the minimal cut problem of cutting model by the minimization problem of multiclass energy function is converted into multilayer figure, utilizes max-flow/minimal cut theory to try to achieve overall approximate optimal solution, can carry out overall near optimal to multiclass energy function and solve.

The multiclass color texture image multilayer figure dividing method based on Variation Model that the present invention proposes, the curve of smooth sealing can be provided, there is stronger antinoise and the ability of shade, and non-linear linearity and continuity probability density descriptive power, therefore there is actual environment using value and researching value widely.For example, in field of video monitoring, by scene and pedestrian are cut apart, extract ROI (Region of Interesting) region, in conjunction with the relevant knowledge such as machine learning and machine intelligence, the important areas such as bank, government department, airport are monitored in real time, reduced to greatest extent security risk, promote the confidence of people to public safety.In word identification, form, figure and character block all need to be split to extract accurately text message.At intelligent transportation field, by being partitioned into vehicle and pedestrian's object carrys out bulk density, and further analyze the jam situation of traffic, for emergency traffic management and dispatching provides traffic data reliably.Meanwhile, can be partitioned into vehicle and license board information in conjunction with tracking technique, judge hypervelocity, suspect vehicle or the traffic violation, for great accident, provide accurately in violation of rules and regulations, data in violation of rules and regulations quickly and efficiently.In military field, SAR (Synthetic Aperture Radar) diameter radar image is carried out to Target Segmentation, by target recognition and tracking, improve precise guidance and the striking capabilities of guided missile.At agriculture field, by satellite remote sensing images is carried out to Region Segmentation, improve disease and insect resistance to crops, drought-resistant, and strengthen the supervision of the outdoor growing state of crop.In living things feature recognition field, need to cut apart biometric image, thereby further face, fingerprint and iris etc. be identified.

Brief description of the drawings

Fig. 1 is 4 neighborhood discrete length approximate diagram of boundary curve of the present invention;

Fig. 2 is space 4 neighborhood system figure of the present invention;

Fig. 3 is 8 neighborhood discrete length approximate diagram of boundary curve of the present invention;

Fig. 4 is space 8 neighborhood system figure of the present invention;

Fig. 5 is 16 neighborhood discrete length approximate diagram of boundary curve of the present invention;

Fig. 6 is space 16 neighborhood system figure of the present invention;

Fig. 7 is the illustration of the present invention's 4 class color texture images;

Fig. 8 is that 3 layers of figure that the present invention's 4 class color texture images are corresponding cut illustraton of model;

Fig. 9 is the credible and insincere judgement figure of cutting apart that multilayer figure of the present invention cuts model.

Embodiment

Below in conjunction with the drawings and specific embodiments, the present invention is described in detail.

The invention provides a kind of multiclass color texture image multilayer figure based on Variation Model and cut optimization dividing method, specifically implement according to following steps:

Step 1, set up the continuous variation movable contour model of multiclass, obtain multiclass variation movable contour model energy function; Specifically implement according to following steps:

Step 1.1, for a width color texture image, be designated as u ₀, the image area of its correspondence is designated as: Ω: R ²→ R, the cut zone border subset that Ω is corresponding is C, it is by color texture image u ₀be divided into the subregion Ω that several are not connected _j, and meet: and wherein N (Ω) represents all disconnected cut zone numbers, and j represents the subscript of cut zone, for image u ₀it is often assumed to be multiclass, and supposes that the result that image is cut apart is the region of piecewise constant, i.e. region Ω _jinside constant c _jdescribe;

Non-linear and the continuity of intra-zone can be effectively portrayed in the description at step 1.2, this constant density center.In actual applications, because most features meet Gaussian distribution, in order to describe more accurately each non-homogeneous target area, the present invention adopts multivariate Gaussian distribution to each Ω _jportray in region, and set up the continuous movable contour model energy function (MSACM) of initial multiclass:

Here, the continuous movable contour model of multiclass can be described the continuous active contour of multiclass, for each category regions Ω _jit is continuous that inner feature distribution is described, the dimension of D representative feature; K _phosebe total category regions number, it is for total number of picture engraving non-homogeneous target area.For k region, use Gaussian distribution Θ _k={ α _k, u _k, ∑ _kwherein u is described _kk region Ω _kmean vector, ∑ _kcorresponding covariance matrix, it is the weight in k class region.For effective number of regions K _phoseand relevant statistical parameter Θ _k={ α _k, u _k, ∑ _kinitialization, can utilize gauss hybrid models (Gaussian Mixture Model, GMM) to carry out probability density distribution modeling to image.

In step 1.3, step 1.2 although edge item has carried out the constraint of edge length, but it is for having concavity border, shadow interference, and fuzzy zone boundary, it lacks effective edge capture ability, and the multiclass movable contour model that causes formula (1) to propose easily sinks into local minimum.And the geodesic active contour that Caselles proposes,

C (s) represents the parametrization boundary curve of cutting apart, and g (C (s)) represents boundary curve to carry out geodesic line detection, and it is monotone decreasing function.

It is the snake model of simplifying, owing to thering is less parameter, and insensitive to initial active profile, and be widely used in various image processing, and it can allow active contour evolve and obtain the minimum value of energy function along the direction of edge normal.

Step 1.4, there is good edge capture ability for Geodesic active contour in formula (2), the edge item constraint in the MSACM model energy function that its expansion can be proposed for step 1.3, new multiclass variation movable contour model is:

Wherein, refer to area item, refer to edge item, it is the part that edge combines with geodesic active contour.

For k region Ω _k, use Gaussian distribution Θ _k={ α _k, u _k, ∑ _kcarry out probability density description, wherein u _kk region Ω _kmean vector, ∑ _kcorresponding covariance matrix, it is the weight in k class region.

Here, be edge decision-making subtraction function, it detects for the gradient at edge, and the value corresponding in target area edge is less, and is 1 in inner its value in the target area of approximate homogeneity.This means for the feature of non-boundary and there is larger penalty value, for ensure to converge on object edge at the process active contour of cutting apart as far as possible, and mutually combining by area item and edge item, ensure that the border that final active contour is corresponding is as far as possible smooth, the finally real border of target acquisition accurately, and improve the overall descriptive power in homogeneity texture object region.

Step 2, utilize Cauchy-Crofton theory to carry out discrete expression to the multiclass variation movable contour model energy function obtaining in step 1, obtain the class variation movable contour model energy function that discretize is expressed;

The thought of this step is:

(2-1) two dimensional image is carried out to discretize trrellis diagram and represent, the label area of simultaneously introducing trrellis diagram detects auxiliary function, for area item and the edge item discretize of continuity multiclass Variation Model are prepared.

(2-2) build different space field systems, the edge length of continuously active profile is carried out to the discretize length computation under different field system.For the boundary curve C of the continuous active contour of multiclass, can utilize Cauchy-Crofton formula to carry out the length of curve of approximation and corresponding to different field system, boundary curve C corresponding family of straight lines on two dimensional surface can be expressed as { (ρ, θ) | xcos (θ)+ysin (θ)=ρ }, and can further calculate Euclid's length of continuum boundary curve C | C| _e.

(2-3) consider two-dimentional network flow graph G=(V, E, W), wherein V is the vertex set of trrellis diagram, and E is the set on border, and W is the non-negative weight set corresponding to limit collection E.In V, comprise two special end points S, T, according to cutting criterion, boundary curve C cuts S and T open, and corresponding cost can be expressed as | C| _g, it represents the cutting cost of boundary curve C.Due to Euclid's length of continuum boundary curve C | C| _ewith | C| _gall represent the cutting cost of boundary curve C, the in the situation that of two dimensional surface discretize, their approximately equals | C| _e≈ | C| _g.

(2-4) cut the boundary curve C of multiple cut zone that G is corresponding and the Q neighborhood label of correspondence according to figure, area item and the edge item of multiclass variation continuously active skeleton pattern in formula (3) are carried out to discretize expression.

As shown in Fig. 1-Fig. 6, having described the discretize of the multiclass variation active contour of the present invention's proposition expresses, continuous function for multiclass variation energy function (MSACM), it is difficult to directly apply to cutting apart of discrete picture, if adopt level set to solve, easily sink into local minimum, therefore, cut before model carries out optimization building multilayer figure, need carry out discretize expression to multiclass variation energy function.Concrete discretize process comprises following step:

Step 2.1, two dimensional image is carried out to discretize trrellis diagram represent, the label area of simultaneously introducing trrellis diagram detects auxiliary function, for area item and the edge item discretize of continuity multiclass Variation Model are prepared;

Suppose image u ₀can be expressed as two-dimentional trrellis diagram M={m (i, j) | i ∈ 1,2 ..., W}, j ∈ 1,2 ..., and H}}, W and H difference representative image is wide and high here.In order to facilitate discretize to describe, introduce auxiliary function it meets formula (4) below,

For two-dimentional table images M, suppose that corresponding to the class label of m position be ψ (m), the label figure that M is corresponding may be defined as ψ (m) | ψ (m) ∈ 1,2 ..., K _phose∩ m ∈ M};

Step 2.2, by the area item in formula (3), the discrete E1 that turns to, is specially:

If $p_{k,m}=\frac{1}{{\left(\sqrt{2\mathrm{\π}}\right)}^{(D+4)/2}{\left|{\mathrm{\Σ}}_k\right|}^{1/2}}\exp [-\frac{1}{2}{(u_0\left(m\right)-u_k)}^T{\mathrm{\Σ}}_k^{-1}(u_0\left(m\right)-u_k)],$ It has described color texture feature to the probability similarity degree that is under the jurisdiction of k class region, probability similarity is got to negative logarithm, i.e. E ₁abbreviation is

Step 2.3, for the edge item of multiclass variation energy function, the boundary length that it not only comprises active contour retrains, introduced the geodesic line gradient calculation on border simultaneously, for boundary length is effectively calculated, the cutting cost of Euclid's boundary length can be converted into the cutting cost of network flow graph, concrete Proof Equivalence and discretize represent, specifically implement according to following steps:

Step 2.3.1, for the boundary curve C of the continuous active contour of multiclass, can utilize Cauchy-Crofton formula to carry out the length of curve of approximation as shown in Fig. 1-Fig. 6, corresponding to different field system, boundary curve C can adopt Q=4, and 8,16 neighborhood approaches.All straight lines on two dimensional surface can be expressed as { (ρ, θ) | xcos (θ)+ysin (θ)=ρ }, Euclid's length of boundary curve C | C| _ecan be expressed as:

${\left|C\right|}_E=\frac{1}{2}\underset{-\∞}{\overset{+\∞}{\∫}}\underset{0}{\overset{\mathrm{\π}}{\∫}}{n}_c(\mathrm{\ρ},\mathrm{\θ})\mathrm{d\ρd\θ}$

N _c(ρ, θ) represents straight line xcos (θ)+ysin (the θ)=ρ total degree crossing with boundary curve C on two dimensional surface, and wherein (ρ, θ) is corresponding to a parallel family of straight lines.

Step 2.3.2, for Q=n _gwhen neighborhood, in Fig. 1, space plane neighborhood system corresponding to two-dimentional trrellis diagram can be expressed as N _q={ e _k| 0≤k≤n _g, the angle between two vectors of arest neighbors is made as for example, for 8 neighborhood systems can utilize Cauchy-Crofton formula approximate treatment length of curve | C| _e, Euclid's length is utilized discrete the turning to of lattice point in Q field:

${\left|C\right|}_E=\underset{k=1}{\overset{n_0}{\mathrm{\Σ}}}{n}_c\left(k\right)\frac{{\mathrm{\δ}}^2\·{\mathrm{\Δ\θ}}_k}{2\·\left|e_k\right|}$

Here, | e _k| be illustrated in the length of direction vector in two-dimentional trrellis diagram, suppose that family of straight lines corresponding to equidirectional vector has identical weight | C| _efurther abbreviation is

${\left|C\right|}_E=\underset{k=1}{\overset{n_0}{\mathrm{\Σ}}}{n}_c\left(k\right)\·{\mathrm{\ω}}_k$

Step 2.3.3, consider two-dimentional network flow graph G=(V, E, W), wherein V is the vertex set of trrellis diagram, and E is the set on border, and W is the non-negative weight set corresponding to limit collection E.In V, comprise two special end points S, T, according to cutting criterion, boundary curve C cuts S and T open, and corresponding cost can be expressed as | C| _g,

Here (m, n) presentation graphs cuts the limit that G is cut open by boundary curve C in Q neighborhood, and the limit weight of its correspondence is w _{m, n}, and | C| _grepresent the cutting cost of boundary curve C.Due to | C| _ewith | C| _gall represent the cutting cost of boundary curve C,, the in the situation that of two dimensional surface discretize, their approximately equals

|C| _E≈|C| _G

Step 2.3.4, cut the boundary curve C of multiple cut zone that G is corresponding and corresponding discrete the turning to of Q neighborhood label according to figure

Here N, _q(m) represent the m Q field point set of ordering, above utilization the formula of (3-4) step can step 1 in the edge item energy function E of formula (1-4) ₂discrete turning to,

Step 2.4, as far as possible smooth in order to ensure the edges of regions that multiclass cuts apart ensures to have stronger noise resisting ability simultaneously, has added the multiclass variation movable contour model energy function that the discretize of anti-noise constant expresses to be

Step 3, the multiclass variation movable contour model energy function that the discretize in step 2 is expressed solve, and obtain Approximate Global Optimal Solution;

Here, optimum solution refers to for each location of pixels m in image, and all distribute a class label ψ (m), it is in fact corresponding to category regions Ω _m.Wherein, ψ (m) ∈ 1,2 ..., K _phose.

Solving thought is: (3-1) plane of delineation is defined as to two-dimentional trrellis diagram, corresponding to any one pixel on image, it is to K _phoseany class of class has a similarity probability, in order to describe any one pixel to K _phosethe probability of class, two-dimentional trrellis diagram is configured to three-dimensional trrellis diagram by the present invention, and three-dimensional trrellis diagram has two special end points, a source point S and a meeting point T, network flow flows to meeting point from source point, and three-dimensional trrellis diagram has K _phose-1 layer, the limit between wherein arbitrarily two-layer is n-link, and its represents the probability similarity of pixel to a certain class.And be t-link with the limit between the pixel in layer trrellis diagram, it has described the constraint between neighborhood space pixel.

(3-2) for area item and edge item in the convenient new multiclass variation movable contour model energy function that step 1 is obtained are converted into K _phose-1 layer of figure cuts n-link and the t-link of model, need to define respectively t-link (area item) limit collection E to area item and edge item _dwith n-link limit collection (item limit, edge collection) E _s.

(3-3) for the multilayer figure G of new structure, need in the process of cutting apart, get rid of invalid cutting apart in order to try to achieve overall approximate optimal solution,, need to define a believable minimal cut C here _gmust meet condition below:, for a lattice point m ∈ M arbitrarily, its corresponding t-link limit in multilayer figure G integrates as E _m, be assigned with unique class label ψ (m), minimal cut C owing to cutting apart rear m point _gcan only be by E _min a limit cut open, otherwise this is cut apart is insincere.

(3-4) utilize max-flow/minimal cut algorithm to try to achieve multilayer figure to cut the overall approximate optimal solution of model.

Specifically implement according to following steps:

The multiclass variation movable contour model energy function that step 3.1, the discretize obtaining for solution procedure 2 are expressed, the present invention builds a multilayer figure G=(V, E, W), its the corresponding two-dimentional trrellis diagram M of every one deck, each the some m above it is corresponding to color texture image u ₀a pixel, therefore, multilayer figure G is just corresponding to a three-dimensional trrellis diagram, it can be defined as { (l, m) ∈ R ²× R|l ∈ 1,2 ..., K _phase-1}, m ∈ M}.Can be expressed as v for any one lattice point (l, m) on multilayer figure _{l, m}, the limit e (v between adjacent two layers figure _{l, m}, v _{l+1, m}) represent t-link, be positioned at the limit e (v in same layer trrellis diagram _{l, m}, v _{l, n}) expression n-link.In the process of structure multilayer figure G, vertex set V can be expressed as discrete multiclass energy function area item energy E ₁with edge item energy E ₂, the summit in available vertex set V, is expressed as t-link limit collection E _dwith n-link limit collection E _s.

Step 3.2, for area item limit collection E _dit is expressed as:

E _D＝∪{E _m|m∈M}，

$E_m=e(s,v_{1,m}){\∪}_{l=1}^{K_{\mathrm{Phose}}-2}e(v_{l,m},v_{l+1,m})\∪e(v_{K_{\mathrm{phose}}-1,m},t).$

In multilayer figure G, weight corresponding to data item limit is made as w (e (v _{l, m}, v _{l+1, m})), the weights of its correspondence are,

${\mathrm{\α}}_{l+1}\·-\log \left(p_{l+1,m}\right)=$

$-{\mathrm{\α}}_{l+1}\·\log \left(\frac{1}{{\left(\sqrt{2\mathrm{\π}}\right)}^{(D+4)/2}{\left|{\mathrm{\Σ}}_k\right|}^{1/2}}\exp \right[-\frac{1}{2}{(u_0\left(m\right)-u_{l+1})}^T{{\mathrm{\Σ}}_{l+1}}^{-1}(u_0\left(m\right)-u_{l+1})\left]\right),$

It is mainly used in the region similarity cluster of textural characteristics.

Step 3.3, item limit, edge collection E _scan be expressed as:

E _S＝(e(V _l，m，V _i，n)|l∈{1，2，...，K _Phose-1)，m，n∈M∩n∈N _Q(m)}

Limit e (v _{l, m}, v _{l, n}) corresponding weight is because it has introduced the difference between restriction relation and the feature in space, field, in the process that can ensure to cut apart, capture the true limit of target as far as possible.Color texture image as shown in Figure 7, it comprises 4 class (K _phoseclass) texture region of non-homogeneous, by limit collection E above _d, E _sand corresponding limit weight, can build 3 layers of digraph G that obtain Weight, in Fig. 8, limit has between layers represented t-link, and it portrays the similarity that unique point is under the jurisdiction of a certain class, and thicker border is corresponding to larger similarity value, as the same on the contrary.And the limit that is arranged in same figure layer represents n-link, it has represented the restriction relation of space field inner edge to have larger difference value between two adjacent unique points, they to be assigned to the possibility of identical category less, therefore there is narrower limit, as the same on the contrary.In order to solve the minimum value of energy function, can utilize max-flow/minimal cut to solve.

Color texture image corresponding to step 3.4, Fig. 7 can be converted into 1D form by row mode from left to right and express, the multilayer figure of its correspondence as shown in Figure 8, its number of plies K _phose-1=3.For a believable minimal cut C of multilayer figure G _gmust meet condition below: for a lattice point m ∈ M arbitrarily, its corresponding t-link limit collection in multilayer figure G is $E_m=e(s,v_{1,m}){\∪}_{l=1}^{K_{\mathrm{Phose}}-2}e(v_{l,m},v_{l+1,m})\∪e(v_{K_{\mathrm{phose}}-1,m},t),$ Be assigned with unique class label ψ (m), minimal cut G owing to cutting apart rear m point _gcan only be by E _min a limit cut open, otherwise this is cut apart is can not.In Fig. 9, cutting (ABCDEFGHMNOPQIL) corresponding to red curve is incredible cutting apart, because t-link limit collection with all cut open 3 times, for example lattice point X ₃corresponding t-link limit e (s, v _{1, X3}), e (v _{1, X3}, v _{2, X3}) and e (v _{2, X3}, v _{3, X3}) all cut open the class label ψ (X that lattice point X3 is corresponding after cutting apart ₃)={ 1,2,3} formula, obviously, this and minimal cut C above _gdefinition contradicts.And cutting (A*B*C*D*EFGHIL) corresponding to green curve, due to each lattice point m ∈ M, the t-link limit collection E that it is corresponding _monly by minimal cut C _gcut open once, therefore this is believable segmentation result, and cutting apart the class label that rear trrellis diagram M is corresponding is (3,2,3,3,4,1, Isosorbide-5-Nitrae, 1).Therefore, in the process of cutting apart, can utilize minimal cut principle to get rid of incredible cutting apart.

The mode of step 4, employing iteration is carried out the optimization of multilayer figure minimal cut to the discrete variation active contour energy of multiclass, realizes stable cutting apart.

Specifically implement according to following steps:

Step 4.1, carry out in the minimized process of multilayer figure at discrete MSACM energy function, because the data item of energy function and the mediation parameter v of edge item are difficult to adaptively determine, cause the result once cut apart unsatisfactory, in order to obtain stable segmentation result, we adopt the mode of iteration to realize to cut apart: multilayer figure is being carried out after Graph Cuts cuts apart at every turn, owing to having occurred a small amount of noise region or less zone of dispersion, they have had a strong impact on the segmentation effect of image, in order to improve target integrality and the overall visual effect of cut zone, can utilize the boundary information in region for less zone of dispersion and noise region, the size information in region, and the letter such as the syntople in region is deleted.After deleting, region needs effective classification number to upgrade, and utilize the region area pixel label corresponding with it after erased noise, again upgrade the probability density (PDF) of each effective class and describe, and by rebuilding multilayer figure, realize optimization in the mode of iteration and cut apart.Suppose after t iteration cut apart, statistical parameter corresponding to k class is Θ ^(t) _k={ α ^(t) _k, u ^(t) _k, ∑ ^(t) _k, it can utilize corresponding class label and color texture feature, adopts mode below to upgrade:

For the self-adaptation that realizes multiclass iteration cutting procedure intersects control, conventionally adopt the variation of adjacent two sub-region labels to realize.This mode computing velocity is fast, and has the ability of describing overall label variations.But it is difficult to measure the feature difference of cutting apart between rear zones of different, and probability density stability corresponding to cut zone, is therefore seldom used.Kullback-Leibler (KL) divergence distance is widely used in the probability density interval tolerance of GMM, it can describe the otherness of zones of different probability density, therefore, we are expanded to the multiclass probability density interval tolerance that MSACM model is corresponding.Cut apart the variation of rear label area and the probability density interval of multiclass cut zone and change the Intersection of jointly realizing cutting procedure and differentiate in order to utilize the density information co-controlling iteration cutting procedure of overall label information and cut zone, can to utilize.

Suppose after t iteration cut apart, between adjacent twice iteration, the not variability of label area is it can be calculated as follows:

Here, | total pixel count of M| representative image, in the time that classification number changes, lose contact owing to cutting apart corresponding image category label adjacent twice, in order not affect successive iterations process, not variability be made as 0.In addition, the not variability of the overall label area of image in adjacent twice iteration cutting procedure has been described.

Step 4.2, the not variability of label area of step 4.1 above, the variation that it can calculate label area fast, and there is the ability of describing overall label variations, but it is difficult to measure the feature difference of cutting apart between rear zones of different, and probability density stability corresponding to cut zone.But KL divergence distance can be applicable to the probability density interval of metric G MM, therefore, it can be for describing the probability density otherness of the different label areas of class.When t iteration, image M is corresponding class probability density interval is made as because every class label area utilizes a multivariate Gauss Gaussian ^(t)(k) distribute and describe, the statistic of its correspondence is Θ (t) _k={ α ^(t) _k, u ^(t) _k, ∑ ^(t) _k, can utilize KL divergence to calculate, suppose that k class is D to the KL divergence distance of n class ^(t)(k, n), it may be calculated:

$D^{\left(t\right)}(k,n)=\mathrm{KL}\left({\mathrm{Gaussian}}^{\left(t\right)}\left(k\right)\right|\left|{\mathrm{Gaussian}}^{\left(t\right)}\left(n\right)\right)$

$=\frac{1}{2}[\log \frac{\left|{\mathrm{\Σ}}_n^{\left(t\right)}\right|}{\left|{\mathrm{\Σ}}_k^{\left(t\right)}\right|}+\mathrm{tr}\left({\mathrm{\Σ}}_n^{\left(t\right)-1}{\mathrm{\Σ}}_k^{\left(t\right)}\right)+{({\mathrm{\μ}}_k^{\left(t\right)}-{\mathrm{\μ}}_n^{\left(t\right)})}^T{\mathrm{\Σ}}_n^{\left(t\right)-1}({\mathrm{\μ}}_k^{\left(t\right)}-{\mathrm{\μ}}_n^{\left(t\right)})]$

For the probability density interval of whole image M it can utilize any class in class arrives other the minimum KL divergence distance value sum of class represents,

$E_{\mathrm{KL}}^{\left(t\right)}=\underset{k=1}{\overset{K_{\mathrm{Phose}}^{\left(t\right)}}{\mathrm{\Σ}}}\underset{k\∈\{1,...,K_{\mathrm{Phose}}^{\left(t\right)}\}\∩\{k\≠n\}}{{\mathrm{\α}}_k^{\left(t\right)}\·\mathrm{Min}}{D}^{\left(t\right)}(k,n)$

Step 4.3, for image M the t time with the t-1 time between corresponding probability density rate of change be made as it can utilize the normalization probability density interval difference of adjacent twice iteration to calculate:

And overall label variations and probability density variation can utilize (4-1) and the formula in (4-2) to carry out the crossing process of co-controlling iteration, Intersection is differentiated as follows:

$E_L^{\left(t\right)}\≥{\mathrm{\β}}_1\mathrm{and\Δ}{E}_{\mathrm{KL}}^{\left(t\right)}\≥{\mathrm{\β}}_2$

Wherein β ₁with β ₂be convergence controlling elements, they are respectively used to label and probability density to differentiate, and realize the termination of iteration cutting procedure.In the time getting larger value, can cause cutting procedure convergence slower, and get less value, be difficult to again ensure the resistance to overturning of segmentation result.By rational experimental analysis and test, get β in the present invention ₁=0.95, β ₁=0.99, they can be good at the speed of balance convergence and cut apart accuracy, and obtain stable segmentation result.

The present invention has carried out the analysis and test of system on artificial synthetic color texture image and Berkeley natural image storehouse.Visible by a large amount of color texture image segmentation results: the multiclass based on Variation Model that (1) the present invention proposes is without supervision color texture image multilayer figure dividing method, after edge item is introduced geodesic line, it can effectively be partitioned into the limit with concavity, and has stronger antinoise and the ability of anti-shade.(2) the multiclass variation movable contour model that the present invention proposes, it has broken the hypothesis of constant density, when color texture image comprise have linear during with nonlinear probability variable density, the non-linear variable density that it can effectively portray feature space.(3) by building multilayer figure and solving in conjunction with the mode of max-flow/minimal cut, it can overcome the slower problem of multiclass Level Set Method speed of convergence, and tries to achieve fast overall approximate optimal solution.(4) adaptive iteration cutting procedure, by the probability density information in conjunction with regional area and overall label information, ensures final cutting procedure Fast Convergent.(5) the quantitative statistics result of finally cutting apart has higher quantification accuracy rate.

The multiclass color texture image multilayer figure dividing method based on Variation Model that the present invention proposes, the curve of smooth sealing can be provided, there is stronger antinoise and the ability of shade, and non-linear linearity and continuity probability density descriptive power, therefore there is actual environment using value and researching value widely.For example, in field of video monitoring, by scene and pedestrian are cut apart, extract ROI (Region of Interesting) region, in conjunction with the relevant knowledge such as machine learning and machine intelligence, the important areas such as bank, government department, airport are monitored in real time, reduced to greatest extent security risk, promote the confidence of people to public safety.In word identification, form, figure and character block all need to be split to extract accurately text message.At intelligent transportation field, by being partitioned into vehicle and pedestrian's object carrys out bulk density, and further analyze the jam situation of traffic, for emergency traffic management and dispatching provides traffic data reliably.Meanwhile, can be partitioned into vehicle and license board information in conjunction with tracking technique, judge hypervelocity, suspect vehicle or the traffic violation, for great accident, provide accurately in violation of rules and regulations, data in violation of rules and regulations quickly and efficiently.In military field, SAR (Synthetic Aperture Radar) diameter radar image is carried out to Target Segmentation, by target recognition and tracking, improve precise guidance and the striking capabilities of guided missile.At agriculture field, by satellite remote sensing images is carried out to Region Segmentation, improve disease and insect resistance to crops, drought-resistant, and strengthen the supervision of the outdoor growing state of crop.In living things feature recognition field, need to cut apart biometric image, thereby further face, fingerprint and iris etc. be identified.

Claims (5)

1. the multiclass color texture image multilayer figure based on Variation Model cuts an optimization dividing method, it is characterized in that, specifically implements according to following steps:

Step 1, set up the continuous variation movable contour model of multiclass, obtain multiclass variation movable contour model energy function;

Step 2, utilize Cauchy-Crofton theory to carry out discrete expression to the multiclass variation movable contour model energy function obtaining in step 1, obtain the class variation movable contour model energy function that discretize is expressed;

Step 3, set up multilayer figure and cut model, the multiclass variation movable contour model energy function that the discretize in step 2 is expressed solves, and obtains Approximate Global Optimal Solution;

The mode of step 4, employing iteration is carried out the optimization of multilayer figure minimal cut to the discrete variation active contour energy of multiclass, realizes stable cutting apart.

2. the multiclass color texture image multilayer figure based on Variation Model according to claim 1 cuts optimization dividing method, it is characterized in that, the described continuous variation movable contour model of multiclass of setting up is specifically implemented according to following steps:

Step 1.1, for a width color texture image, be designated as u ₀, the image area of its correspondence is designated as: Ω: R ²→ R, the cut zone border subset that Ω is corresponding is C, it is by color texture image u ₀be divided into the subregion Ω that several are not connected _jand meet: and wherein N (Ω) represents all disconnected cut zone numbers, and j represents the subscript of cut zone, i.e. region Ω _jinside constant c _jdescribe;

Step 1.2, employing multivariate Gaussian distribution are to each Ω _jportray in region, sets up the continuous movable contour model energy function of initial multiclass:

Wherein, K _phoseit is total category regions number;

it is edge item;

K region, uses Gaussian distribution Θ _k={ α _k, u _k, ∑ _kwherein u is described _kk region Ω _kmean vector, ∑ _kcorresponding covariance matrix, it is the weight in k class region; The dimension of D representative feature;

For effective number of regions K _phoseand relevant statistical parameter Θ _k={ α _k, u _k, ∑ _kinitialization, utilize GMM to carry out probability density distribution modeling to image;

Step 1.3, geodesic active contour is expanded in the edge item constraint of the continuous variation movable contour model of multiclass, obtain multiclass variation movable contour model;

Be specially: by geodesic active contour model expand to the edge item in formula (1) obtain multiclass variation movable contour model energy function:

Wherein, for k region Ω _k, use Gaussian distribution Θ _k={ α _k, u _k, ∑ _kcarry out probability density description, wherein u _kk region Ω _kmean vector, ∑ _kcorresponding covariance matrix, it is the weight in k class region.

3. the multiclass color texture image multilayer figure based on Variation Model according to claim 1 cuts optimization dividing method, it is characterized in that, the described Cauchy-Crofton of utilization theory is carried out discrete expression to the multiclass variation movable contour model energy function obtaining in step 1, specifically implements according to following steps:

Step 2.1, image u0 is expressed as to two-dimentional trrellis diagram M={m (i, j) | i ∈ 1,2 ..., W}, j ∈ 1,2 ..., and H}}, W and H representative image wide and high respectively, introduces auxiliary function it meets formula below,

For two-dimentional table images M, suppose that corresponding to the class label of m position be ψ (m), the label figure that M is corresponding be defined as ψ (m) | ψ (m) ∈ 1,2 ..., K _phose∩ m ∈ M};

Step 2.2, by the area item in multiclass variation movable contour model energy function, the discrete E1 that turns to, is specially:

If $p_{k,m}=\frac{1}{{\left(\sqrt{2\mathrm{\π}}\right)}^{(D+4)/2}{\left|{\mathrm{\Σ}}_k\right|}^{1/2}}\exp [-\frac{1}{2}{(u_0\left(m\right)-u_k)}^T{\mathrm{\Σ}}_k^{-1}(u_0\left(m\right)-u_k)],$ It has described color texture feature to the probability similarity degree that is under the jurisdiction of k class region, probability similarity is got to negative logarithm, i.e. E ₁abbreviation is

Step 2.3, for the edge item of multiclass variation energy function, the cutting cost of Euclid's boundary length is converted into the cutting cost of network flow graph, concrete Proof Equivalence and discretize represent, specifically implement according to following steps:

Step 2.3.1, for the boundary curve C of the continuous active contour of multiclass, utilize Cauchy-Crofton formula to carry out the length of curve of approximation all straight lines on two dimensional surface are expressed as { (ρ, θ) | xcos (θ)+ysin (θ)=ρ }, Euclid's length of boundary curve C | C| _ebe expressed as:

${\left|C\right|}_E=\frac{1}{2}\underset{-\∞}{\overset{+\∞}{\∫}}\underset{0}{\overset{\mathrm{\π}}{\∫}}{n}_c(\mathrm{\ρ},\mathrm{\θ})\mathrm{d\ρd\θ}$

N _c(ρ, θ) represents straight line xcos (θ)+ysin (the θ)=ρ total degree crossing with boundary curve C on two dimensional surface, and wherein (ρ, θ) is corresponding to a parallel family of straight lines;

Step 2.3.2, for Q=n _gwhen neighborhood, space plane neighborhood system corresponding to two-dimentional trrellis diagram is expressed as N _q={ e _k| 0≤k≤n _g, the angle between two vectors of arest neighbors is made as utilize Cauchy-Crofton formula approximate treatment length of curve | C| _e, Euclid's length is utilized discrete the turning to of lattice point in Q field:

${\left|C\right|}_E=\underset{k=1}{\overset{n_0}{\mathrm{\Σ}}}{n}_c\left(k\right)\frac{{\mathrm{\δ}}^2\·{\mathrm{\Δ\θ}}_k}{2\·\left|e_k\right|}$

Here, | e| _kbe illustrated in the length of direction vector in two-dimentional trrellis diagram, suppose that family of straight lines corresponding to equidirectional vector has identical weight | C| _efurther abbreviation is

${\left|C\right|}_E=\underset{k=1}{\overset{n_0}{\mathrm{\Σ}}}{n}_c\left(k\right)\·{\mathrm{\ω}}_k$

The network flow graph G=(V, E, W) of step 2.3.3, two dimension, wherein V is the vertex set of trrellis diagram, and E is the set on border, and W is the non-negative weight set corresponding to limit collection E; In V, comprise two special end points S, T, according to cutting criterion, boundary curve C cuts S and T open, and corresponding cost is expressed as | C| _g,

Here (m, n) diagram cuts the limit that G is cut open by boundary curve C in Q neighborhood, and the limit weight of its correspondence is w _{m, n}, and | C| _grepresent the cutting cost of boundary curve C; Due to | C| _ewith | C| _gall represent the cutting cost of boundary curve C,, the in the situation that of two dimensional surface discretize, their approximately equals

|C| _E≈|C| _G

Step 2.3.4, cut the boundary curve C of multiple cut zone that G is corresponding and corresponding discrete the turning to of Q neighborhood label according to figure

Here N, _q(m) represent the Q field point set that m is ordered, utilize above-mentioned formula by the edge item energy function E of multiclass variation movable contour model energy function in step 1 ₂discrete turning to:

The discretize of the multiclass variation movable contour model energy of step 2.4, interpolation anti-noise constant is expressed as:

4. the multiclass color texture image multilayer figure based on Variation Model according to claim 1 cuts optimization dividing method, it is characterized in that, the described multiclass variation movable contour model energy that discretize in step 2 is expressed solves, and specifically implements according to following steps:

Step 3.1, a multilayer figure G=of structure (V, E, W), its corresponding two-dimentional trrellis diagram M of every one deck, each the some m above it is corresponding to color texture image u ₀a pixel, multilayer figure G is just corresponding to a three-dimensional trrellis diagram, it is defined as { (l, m) ∈ R ²× R|l ∈ 1,2 ..., K _phose-1}, m ∈ M}; Be expressed as v for any one lattice point (l, m) on multilayer figure _{l, m}, the limit e (v between adjacent two layers figure _{l, m}, v _{l+1, m}) represent t-link, be positioned at the limit e (v in same layer trrellis diagram _{l, m}, v _{l, n}) expression n-link; In the process of structure multilayer figure G, vertex set V is expressed as discrete multiclass energy function area item energy E ₁with edge item energy E ₂, with the summit in vertex set V, be expressed as t-link limit collection E _dwith n-link limit collection E _s;

Step 3.2, for area item limit collection E _dit is expressed as:

E _D＝∪{E _m|m∈M}，

$E_m=e(s,v_{1,m}){\∪}_{l=1}^{K_{\mathrm{Phose}}-2}e(v_{l,m},v_{l+1,m})\∪e(v_{K_{\mathrm{phose}}-1,m},t)$

Step 3.3, in multilayer figure G, weight corresponding to data item limit is made as w (e (v _{l, m}, v _{l+1, m})), the weights of its correspondence are:

${\mathrm{\α}}_{l+1}\·-\log \left(p_{l+1,m}\right)=$

$-{\mathrm{\α}}_{l+1}\·\log \left(\frac{1}{{\left(\sqrt{2\mathrm{\π}}\right)}^{(D+4)/2}{\left|{\mathrm{\Σ}}_k\right|}^{1/2}}\exp \right[-\frac{1}{2}{(u_0\left(m\right)-u_{l+1})}^T{{\mathrm{\Σ}}_{l+1}}^{-1}(u_0\left(m\right)-u_{l+1})\left]\right)$

It is for the region similarity cluster of textural characteristics;

Step 3.3, item limit, edge collection E _sbe expressed as:

E _S＝{e(v _l，m，v _l，n)|l∈{1，2，...，K _Phose-1)，m，n∈M∩n∈N _Q(m)}

Limit e (v _{l, m}, v _{l, n}) corresponding weight is

Step 3.4, utilize the multiclass variation movable contour model energy function that discretize that max-flow/minimal cut obtains step 2 is expressed to solve.

5. the multiclass color texture image multilayer figure based on Variation Model according to claim 1 cuts optimization dividing method, it is characterized in that, the mode of described employing iteration is optimized and the discrete variation active contour energy of multiclass is carried out to the optimization of multilayer figure minimal cut is specifically implemented according to following steps:

Step 4.1, after t iteration cut apart, between adjacent twice iteration, the not variability of label area is it is calculated as follows:

Here, | total pixel count of M| representative image, not variability be made as 0, the not variability of the overall label area of image in adjacent twice iteration cutting procedure has been described;

Step 4.2, the probability density otherness of the different label areas of class is described by KL divergence distance, when t iteration, image M is corresponding class probability density interval is made as every class label area utilizes a multivariate Gauss Gaussian ^(t)(k) distribute and describe, the statistic of its correspondence is Θ ^(t) _k={ α ^(t)k, u ^(t) _k, ∑ ^(t) _k, utilize KL divergence to calculate, establishing k class is D to the KL divergence distance of n class ^(t)(k, n), is calculated as:

$D^{\left(t\right)}(k,n)=\mathrm{KL}\left({\mathrm{Gaussian}}^{\left(t\right)}\left(k\right)\right|\left|{\mathrm{Gaussian}}^{\left(t\right)}\left(n\right)\right)$

$=\frac{1}{2}[\log \frac{\left|{\mathrm{\Σ}}_n^{\left(t\right)}\right|}{\left|{\mathrm{\Σ}}_k^{\left(t\right)}\right|}+\mathrm{tr}\left({\mathrm{\Σ}}_n^{\left(t\right)-1}{\mathrm{\Σ}}_k^{\left(t\right)}\right)+{({\mathrm{\μ}}_k^{\left(t\right)}-{\mathrm{\μ}}_n^{\left(t\right)})}^T{\mathrm{\Σ}}_n^{\left(t\right)-1}({\mathrm{\μ}}_k^{\left(t\right)}-{\mathrm{\μ}}_n^{\left(t\right)})]$

For the probability density interval of whole image M utilize any class in class arrives other the minimum KL divergence distance value sum of class represents,

$E_{\mathrm{KL}}^{\left(t\right)}=\underset{k=1}{\overset{K_{\mathrm{Phose}}^{\left(t\right)}}{\mathrm{\Σ}}}\underset{k\∈\{1,...,K_{\mathrm{Phose}}^{\left(t\right)}\}\∩\{k\≠n\}}{{\mathrm{\α}}_k^{\left(t\right)}\·\mathrm{Min}}{D}^{\left(t\right)}(k,n)$

Step 4.3, for image M the t time with the t-1 time between corresponding probability density rate of change be made as it utilizes the normalization probability density interval difference of adjacent twice iteration to calculate:

${\mathrm{\ΔE}}_{\mathrm{KL}}^{\left(t\right)}=\exp (-\frac{|E_{\mathrm{KL}}^{\left(t\right)}-E_{\mathrm{KL}}^{(t-1)}|}{E_{\mathrm{KL}}^{\left(t\right)}})$

And overall label variations and probability density variation utilize step 4.1 and the formula in step 4.2 to carry out the crossing process of co-controlling iteration, Intersection is differentiated as follows:

$E_L^{\left(t\right)}\≥{\mathrm{\β}}_1\mathrm{and\Δ}{E}_{\mathrm{KL}}^{\left(t\right)}\≥{\mathrm{\β}}_2$

Wherein β ₁with β ₂be convergence controlling elements, be respectively used to label and probability density to differentiate, and realize the termination of iteration cutting procedure.