CN105741264A - Two-phase image segmentation method based on semi-local texture features - Google Patents

Abstract

The invention discloses a two-stage image segmentation method based on semi-local texture features, which mainly includes: dividing the image into non-overlapping small blocks of M×M pixels; extracting the texture of each block based on Beltrami framework and semi-local information features, and then use the K?means algorithm for block clustering to divide the picture into four regions; determine the best position of the target according to the principle of photographic composition, thereby extracting the target and completing the rough segmentation; use the geometric active contour model to extract the Targets are finely segmented to obtain more accurate segmentation results. The beneficial effect of the present invention is: a kind of segmentation method that carries out rough segmentation to extract target object first and then fine segmentation is proposed, this segmentation strategy from coarse to fine can be used for segmenting the picture with fuzzy or complicated background; Define a A new type of texture feature based on the Beltrami framework and semi-local information has stronger discrimination than a single feature and has a strong anti-noise ability. Using this texture feature in clustering and image segmentation can get more accurate Experimental results.

Description

A two-stage image segmentation method based on semi-local texture features

technical field

The invention relates to the fields of image segmentation method, image processing, pattern recognition and artificial intelligence, in particular to a two-stage image segmentation method based on semi-local texture features.

Background technique

Texture segmentation is a very challenging problem in image segmentation. Human eyes can easily distinguish different textures, but it is difficult to define texture in mathematical terms, so it is difficult to describe it with a model. In addition, texture may lead to loss of important edges and uneven distribution of gray levels. A currently widely accepted definition is that texture is a series of fine feature details with periodicity and oscillation.

Commonly used image features include: features based on filtering, features based on semi-local information, and features based on the Beltrami framework. Among them, filtering-based features such as gradient filtering and wavelet porous filtering have been applied to feature extraction and image segmentation. Features extracted by Gabor or Morlet wavelet transform are an important basis for distinguishing textures of different directions and scales; obtaining semi-local information based The main method of feature is: extract the gray information of the blocks adjacent to the existing pixels, so as to obtain the semi-local information of each pixel. The idea of this block-based feature vector was first proposed when texture synthesis was introduced, and later , Buades et al. proposed the idea of image denoising based on block differences and non-local averages, Gilboa and Osher proposed a non-local denoising model based on a variable framework, and finally, Bresson and Chan also proposed a model based on the differences between blocks A variable unsupervised segmentation method; the feature based on the Beltrami framework is a new geometric representation of the image, which regards the image feature as a Riemannian manifold embedded in a high-dimensional space. The advantage of this method is that it allows the use of Different geometric tools are used for different image processing (such as noise reduction and segmentation), and can handle any N-dimensional image, but the disadvantage is that it is very sensitive to noise. Therefore, the present invention combines the latter two features, and introduces the extracted features based on semi-local information into the Beltrami framework through mapping, thereby obtaining a new texture feature with strong noise resistance.

The most widely known and successful model in image segmentation is the active contour model first proposed by Kass, Witkin et al., which has been successfully applied to extract anatomical structures in medical imaging. But the disadvantage of this model is that it is sensitive to the initial position of the active contour and does not converge well at the concave boundary of the object. Then Caselles, people such as kimmel improved active contour model, proposed geometric active contour model (GAC), this model can obtain better segmentation result in image segmentation, so the subdivision stage of the present invention just adopts this kind of model.

The present invention proposes a segmentation method different from traditional segmentation ideas, which is mainly divided into two stages: rough segmentation and fine segmentation. First, divide the image into non-overlapping blocks of M×M pixels, extract the texture features of each block based on the Beltrami framework and semi-local information, and then use the K-means algorithm for block clustering to divide the image into four regions According to the principle of photographic composition , the optimal position of the target is determined, and the target is extracted to complete the rough segmentation; finally, the extracted target is finely segmented by the geometric active contour model (GAC), so as to obtain a more accurate segmentation result.

Contents of the invention

The main purpose of the present invention is to propose an idea of coarsely segmenting the target object and then performing fine segmentation, and combine a new texture feature based on the Beltrami framework and semi-local information to apply it to clustering and image segmentation , to obtain more accurate segmentation results.

The technical scheme that the purpose of the present invention and the solution to its technical problem is to adopt is: a kind of two-stage image segmentation method based on semi-local texture features, comprising the following contents:

Let P _{x , y} be a block with pixel (x, y) as the center and size τ×τ, then we have

Use the following mapping X to introduce texture features into the Beltrami framework:

X: (x, y)→(X ₁ =x, X ₂ =y, X ₃ =P _{x , y} (I)) (2)

This map contains local information (spatial location) and semi-local image information (values of pixel blocks around the central pixel). Assume that given a complex texture pattern, the geometric manifold mosaicked to the high-dimensional space by mapping (2) is consistent with the texture we observe (this assumption is true for most natural images). This means that the metric tensor of the manifold in the same texture area is the same. The metric tensor is a variable used to measure the distance between two points on the manifold. When the manifold in a particular area is almost a plane When , the distance between any two points in this area is equal, combined with semi-local image information, it can be seen that the manifold obtained by mapping (2) is almost flat, so this area has the same texture. The corresponding metric tensor in mapping (2) is defined as:

Finally, the texture feature descriptor F is defined as

$\mathrm{<span\; class="notranslate">\; f</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; exp</span>}<span\; class="notranslate">\; (</span><span\; class="notranslate">\; -</span>\frac{\mathrm{<span\; class="notranslate">\; det</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; g</span>}}_{\mathrm{<span\; class="notranslate">\; x</span>}\mathrm{<span\; class="notranslate">\; the\; y</span>}}<span\; class="notranslate">\; )</span>}{{\mathrm{<span\; class="notranslate">\; \&sigma;</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 4</span>}<span\; class="notranslate">\; )</span>$

Among them, σ>0 is a scale parameter, and the Gaussian kernel function is used as a low-pass filter to control the degree of describing image details.

In addition, for color images, the derivation process is also very simple. Let the color image be I=(I ₁ , I ₂ , . . . , I _k ), where k is the dimension of the image, and the corresponding semi-local mapping is:

X: (x, y) → (X ₁ = x, X ₂ = y, X ₃ = P _{x , y} (I ₁ ), ..., X _2+k = P _{x , y} (I _k )) (5)

The corresponding metric tensor is written in the following form:

In addition, the geometric active contour model can be transformed into the following minimization problem:

$\begin{array}{cc}\underset{\mathrm{<span\; class="notranslate">\; C</span>}}{\mathrm{<span\; class="notranslate">\; m</span>}\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; no</span>}}& <span\; class="notranslate">\; \{</span>{\mathrm{<span\; class="notranslate">\; E.</span>}}_{\mathrm{<span\; class="notranslate">\; G</span>}\mathrm{<span\; class="notranslate">\; 4</span>}\mathrm{<span\; class="notranslate">\; C</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; C</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>{<span\; class="notranslate">\; \&Integral;</span>}_{\mathrm{<span\; class="notranslate">\; 0</span>}}^{\mathrm{<span\; class="notranslate">\; L</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; C</span>}<span\; class="notranslate">\; )</span>}\mathrm{<span\; class="notranslate">\; g</span>}<span\; class="notranslate">\; (</span><span\; class="notranslate">\; |</span><span\; class="notranslate">\; \&dtri;</span>{\mathrm{<span\; class="notranslate">\; I</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; C</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; the\; s</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; )</span><span\; class="notranslate">\; |</span><span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; d</span>}\mathrm{<span\; class="notranslate">\; the\; s</span>}<span\; class="notranslate">\; \}</span>\end{array}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 7</span>}<span\; class="notranslate">\; )</span>$

where ds is the length of the Euclidean element, is the length of curve C. Therefore, the energy functional (7) is actually a new length obtained by integrating the function g containing object boundary information by ds. The function g is an edge indicator function used to eliminate such as For the edge of such an object, I ₀ is the original image, and β is an arbitrary constant. The Euler-Lagrange equation of the function E _GAC can be obtained by the variational method, and the gradient descent method can minimize E _GAC as quickly as possible:

in, t is an artificially specified time parameter, k and N are the curvature and the normal of the curve C, respectively, and there is a unique solution to the evolution equation of the active contour defined in formula (8). The level set method proposed by Osher and Sethian effectively solves the contour extension problem and handles the topology change problem. Equation (8) can be written in the following level set form:

Among them, φ is the level set function embedded in the constantly evolving activity profile C (such as C(t)={x∈R ^N |φ(x,t)=0}), based on the law of hyperbolic conservation, the partial differential equation ( 9) It can be applied to various numerical solutions to obtain quite accurate segmentation results.

Compared with the prior art, the advantages and effects of the present invention are: 1) It proposes a segmentation method that first performs rough segmentation to extract the target object and then performs fine segmentation. This coarse-to-fine segmentation strategy can be used to segment objects with Pictures with blurry or complex backgrounds. 2) A new type of texture feature based on the Beltrami framework and semi-local information is defined, which has stronger discrimination than a single feature and has a strong anti-noise ability. The texture feature is used in clustering and image segmentation. More accurate experimental results can be obtained.

Description of drawings

Fig.1 Flow chart of a two-stage image segmentation method based on semi-local texture features

detailed description

As shown in Figure 1 , the overall process of the present invention is as follows: firstly, the image is divided into non-overlapping small blocks of M×M pixels; secondly, the texture features based on the Beltrami framework and semi-local information of each block are extracted, and then K -means algorithm for block clustering, divide the picture into four areas; then determine the best position of the target according to the principle of photographic composition , so as to extract the target and complete the rough segmentation; finally use the geometric active contour model (GAC) to analyze the extracted The resulting target is finely segmented to obtain more accurate segmentation results.

Concrete steps of the present invention are as follows:

Step S101: Divide the image into non-overlapping small blocks of M×M pixels

Considering the effect of texture features and the time complexity of the algorithm, all pictures are normalized to 126×189 or 189×126, and the size of the divided small blocks is 3×3, so each normalized image includes 2646 small blocks.

Step S102: Extract the texture features of each block based on the Beltrami framework and semi-local information, and then use the K-means algorithm for block clustering to divide the picture into four regions

1) Select a block P _{x , y} whose size is τ×τ centered on the pixel (x, y):

2) Use the following mapping X to introduce texture features into the Beltrami framework:

X: (x, y) → (X ₁ =x, X ₂ =y, X ₃ =P _{x , y} (I)) (11)

This map contains local information (spatial location) and semi-local image information (values of pixel blocks around the central pixel). Assuming that given a complex texture pattern, the geometric manifold mosaiced into the high-dimensional space by mapping (11) is consistent with the texture we observe, the corresponding metric tensor in mapping (11) is defined as:

3) Extract the texture features of each block based on the Beltrami framework and semi-local information

Finally, the texture feature descriptor F is obtained as

$\mathrm{<span\; class="notranslate">\; f</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; exp</span>}<span\; class="notranslate">\; (</span><span\; class="notranslate">\; -</span>\frac{\mathrm{<span\; class="notranslate">\; det</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; g</span>}}_{\mathrm{<span\; class="notranslate">\; x</span>}\mathrm{<span\; class="notranslate">\; the\; y</span>}}<span\; class="notranslate">\; )</span>}{{\mathrm{<span\; class="notranslate">\; \&sigma;</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 13</span>}<span\; class="notranslate">\; )</span>$

Among them, σ>0 is a scale parameter, and the Gaussian kernel function is used as a low-pass filter to control the degree of describing image details.

4) Clustering with the K-means method, clustering the images into four categories

Step S103: Determine the best position of the target according to the principle of photographic composition , so as to extract the target and complete the rough segmentation

1) Merge the results obtained in the previous step

A given image only needs to be divided into the foreground area and the background area in the end, and the areas that meet a certain similarity in the image obtained in the previous step are merged. The similarity measure is defined as:

$\mathrm{<span\; class="notranslate">\; the\; s</span>}\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span><span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; d</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ;</span>\mathrm{<span\; class="notranslate">\; d</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span><span\; class="notranslate">\; |</span><span\; class="notranslate">\; |</span>{\stackrel{<span\; class="notranslate">\; \&Right\; Arrow;</span>}{\mathrm{<span\; class="notranslate">\; R</span>}}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; -</span>{\stackrel{<span\; class="notranslate">\; \&Right\; Arrow;</span>}{\mathrm{<span\; class="notranslate">\; R</span>}}}_{\mathrm{<span\; class="notranslate">\; j</span>}}<span\; class="notranslate">\; |</span><span\; class="notranslate">\; |</span>$

i, j=0, 1, ..., N _r , i≠j (14)

Among them, R _i is the texture feature vector, d(R _i , R _j ) is the distance between the vectors R _i and R _j , the similarity measure is inversely proportional to the distance, so the region with the largest similarity (minimum distance) is calculated After merging, the eigenvectors of the new merged regions are recomputed until only two regions are left in the image.

2) Determine the best position of the target according to the principle of photographic composition

There are generally two methods for determining the best position in photographic composition : the method of thirds and the method of dynamic symmetry. The method of thirds composition refers to dividing the image into thirds horizontally and vertically, and the position of the four intersection points in the image is the best position of the target, that is, the foreground area. The dynamic symmetry method refers to making a diagonal line of the image, and then drawing vertical lines from the other two corners to the diagonal line. The position of the two intersection points in the image is the best position of the target, and the other areas are the background area. .

3) Extract the target object

First obtain the binary images of the foreground and background regions respectively, and then perform the AND operation on the mask table of the thirds composition method or the dynamic symmetry method with the two binary images, and extract the target from the binary image with the largest number of pixels, and then One is the background area by default.

Step S104: use the geometric active contour model to subdivide the extracted target, so as to obtain a more accurate segmentation result

1) Geometric active contour model (GAC)

The geometric active contour model (GAC) can be transformed into the following minimization problem:

$\begin{array}{cc}\underset{\mathrm{<span\; class="notranslate">\; C</span>}}{\mathrm{<span\; class="notranslate">\; m</span>}\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; no</span>}}& <span\; class="notranslate">\; \{</span>{\mathrm{<span\; class="notranslate">\; E.</span>}}_{\mathrm{<span\; class="notranslate">\; G</span>}\mathrm{<span\; class="notranslate">\; 4</span>}\mathrm{<span\; class="notranslate">\; C</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; C</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>{<span\; class="notranslate">\; \&Integral;</span>}_{\mathrm{<span\; class="notranslate">\; 0</span>}}^{\mathrm{<span\; class="notranslate">\; L</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; C</span>}<span\; class="notranslate">\; )</span>}\mathrm{<span\; class="notranslate">\; g</span>}<span\; class="notranslate">\; (</span><span\; class="notranslate">\; |</span><span\; class="notranslate">\; \&dtri;</span>{\mathrm{<span\; class="notranslate">\; I</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; C</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; the\; s</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; )</span><span\; class="notranslate">\; |</span><span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; d</span>}\mathrm{<span\; class="notranslate">\; the\; s</span>}<span\; class="notranslate">\; \}</span>\end{array}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 15</span>}<span\; class="notranslate">\; )</span>$

where ds is the length of the Euclidean element, is the length of curve C. Therefore, the energy functional (15) is actually a new length obtained by integrating the function g containing object boundary information by ds. The function g is an edge indicator function used to eliminate such as For the edge of such an object, I ₀ is the original image, and β is an arbitrary constant. The Euler-Lagrange equation of the function E _GAC can be obtained by the variational method, and the gradient descent method can minimize E _GAC as quickly as possible:

in, t is an artificially specified time parameter, k and N are the curvature and the normal of the curve C, respectively, and there is a unique solution to the evolution equation of the active contour defined in formula (16).

2) Rewrite the level set function

The level set method proposed by Osher and Sethian effectively solves the contour extension problem and handles the topology change problem. Equation (16) can be written in the following level set form:

Among them, φ is the level set function embedded in the constantly evolving activity profile C (such as C(t)={x∈R ^N |φ(x,t)=0}), based on the law of hyperbolic conservation, the partial differential equation ( 17) It can be applied to various numerical solutions to obtain quite accurate segmentation results.

3) Perform fine segmentation on the target object extracted by the rough segmentation to obtain the segmentation result.

Claims (5)

1. a two-stage image segmentation method based on semi-local texture feature, is characterized in that, comprises the following steps: Step 1, dividing the image into non-overlapping small blocks of M×M pixels; Step 2, extract the texture features based on the Beltrami framework and semi-local information of each block, then use the K-means algorithm to cluster the blocks, and divide the picture into four regions; Step 3. Determine the best position of the target according to the principle of photographic composition , so as to extract the target and complete the rough segmentation; Step 4, use the geometric active contour model to subdivide the extracted target, so as to obtain a more accurate segmentation result. 2. the two-stage image segmentation method based on semi-local texture features according to claim 1, in said step 1, the image is segmented into non-overlapping small blocks of M * M pixels, characterized in that: Considering the effect of texture features and the time complexity of the algorithm, all pictures are normalized to 126×189 or 189×126, and the size of the divided small blocks is 3×3, so each normalized image includes 2646 small blocks. 3. the two-stage image segmentation method based on semi-local texture feature according to claim 1, in the described step 2, extract the texture feature based on Beltrami framework and semi-local information of each block, then carry out with K-means algorithm Block clustering, which divides the picture into four regions, is characterized by: 1) Select a block P _{x , y} whose size is τ×τ centered on the pixel (x, y): 2) Use the following mapping X to introduce texture features into the Beltrami framework: X: (x, y) → (X ₁ =x, X ₂ =y, X ₃ =P _{x , y} (I)) (2) This map contains local information (spatial location) and semi-local image information (values of pixel blocks around the central pixel). Assuming a complex texture pattern is given, the geometric manifold mosaiced into the high-dimensional space by mapping (2) is consistent with the texture we observe, and the corresponding metric tensor in mapping (2) is defined as: 3) Extract the texture features of each block based on the Beltrami framework and semi-local information Finally, the texture feature descriptor F is obtained as Among them, σ>0 is a scale parameter, and the Gaussian kernel function is used as a low-pass filter to control the degree of describing image details. 4) Carry out clustering with the K-means method, and cluster the images into four categories. 4. the two-stage image segmentation method based on semi-local texture features according to claim 1, in said step 3, determine the optimal position of the target according to the photographic composition principle, thereby extracting the target, and completing the rough segmentation, its feature in: 1) Merge the results obtained in the previous step A given image only needs to be divided into the foreground area and the background area in the end, and the areas that meet a certain similarity in the image obtained in the previous step are merged. The similarity measure is defined as: Among them, R _i is the texture feature vector, d(R _i , R _j ) is the distance between the vectors R _i and R _j , the similarity measure is inversely proportional to the distance, so the region with the largest similarity (minimum distance) is calculated After merging, the eigenvectors of the new merged regions are recomputed until only two regions are left in the image. 2) Determine the best position of the target according to the principle of photographic composition There are generally two methods for determining the best position in photographic composition : the method of thirds and the method of dynamic symmetry. The method of thirds composition refers to dividing the image into thirds horizontally and vertically, and the position of the four intersection points in the image is the best position of the target, that is, the foreground area. The dynamic symmetry method refers to making a diagonal line of the image, and then drawing vertical lines from the other two corners to the diagonal line. The position of the two intersection points in the image is the best position of the target, and the other areas are the background area. . 3) Extract the target object First obtain the binary images of the foreground and background regions respectively, and then perform the AND operation on the mask table of the thirds composition method or the dynamic symmetry method with the two binary images, and extract the target from the binary image with the largest number of pixels, and then One is the background area by default. 5. The two-stage image segmentation method based on semi-local texture features according to claim 1, in said step 4, the extracted target is finely segmented with a geometric active contour model, thereby obtaining a more accurate segmentation result, It is characterized by: 1) Geometric active contour model (GAC) The geometric active contour model (GAC) can be transformed into the following minimization problem: where ds is the length of the Euclidean element, is the length of curve C. Therefore, the energy functional (6) is actually a new length obtained by integrating the function g containing object boundary information by ds. The function g is an edge indicator function used to eliminate such as For the edge of such an object, I ₀ is the original image, and β is an arbitrary constant. The function can be obtained by the method of variation The Euler-Lagrangian equation, the gradient descent method can minimize as quickly as possible in, t is an artificially specified time parameter, k and N are the curvature and the normal of the curve C, respectively, and there is a unique solution to the evolution equation of the active contour defined in formula (7). 2) Rewrite the level set function The level set method proposed by Osher and Sethian effectively solves the contour extension problem and handles the topology change problem. Equation (7) can be written in the following level set form: Among them, φ is the level set function embedded in the constantly evolving activity profile C (such as C(t)={x∈R ^N |φ(x,t)=0}), based on the law of hyperbolic conservation, the partial differential equation ( 8) It can be applied to various numerical solutions to obtain quite accurate segmentation results. 3) Perform fine segmentation on the target object extracted by the rough segmentation to obtain the segmentation result.