CN102289812B - Object segmentation method based on priori shape and CV (Computer Vision) model - Google Patents

Abstract

A target segmentation method based on prior shape and CV model. First, the prior shape is selected to construct the signed distance function, and then the affine transformation is performed on the prior shape signed distance function according to the affine transformation parameter vector. The affine transformation parameters are in the right level When the set function is iterated, it will change and finally tend to be stable. Finally, the active contour curve is evolved according to the level set iterative formula, and the next affine transformation parameters are obtained according to the iterative formula of each affine parameter. On the basis of maintaining the invariance of rotation, scaling and translation of the prior shape model, the present invention adds stretching in the X and Y directions and shear invariant constraint energy items, and expands the adaptive transformation of the prior shape. The invention can achieve better segmentation of space objects with large attitude changes in complex backgrounds.

Description

A kind of Target Segmentation method based on prior shape and CV model

Technical field

The present invention relates to image processing techniques, specifically a kind of Target Segmentation method based on prior shape and CV model.

Background technology

At present, in existing all types of target dividing method, the curve evolvement method is to there being goodish result cutting apart of target, specifically comprise Snake method, active contour line method, distorted pattern and Level Set Method etc., parameterized Snake method allows and the model direct interaction, and the expression of model is compact, is conducive to the quick realization of model, but is difficult to the variation of transaction module topological structure.Can naturally process the variation of evolution curve or curved surface topological structure based on the movable contour model of variation level diversity method, and can naturally boundary information and area information be combined.

Mumford proposed to approach M-S Level Set Models (the Mumford D that solves the rim detection problem by the best of Piecewise Smooth Functions in 1989, Shah J.Optimal approximation by piecewise smooth functionsand associated variational problems.Communication on Pure and Applied Mathematics, 1989,42 (5): 577-685.), Chan and Vese have proposed CV Level Set Models (the Chan T F that simplifies on the basis of M-S model, Vese L A.Active contours without edges.IEEE Transactions on ImageProcessing, 2001,10 (2): 266-277.), a remarkable advantage of this model is exactly global optimization, also can obtain preferably segmentation result at the obscurity boundary place, and the initial profile line can be placed on the optional position of image.But this model is based on the gray scale similarity and divides the target area, therefore there is the defective of three aspects in this model: 1. can not the segmentation object gray scale target similar to background, 2. can not effectively cut apart texture image, 3. can not cut apart be blocked, the target of shortage of data.

In order to overcome above defective, the many scholar's primary studies of recent domestic prior shape information and level set in conjunction with the problem of carrying out image segmentation.But Tony Chan etc. has proposed to utilize prior shape knowledge to carry out deformation model (the Chan T and Zhu W.Level set based shape prior segmentation.IEEEConference on Computer Vision and Pattern Recognition (CVPR) that image segmentation is processed, 2005:1164-1170.), this model adds prior shape information on the basis of CV model, can be partitioned into shortage of data in image, be blocked or target that the target gray scale is similar to background.But the prior shape item in this model only has rotation, zooming and panning invariant feature, and for occur to shear or in X, Y-direction the target of different stretch coefficient is arranged, the segmentation effect of above-mentioned model is relatively poor.

Summary of the invention

The present invention is in order to overcome existing prior shape model to the limitation of the adaptive change existence of target, be that the prior shape item only has scaled, the translations such as X, Y-direction and rotates three invariant features, a kind of Target Segmentation method based on prior shape and CV model is provided, the present invention has increased X on original prior shape variation level set model basis, Y-direction stretches and shear the constraint independent of time energy term, by the expansion to the adaptive transformation of prior shape, this method can realize the larger target of posture changing under the complex background is accurately cut apart.

The present invention is achieved through the following technical solutions:

A kind of Target Segmentation method based on prior shape and CV model, be the Image Segmentation Model based on the variation level diversity method, it incorporates prior shape information naturally incorporating on the image area information basis, has processed well some traditional insurmountable problems of geometric active contour model.

Constructed energy function corresponding to model of the present invention is expressed as follows:

E(c ₁，c ₂，φ，ψ)＝E _CV(c ₁，c ₂，φ)+λE _shape(φ，ψ) (1)

Wherein: c ₁And c ₂Be respectively the gradation of image mean value in inside and outside zone of zero level collection curve corresponding to φ, λ is weight coefficient corresponding to prior shape energy term, CV energy term E _CV(c ₁, c ₂, φ) with prior shape item E _Shape(φ, ψ) is expressed as follows respectively:

$E_{\mathrm{CV}}(c_1,c_2,\mathrm{\φ})=\mathrm{\μ}{\∫}_{\mathrm{\Ω}}\mathrm{\δ}\left(\mathrm{\φ}\right)|\▿\mathrm{\φ}|\mathrm{dxdy}+{\mathrm{\λ}}_1{\∫}_{\mathrm{\Ω}}{(f-c_1)}^{2}H\left(\mathrm{\φ}\right)\mathrm{dxdy}+{\mathrm{\λ}}_2{\∫}_{\mathrm{\Ω}}{(f-c_2)}^2(1-H\left(\mathrm{\φ}\right))\mathrm{dxdy}---\left(2\right)$

E _shape(φ，ψ)＝∫ _Ω(H(φ)-H(ψ)) ²dxdy (3)

$\mathrm{\ψ}(x,y):={\mathrm{\ψ}}_0\left(h_{X_T}(x,y)\right)$ $\left(4\right)$

$h_{X_T}{(x,y)}^T=R_{\mathrm{sc}}{R}_{\mathrm{\θ}}{R}_{\mathrm{sh}}{(\tilde{x},\tilde{y})}^T+T---\left(5\right)$

Wherein: $R_{\mathrm{sc}}=\left(\begin{array}{cc}{S}_x& 0\\ 0& S_y\end{array}\right),$ $R_{\mathrm{\θ}}=\left(\begin{array}{cc}\cos \mathrm{\θ}& \sin \mathrm{\θ}\\ -\sin \mathrm{\θ}& \cos \mathrm{\θ}\end{array}\right),$ $R_{\mathrm{sh}}=\left(\begin{array}{cc}1& \mathrm{shx}\\ \mathrm{shy}& 1\end{array}\right),$ $T=\left(\begin{array}{c}{T}_x\\ T_y\end{array}\right),$ $\left(\begin{array}{c}\tilde{x}\\ \tilde{y}\end{array}\right)={(\frac{x-x_g}{S_x},\frac{y-y_g}{S_y})}^T$

X _T=(S _x, S _y, θ, shx, shy, T _x, T _y), S wherein _xAnd S _yBe respectively two zoom factors on X, the Y-direction, θ is the angle rotation parameter, and shx, shy are respectively two pruning parameters on X, the Y-direction, T _x, T _yBe respectively two translation parameterss on X, the Y-direction; F is the gray-scale value that is defined on the image area Ω; ψ is the level set function ψ of prior shape ₀Affined transformation through formula (4) obtains, and is used for the prior shape energy term of formula (3) is retrained.

Energy term E (c to formula (1) ₁, c ₂, φ, ψ) minimize, adopt the variational method and Gradient Descent flow equation to make up numerical evaluation form corresponding to evolutionary model, order

To formula (1) energy term E (c ₁, c ₂, φ, ψ) and changes persuing divides, and can get c ₁, c ₂, affine transformation parameter X _T=(S _x, S _y, θ, shx, shy, T _x, T _y) and steepest descent equation corresponding to level set function φ that develops be:

$c_1=\frac{{\∫}_{\mathrm{\Ω}}f(x,y)H\left(\mathrm{\φ}\right)\mathrm{dxdy}}{{\∫}_{\mathrm{\Ω}}H\left(\mathrm{\φ}\right)\mathrm{dxdy}}$ $c_2=\frac{{\∫}_{\mathrm{\Ω}}f(x,y)(1-H\left(\mathrm{\φ}\right))\mathrm{dxdy}}{{\∫}_{\mathrm{\Ω}}(1-H\left(\mathrm{\φ}\right))\mathrm{dxdy}}---\left(6\right)$

$\frac{{\∂S}_x}{\∂t}={\∫}_{\mathrm{\Ω}}(H\left(\mathrm{\ψ}\right)-H\left(\mathrm{\φ}\right))\·2\mathrm{\δ}\left(\mathrm{\ψ}\right)\·{\mathrm{\ψ}}_x\·(\tilde{x}\·(\cos \mathrm{\θ}+\mathrm{shy}\·\sin \mathrm{\θ})+\tilde{y}\·(\cos \mathrm{\θ}\·\mathrm{shx}+\sin \mathrm{\θ}))\mathrm{dxdy}---\left(7\right)$

$\frac{{\∂S}_y}{\∂t}={\∫}_{\mathrm{\Ω}}(H\left(\mathrm{\ψ}\right)-H\left(\mathrm{\φ}\right))\·2\mathrm{\δ}\left(\mathrm{\ψ}\right)\·{\mathrm{\ψ}}_y\·(\tilde{x}\·(-\sin \mathrm{\θ}+\cos \mathrm{\θ}\·\mathrm{shy})+\tilde{y}\·(-\sin \mathrm{\θ}\·\mathrm{shx}+\cos \mathrm{\θ}))\mathrm{dxdy}---\left(8\right)$

$\frac{\∂\mathrm{\θ}}{\∂t}=-{\∫}_{\mathrm{\Ω}}(H\left(\mathrm{\ψ}\right)-H\left(\mathrm{\φ}\right))\·2\mathrm{\δ}\left(\mathrm{\ψ}\right)\·({\mathrm{\ψ}}_x\·(\tilde{x}\·(S_x\·\sin \mathrm{\θ}-S_x\·\mathrm{shy}\·\cos \mathrm{\θ})+\tilde{y}\·(S_x\·\mathrm{shx}\·\sin \mathrm{\θ}-S_x\·\cos \mathrm{\θ}))---\left(9\right)$

${+\mathrm{\ψ}}_y\·(\tilde{x}\·(S_y\·\cos \mathrm{\θ}+S_y\·\mathrm{shy}\·\sin \mathrm{\θ})+\tilde{y}\·(S_y\·\mathrm{shx}\·\cos \mathrm{\θ}+S_y\·\sin \mathrm{\θ})))\mathrm{dxdy}$

$\frac{\∂\mathrm{shx}}{\∂t}={\∫}_{\mathrm{\Ω}}(H\left(\mathrm{\ψ}\right)-H\left(\mathrm{\φ}\right))\·2\mathrm{\δ}\left(\mathrm{\ψ}\right)\·({\mathrm{\ψ}}_x\·\tilde{y}\·S_x\·\cos \mathrm{\θ}-{\mathrm{\ψ}}_y\·\tilde{y}\·S_y\·\sin \mathrm{\θ}\left)\right)\mathrm{dxdy}---\left(10\right)$

$\frac{\∂\mathrm{shy}}{\∂t}={\∫}_{\mathrm{\Ω}}(H\left(\mathrm{\ψ}\right)-H\left(\mathrm{\φ}\right))\·2\mathrm{\δ}\left(\mathrm{\ψ}\right)\·({\mathrm{\ψ}}_x\·\tilde{x}\·S_x\·\sin \mathrm{\θ}+{\mathrm{\ψ}}_y\·\tilde{x}\·S_y\·\cos \mathrm{\θ}\left)\right)\mathrm{dxdy}---\left(11\right)$

$\frac{{\∂T}_x}{\∂t}={\∫}_{\mathrm{\Ω}}(H\left(\mathrm{\ψ}\right)-H\left(\mathrm{\φ}\right))\·2\mathrm{\δ}\left(\mathrm{\ψ}\right)\·{\mathrm{\ψ}}_x\mathrm{dxdy}---\left(12\right)$

$\frac{{\∂T}_y}{\∂t}={\∫}_{\mathrm{\Ω}}(H\left(\mathrm{\ψ}\right)-H\left(\mathrm{\φ}\right))\·2\mathrm{\δ}\left(\mathrm{\ψ}\right)\·{\mathrm{\ψ}}_y\mathrm{dxdy}---\left(13\right)$

$\frac{\∂\mathrm{\φ}}{\∂t}=\mathrm{\δ}\left(\mathrm{\φ}\right)\·({(f-c_1)}^2-{(f-c_2)}^2+2\mathrm{\λ}(H\left(\mathrm{\ψ}\right)-H\left(\mathrm{\φ}\right)))---\left(14\right)$

The present invention includes following steps:

1, utilize the prior shape sample to make up the symbolic distance function:

The target image of selection standard attitude is as making up the prior shape model sample from sequence chart, then the prior shape sample of choosing is carried out Threshold segmentation, the size of threshold value is manually adjusted according to the complexity of sample background, the background of carrying out image after next adopts the Mathematical Morphology operator to Threshold segmentation suppresses and with the two-value edge contour of Sobel operator extraction target, utilizes at last the two-value outline line structure prior shape symbolic distance function that generates;

2, according to initialized affine transformation parameter, utilize formula (4), (5) that symbolic distance function corresponding to prior shape model sample carried out affined transformation:

The present invention has expanded the affined transformation item of original prior shape, and namely affined transformation is expanded from quaternary relation (a, b, r, θ) and is (S _x, S _y, θ, shx, shy, T _x, T _y), S wherein _xAnd S _yBe respectively two zoom factors on X, the Y-direction, θ is the angle rotation parameter, and shx, shy are respectively two pruning parameters on X, the Y-direction, T _x, T _yBe respectively two translation parameterss on X, the Y-direction;

3, utilize formula (6～14) that image is carried out the computing of level set global iterative:

Quantize to calculate and adopt Regularization function

The Dirac function

Replace respectively H (z) and δ (z), so that katabatic drainage equation (14) can act on all level sets, thereby can all targets of image-region be detected automatically, and make energy function E (c ₁, c ₂, φ, ψ) and reach global minimum.

The invention has the beneficial effects as follows:

1, because the present invention has expanded the adaptive change mode of prior shape to target, when using improved prior shape Level Set Models that target is cut apart, can be partitioned into that attitude changes greatly and complicated target under the complex background.

2, the experiment simulation data of the present invention test are the one group of video scenes that is produced by the satellite simulation kit STK of U.S. AGI company software, utilize STK8.0 to calculate track profile information, and obtain the target aircraft analog image information seen from observation platform.For making emulated data as far as possible true to nature, with test-target detection, recognition and tracking method, in generating the analog image process, what time followingly considered: the size of (1) target aircraft in the visual field must change according to two aircraft actual distances; (2) target aircraft will have certain rotation; (3) target aircraft should not be in visual field central authorities all the time; (4) background should have certain variation, and Celestial Background is arranged, and earth background is arranged, or the starry sky earth background alternately changes.

Below in conjunction with accompanying drawing and case study on implementation the present invention is elaborated.

Description of drawings

Fig. 1 is 5 width of cloth typical case attitude of satellite picture of choosing under earth background and Celestial Background.

Fig. 2 is prior shape sample (Fig. 2 (a) and corresponding binary map Fig. 2 (b), the two-value profile diagram Fig. 2 (c) thereof that chooses.

Fig. 3 is based on the artificial composite diagram that Fig. 2 (b) generates.

Fig. 4 is initial profile line chart corresponding to Fig. 3 (a) and the segmentation effect figure under the different model.

Fig. 5 is initial profile line chart corresponding to Fig. 3 (b) and the segmentation effect figure under the different model.

Fig. 6 is initial profile line chart corresponding to Fig. 3 (c) and the segmentation effect figure under the different model.

Fig. 7 is initial profile line stacking diagram corresponding to each figure among Fig. 1.

Fig. 8 is that traditional CV model is to the segmentation result of each figure among Fig. 1.

Fig. 9 is that traditional CV model based on prior shape is to the segmentation result of each figure among Fig. 1.

Figure 10 the present invention is based on the CV model of prior shape to the segmentation result of each figure among Fig. 1.

Figure 11 is the process flow diagram of the inventive method.

Embodiment

Elaborate to of the present invention below in conjunction with drawings and Examples: the example that present embodiment is implemented under take technical solution of the present invention as prerequisite provided detailed embodiment and process, but protection scope of the present invention should not be limited to following embodiment.

When from space target being followed the tracks of, the sequence image that gathers is because the angle of taking and the attitude adjustment of self, substantially meet affine transformation relationship between the image object outline line that extracts, 5 width of cloth typical case attitude of satellite picture that present embodiment is chosen under earth background and the Celestial Background is used for checking " based on the Target Segmentation method of prior shape and CV model " set forth in the present invention performance, as shown in Figure 1, present embodiment is chosen Fig. 2 (a) simultaneously as the prior shape sample, and the implementation step of Target Segmentation method that the present invention is based on prior shape and CV model is as follows:

1, utilize the prior shape sample to make up the symbolic distance function:

(a) carries out Threshold segmentation to prior shape sample graph 2, the threshold value that present embodiment is cut apart elects 128 as, then utilize morphological operator that the image after suppressing is carried out morphology and process and generate binary map, i.e. 2 (b), next utilizes the Sobel operator that Fig. 2 (b) is carried out edge extracting, obtain two-value outline line corresponding to prior shape, be Fig. 2 (c), make up prior shape sample (symbolic distance function ψ and ψ that Fig. 2 (a) is corresponding based on Fig. 2 (b) and Fig. 2 (c) at last ₀2, the initialized affine parameter of present embodiment is followed successively by: (1,1,0,0,0,0,0), i.e. prior shape symbolic distance function ψ and ψ in the formula (3) ₀Identical, in the minimization process to energy function formula (3), affine parameter vector (S _x, S _y, θ, shx, shy, T _x, T _y) corresponding numerical value constantly changes, thereby so that prior shape can be mated target to be split gradually, during in object boundary to be split, the numerical value that affine parameter is corresponding tends towards stability in moveable contour stable convergence, stationary value corresponding in the implementation case is (1,1,0,0,0,0,0), namely prior shape no longer changes.

3, the iterations that integrates of given level is as n=1000.

4, utilize formula (6～14) that Fig. 3 and Fig. 1 are carried out the level set interative computation, when the active contour line stabilization, obtain object boundary to be split.

Fig. 4 (b), Fig. 5 (b), Fig. 6 (b) is the segmentation result of traditional C V model, by Tu Kede, when divided target is blocked, traditional CV model can detect target together with shelter, Fig. 4 (c), Fig. 5 (c), Fig. 6 (c) is traditional CV model segmentation result based on prior shape, by Tu Kede, when the relative prior shape of divided target is sheared (Fig. 3 (c)) or at X, the Y zoom factor is (Fig. 3 (b)) not simultaneously, traditional CV model based on prior shape can't provide correct segmentation result, and reason just is that prior shape bound term is to the limitation of radiation conversion.Fig. 4 (d), Fig. 5 (d), Fig. 6 (d) are the improved CV model segmentation result based on prior shape of the present invention, by Tu Kede, because introduced the stretching of X, Y-direction and sheared invariant feature, improved Image Segmentation Model can well be partitioned into each target that is blocked.

Can be got by Fig. 8 (e), have preferably homogeney in target or background area, and be subject to illumination, shade, block, the factor impact such as clutter hour, traditional CV method can obtain satisfied segmentation result.Otherwise the effect that traditional CV method is cut apart is relatively poor, shown in Fig. 8 (a), 8 (b), 8 (c), 8 (d).Can be got by Fig. 9, very little and when the drawing coefficient of X, Y-direction differs also very little when the shearing factor of the relative prior shape of divided target, traditional CV model based on prior shape can be partitioned into satisfied result, such as Fig. 9 (a), 9 (b), 9 (c); Otherwise the segmentation effect of traditional CV model based on prior shape is then poor, such as Fig. 9 (d), 9 (e).With respect to traditional C V model with based on the CV model of prior shape, the improved variation level aggregation model of the present invention can improve the satellite segmentation effect under the complicated earth and the Celestial Background significantly, as shown in figure 10.

Claims (1)

1. the Target Segmentation method based on prior shape and CV model is characterized in that comprising the following steps:

1. utilize the prior shape sample to make up the symbolic distance function:

The target image of selection standard attitude is as the prior shape sample from sequence chart, then the prior shape sample of choosing is carried out Threshold segmentation, the size of threshold value is manually adjusted according to the complexity of sample background, the background of carrying out image after next adopts the Mathematical Morphology operator to Threshold segmentation suppresses and with the edge two-value outline line of Sobel operator extraction target, utilizes at last described two-value outline line structure prior shape symbolic distance function ψ ₀

2. set and according to initialized affine transformation parameter, to the symbolic distance function ψ of prior shape sample ₀Carry out affined transformation, obtain the symbolic distance function ψ after the conversion:

Affine transformation parameter is S _x, S _y, θ, shx, shy, T _x, T _y, S wherein _xAnd S _yBe respectively two zoom factors on X, the Y-direction, θ is the angle rotation parameter, and shx, shy are respectively the pruning parameter on X, the Y-direction, T _x, T _yBe respectively the translation parameters on X, the Y-direction;

$\mathrm{\Ψ}(x,y)={\mathrm{\Ψ}}_0\left(h_{X_T}^T(x,y)\right)---\left(1\right)$

$h_{X_T}(x,y)=R_{\mathrm{sc}}{R}_{\mathrm{\θ}}{R}_{\mathrm{sh}}{(\tilde{x},\tilde{y})}^T+T---\left(2\right)$

Wherein: $R_{\mathrm{sc}}=\left(\begin{array}{cc}{S}_x& 0\\ 0& S_y\end{array}\right),$ $R_{\mathrm{\θ}}=\left(\begin{array}{cc}\cos \mathrm{\θ}& \sin \mathrm{\θ}\\ -\sin \mathrm{\θ}& \cos \mathrm{\θ}\end{array}\right),$ $R_{\mathrm{sh}}=\left(\begin{array}{cc}1& \mathrm{shx}\\ \mathrm{shy}& 1\end{array}\right),$ $T=\left(\begin{array}{c}{T}_x\\ T_y\end{array}\right),$ $\left(\begin{array}{c}\tilde{x}\\ \tilde{y}\end{array}\right)={(\frac{x-x_g}{S_x},\frac{y-y_g}{S_y})}^T$

X _T＝(S _x，S _y，θ，shx，shy，T _x，T _y)；

3. utilize following formula (3)～formula (11) that image is carried out the computing of level set global iterative, when the active contour line stabilization, namely obtain object boundary to be split:

$c_1=\frac{{\∫}_{\mathrm{\Ω}}f(x,y)H\left(\mathrm{\φ}\right)\mathrm{dxdy}}{{\∫}_{\mathrm{\Ω}}H\left(\mathrm{\φ}\right)\mathrm{dxdy}}$ $c_2=\frac{{\∫}_{\mathrm{\Ω}}f(x,y)(1-H\left(\mathrm{\φ}\right))\mathrm{dxdy}}{{\∫}_{\mathrm{\Ω}}(1-H\left(\mathrm{\φ}\right))\mathrm{dxdy}}---\left(3\right)$

$\frac{{\∂S}_x}{\∂t}={\∫}_{\mathrm{\Ω}}(H\left(\mathrm{\ψ}\right)-H\left(\mathrm{\φ}\right))\·2\mathrm{\δ}\left(\mathrm{\ψ}\right)\·{\mathrm{\ψ}}_x\·(\tilde{x}\·(\cos \mathrm{\θ}+\mathrm{shy}\·\sin \mathrm{\θ})+\tilde{y}\·(\cos \mathrm{\θ}\·\mathrm{shx}+\sin \mathrm{\θ}))\mathrm{dxdy}---\left(4\right)$

$\frac{{\∂S}_y}{\∂t}={\∫}_{\mathrm{\Ω}}(H\left(\mathrm{\ψ}\right)-H\left(\mathrm{\φ}\right))\·2\mathrm{\δ}\left(\mathrm{\ψ}\right)\·{\mathrm{\ψ}}_y\·(\tilde{x}\·(-\sin \mathrm{\θ}+\cos \mathrm{\θ}\·\mathrm{shy})+\tilde{y}\·(-\sin \mathrm{\θ}\·\mathrm{shx}+\cos \mathrm{\θ}))\mathrm{dxdy}---\left(5\right)$

$\frac{\∂\mathrm{\θ}}{\∂t}=-{\∫}_{\mathrm{\Ω}}(H\left(\mathrm{\ψ}\right)-H\left(\mathrm{\φ}\right))\·2\mathrm{\δ}\left(\mathrm{\ψ}\right)\·({\mathrm{\ψ}}_x\·(\tilde{x}\·(S_x\·\sin \mathrm{\θ}-S_x\·\mathrm{shy}\·\cos \mathrm{\θ})+\tilde{y}\·(S_x\·\mathrm{shx}\·\sin \mathrm{\θ}-S_x\·\cos \mathrm{\θ}))$ $\left(6\right)$

$+{\mathrm{\ψ}}_y\·(\tilde{x}\·(S_y\·\cos \mathrm{\θ}+S_y\·\mathrm{shy}\·\sin \mathrm{\θ})+\tilde{y}\·(S_y\·\mathrm{shx}\·\cos \mathrm{\θ}+S_y\·\sin \mathrm{\θ})))\mathrm{dxdy}$

$\frac{\∂\mathrm{shx}}{\∂t}={\∫}_{\mathrm{\Ω}}(H\left(\mathrm{\ψ}\right)-H\left(\mathrm{\φ}\right))\·2\mathrm{\δ}\left(\mathrm{\ψ}\right)\·({\mathrm{\ψ}}_x\·\tilde{y}\·S_x\·\cos \mathrm{\θ}-{\mathrm{\ψ}}_y\·\tilde{y}\·S_y\·\sin \mathrm{\θ})\mathrm{dxdy}---\left(7\right)$

$\frac{\∂\mathrm{shy}}{\∂t}={\∫}_{\mathrm{\Ω}}(H\left(\mathrm{\ψ}\right)-H\left(\mathrm{\φ}\right))\·2\mathrm{\δ}\left(\mathrm{\ψ}\right)\·({\mathrm{\ψ}}_x\·\tilde{x}\·S_x\·\sin \mathrm{\θ}+{\mathrm{\ψ}}_y\·\tilde{x}\·S_y\·\cos \mathrm{\θ}))\mathrm{dxdy}---\left(8\right)$

$\frac{\∂T_x}{\∂t}={\∫}_{\mathrm{\Ω}}(H\left(\mathrm{\ψ}\right)-H\left(\mathrm{\φ}\right))\·2\mathrm{\δ}\left(\mathrm{\ψ}\right)\·{\mathrm{\ψ}}_x\mathrm{dxdy}---\left(9\right)$

$\frac{\∂T_y}{\∂t}={\∫}_{\mathrm{\Ω}}(H\left(\mathrm{\ψ}\right)-H\left(\mathrm{\φ}\right))\·2\mathrm{\δ}\left(\mathrm{\ψ}\right)\·{\mathrm{\ψ}}_y\mathrm{dxdy}---\left(10\right)$

$\frac{\∂\mathrm{\φ}}{\∂t}=\mathrm{\δ}\left(\mathrm{\φ}\right)\·({(f-c_1)}^2-{(f-c_2)}^2+2\mathrm{\λ}(H\left(\mathrm{\ψ}\right)-H\left(\mathrm{\φ}\right)))---\left(11\right)$

Wherein f is the gray-scale value that is defined on the image area Ω, c ₁And c ₂Be respectively the gradation of image mean value in inside and outside zone of zero level collection curve corresponding to φ, λ is weight coefficient corresponding to prior shape energy term, ψ _x, ψ _yBe respectively level set function ψ gradient in the x and y direction,

Quantize to calculate and adopt Regularization function

The Dirac function Replace H (z) and δ (z), katabatic drainage equation (11) can be acted on all level sets, thereby can all targets of image-region be detected automatically.

Images