CN102542543A - Block similarity-based interactive image segmenting method - Google Patents

Abstract

The invention discloses an interactive image segmentation method based on block similarity, which mainly solves the problems of inaccurate feature similarity analysis and limited performance promotion in the existing method. The implementation steps are: (1) extract the brightness information of the image background and foreground marker blocks, and use the block similarity of the image to perform similarity analysis on the image; (2) calculate the The geodesic distance between a pixel point and the foreground marker point and the background marker point respectively; (3) get the probability that the pixel point belongs to the foreground and the background according to the result of the geodesic distance; (4) divide the image into the foreground and the background according to the size of the probability . The present invention effectively utilizes the feature information of image marking blocks, uses the block information to perform image similarity analysis, is more accurate than traditional image feature similarity analysis, has better segmentation result consistency, and has low background interference, and can be used for natural images segmentation.

Description

An Interactive Image Segmentation Method Based on Block Similarity

technical field

The invention belongs to the technical field of image processing, and in particular relates to an image segmentation method, which can be used for natural image segmentation in the fields of national defense military situation monitoring, environmental change assessment, astronomical images, medical images, and the like.

Background technique

Image segmentation is an image processing technology that divides an image into meaningful regions or parts according to needs, and it is a hot issue in image processing research. An image often contains different parts, such as objects, environments, backgrounds, etc., and there are areas of interest to people in these parts. Therefore, the image is divided into several parts, and the characteristics of the sub-images and the relationship between them are used to describe Image plays an important role in further image analysis.

According to whether the user participates in the segmentation process, image segmentation can be divided into two types: interactive image segmentation and non-interactive image segmentation. Interactive image segmentation is generally aimed at the segmentation of the foreground and background of the image. The interactive operation brings the image prior information needed in their segmentation, while the non-interactive image segmentation has no user participation. It is given an image , the algorithm automatically completes the entire segmentation, and the segmentation effect is poor. In 2007, Alexis Protiere and Guillermo Sapiro proposed interactive image segmentation based on Gabor features. By performing Gabor filtering on the image, the window energy features of each sub-band after filtering were extracted, and Gaussian modeling was performed on the energy features of each sub-band to obtain each pixel. The weight probability matrix belonging to the foreground and background. Finally, the weight probability matrix is regarded as a directed weighted graph, the coordinate values of the image column are used as the vertex values, and the corresponding weights in the weight probability matrix are used as the weights of the edges. The image The segmentation problem is transformed into the shortest path problem from all pixels to the marked pixels of the foreground and background, and the images are divided into two categories according to the shortest path obtained.

Interactive image segmentation based on Gabor features, which considers the similarity of the Gabor feature information of each pixel in the image, and is more accurate for the segmentation of synthetic texture images. Although natural images also have certain effects, they are not very strong for natural images with texture information. Generally speaking, the Gabor feature cannot reflect the similar information between image pixels very well, resulting in inaccurate segmentation results, and the background interference is relatively large.

Contents of the invention

The purpose of the present invention is to overcome the deficiencies of the above-mentioned prior art, and propose an interactive image segmentation method based on block similarity, to accurately reflect similar information between image pixels, improve the consistency of segmentation results, and reduce background interference .

To achieve the above object, the present invention comprises the following steps:

(1) Assuming that the input image to be segmented obeys the Markov distribution, construct the weight probability formula p(x _i |x _j ) of the pixels in the image to be segmented and the background and foreground:

$\mathrm{<span\; class="notranslate">\; p</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; |</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{{\mathrm{<span\; class="notranslate">\; Z</span>}}_{{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}}}\mathrm{<span\; class="notranslate">\; exp</span>}<span\; class="notranslate">\; (</span><span\; class="notranslate">\; -</span>\frac{{<span\; class="notranslate">\; |</span><span\; class="notranslate">\; |</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}<span\; class="notranslate">\; |</span><span\; class="notranslate">\; |</span>}_{\mathrm{<span\; class="notranslate">\; 2</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}{{{\mathrm{<span\; class="notranslate">\; 4</span>}\mathrm{<span\; class="notranslate">\; \&sigma;</span>}}_{{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ,</span>$

为归一化因子，

为像素点x_i与像素点x_j之间的欧式距离，

为以像素点x_i为中心的块方差；Among them, x _i is the pixel to be processed, x _j is the rest of the pixels in the similar window centered on x _i ,

is the normalization factor,

is the Euclidean distance between pixel point x _i and pixel point x _j ,

is the block variance centered on pixel x _i ;

(2) Input the foreground and background labeled images of the image to be segmented, introduce the size of the image block into the obtained weight probability formula, and perform block information similarity analysis on the brightness information of the image to be segmented, and obtain the pixel point x _i to be processed that belongs to Process the weight probability pf( _xi ) of the pixel point x _i and the foreground marker point and the weight probability pb(xi ₎ of the background marker point:

$\mathrm{<span\; class="notranslate">\; pf</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{{\mathrm{<span\; class="notranslate">\; Z</span>}}_{{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}}}\mathrm{<span\; class="notranslate">\; exp</span>}<span\; class="notranslate">\; (</span><span\; class="notranslate">\; -</span>\frac{\mathrm{<span\; class="notranslate">\; df</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; )</span>}{{\mathrm{<span\; class="notranslate">\; 4</span>}\mathrm{<span\; class="notranslate">\; \&sigma;</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}\mathrm{<span\; class="notranslate">\; N</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ,</span>$ $\mathrm{<span\; class="notranslate">\; pb</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{{\mathrm{<span\; class="notranslate">\; Z</span>}}_{{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}}}\mathrm{<span\; class="notranslate">\; exp</span>}<span\; class="notranslate">\; (</span><span\; class="notranslate">\; -</span>\frac{\mathrm{<span\; class="notranslate">\; db</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; )</span>}{{\mathrm{<span\; class="notranslate">\; 4</span>}\mathrm{<span\; class="notranslate">\; \&sigma;</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}\mathrm{<span\; class="notranslate">\; N</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ,</span>$

Where x _i is the pixel to be processed, i ∈ 1, 2, 3... M, M is the size of the image to be segmented, x _j is the foreground or background marker pixel, j ∈ 1, 2, 3... C, C is the marker The number of foreground or background pixels, σ is the variance of the image block centered on _xi , the block size is 7×7, df( _xi ) represents the shortest Euclidean distance between pixel _xi and the foreground marker block, db ( _xi ) represents the shortest Euclidean distance between the pixel point x _i and the background marker block, and N is the size of the block;

得到待处理像素点x_i属于前景的相似性概率PF(x_i)，由公式

得到待处理像素点x_i属于背景的相似性概率PB(x_i)；(3) by the formula

Get the similarity probability PF( _xi ) of the pixel point x _i to be processed belonging to the foreground, by the formula

Obtain the similarity probability PB( _xi ) that the pixel point x _i to be processed belongs to the background;

(4) Take 1-PF(xi ₎ as the weight to calculate the geodesic distance d _f ( _xi ) to the foreground, and use Dijkstra's algorithm to find the shortest path to obtain the distance between the pixel point x _i to be processed and the foreground Geodesic distance d _f ( _xi ), using 1-PB(xi ₎ as the weight to calculate the geodesic distance d _b ( _xi ) to the background, using Dijkstra’s algorithm for finding the shortest path to get The geodesic distance d _b ( _xi ) from the pixel point x _i to the background;

及属于背景的概率

(5) According to the geodesic distance d _f (x _i ), d _b (x _i ), it is obtained that the pixel to be processed belongs to the foreground

and the probability of belonging to the background

${\mathrm{<span\; class="notranslate">\; PB</span>}}_{{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}}<span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; b</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; )</span>}{{\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; b</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; f</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; ,</span>$

${\mathrm{<span\; class="notranslate">\; PF</span>}}_{{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}}<span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; f</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; )</span>}{{\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; b</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; f</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; .</span>$

与背景的概率

的大小得到像素点的分割结果：若把待处理像素点x_i判为背景像素点，若

则把待处理像素点x_i判为背景像素点。(6) According to the probability that the pixel to be processed belongs to the foreground

Probability with background

The size of the pixel to get the segmentation result: if Determine the pixel point x _i to be processed as the background pixel point, if

Then judge the pixel point x _i to be processed as a background pixel point.

(7) Steps (2)-(6) are repeated until all pixels in the input image to be segmented are processed, and the final segmentation result of the image to be segmented is obtained.

Compared with existing methods, the present invention has the following advantages:

Since the present invention uses the Euclidean distance between blocks of image pixels to reflect the characteristic information between image pixels, it can obtain a more accurate similarity probability matrix, better reflect the similarity information between images, and can comprehensively grasp the image The overall information of the segmentation results has less background interference and is not easy to cause misclassification.

Description of drawings

Fig. 1 is a flow chart of the present invention;

Fig. 2 is the natural image that the present invention tests to use;

Fig. 3 is the foreground and the background label diagram of the natural image that the present invention tests to use;

Fig. 4 is a comparison diagram of the segmentation results of Fig. 2 with the present invention and existing methods;

Fig. 5 is a difference diagram between the segmentation result of Fig. 2 and the ideal template by using the present invention and the existing method.

Detailed ways

The embodiments of the present invention are described in detail below: this embodiment is implemented under the premise of the technical solution of the present invention, and detailed implementation methods and processes are provided, but the protection scope of the present invention is not limited to the following embodiments.

With reference to Fig. 1, invention comprises the steps:

Step 1: Under the assumption that the input image to be segmented obeys the Markov distribution, construct the weight probability formula p( _xi |x _j ).

为：(1a) In image denoising, according to the Bayesian estimation theory framework, the estimated value of the pixel

for:

$\stackrel{<span\; class="notranslate">\; ^</span>}{\mathrm{<span\; class="notranslate">\; x</span>}}<span\; class="notranslate">\; =</span>\frac{\underset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{{\mathrm{<span\; class="notranslate">\; N</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}\mathrm{<span\; class="notranslate">\; p</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; |</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}<span\; class="notranslate">\; )</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}}{\underset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{{\mathrm{<span\; class="notranslate">\; N</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}\mathrm{<span\; class="notranslate">\; p</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; |</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; ,</span>$

Among them, x _i is the pixel to be estimated, x _j is the remaining pixels in the similar window centered on x _i , p( _xi | x _j ) is the weight probability of pixel x _i and pixel x _j information, N _i is the size of the search window centered on pixel x _i ;

(1b) Assuming that each pixel in the image to be segmented is independent of each other and obeys the Gaussian Markov distribution, let p( _xi |x _j )=p( _xi -x _j ), then according to the Markov distribution model:

$\mathrm{<span\; class="notranslate">\; p</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; |</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{{\mathrm{<span\; class="notranslate">\; Z</span>}}_{{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}}}\mathrm{<span\; class="notranslate">\; exp</span>}<span\; class="notranslate">\; (</span><span\; class="notranslate">\; -</span>\frac{{<span\; class="notranslate">\; |</span><span\; class="notranslate">\; |</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; \&mu;</span>}}_{{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; \&mu;</span>}}_{{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}}<span\; class="notranslate">\; |</span><span\; class="notranslate">\; |</span>}_{\mathrm{<span\; class="notranslate">\; 2</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}{\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; \&sigma;</span>}}_{{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="2"\; label="i"\; filenames="HDA0000129287140000022.png"\; state="\{\{state\}\}">i</figure-callout></span>}}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; \&sigma;</span>}}_{{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ,</span>$

为以x_i为中心的块均值，

为以x_i为中心的块方差，

为以x_j为中心的块均值，

以x_j为中心的块方差，

为归一化因子；in,

is the block mean centered on _xi ,

is the block variance centered on _xi ,

is the block mean centered on _xj ,

block variance centered at _xj ,

is the normalization factor;

则(2b)中的p(x_i|x_j)变为：(1c) Since all pixels obey the Gaussian Markov distribution, so

Then p( _xi |x _j ) in (2b) becomes:

$\mathrm{<span\; class="notranslate">\; p</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; |</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{{\mathrm{<span\; class="notranslate">\; Z</span>}}_{{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}}}\mathrm{<span\; class="notranslate">\; exp</span>}<span\; class="notranslate">\; (</span><span\; class="notranslate">\; -</span>\frac{{<span\; class="notranslate">\; |</span><span\; class="notranslate">\; |</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}<span\; class="notranslate">\; |</span><span\; class="notranslate">\; |</span>}_{\mathrm{<span\; class="notranslate">\; 2</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}{{{\mathrm{<span\; class="notranslate">\; 4</span>}\mathrm{<span\; class="notranslate">\; \&sigma;</span>}}_{{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ,</span>$

为像素点x_i与像素点x_j之间的欧式距离。in,

is the Euclidean distance between pixel point x _i and pixel point x _j .

Step 2: According to the weight probability p( _xi |x _j ), analyze the block information similarity of the input marked image, and obtain the similarity probabilities of the pixels to be processed with the foreground and background respectively.

(2a) Input the marked image, where the marked points are divided into two types: foreground and background;

(2b) Introduce the size of the image block into the weight probability formula, analyze the similarity of the block information on the brightness information of the image to be segmented, and obtain the similarity weight pf( _xi ) of the pixel point x _i to be processed and the foreground marker point and The similarity probability pb( _xi ) of the background marker points:

$\mathrm{<span\; class="notranslate">\; pf</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{{\mathrm{<span\; class="notranslate">\; Z</span>}}_{{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}}}\mathrm{<span\; class="notranslate">\; exp</span>}<span\; class="notranslate">\; (</span><span\; class="notranslate">\; -</span>\frac{\mathrm{<span\; class="notranslate">\; df</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; )</span>}{{\mathrm{<span\; class="notranslate">\; 4</span>}\mathrm{<span\; class="notranslate">\; \&sigma;</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}\mathrm{<span\; class="notranslate">\; N</span>}}<span\; class="notranslate">\; )</span>$ $\mathrm{<span\; class="notranslate">\; pb</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{{\mathrm{<span\; class="notranslate">\; Z</span>}}_{{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}}}\mathrm{<span\; class="notranslate">\; exp</span>}<span\; class="notranslate">\; (</span><span\; class="notranslate">\; -</span>\frac{\mathrm{<span\; class="notranslate">\; db</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; )</span>}{{\mathrm{<span\; class="notranslate">\; 4</span>}\mathrm{<span\; class="notranslate">\; \&sigma;</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}\mathrm{<span\; class="notranslate">\; N</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ,</span>$

Where x _i is the pixel to be processed, i ∈ 1, 2, 3... M, M is the size of the image to be segmented, x _j is the foreground or background marker pixel, j ∈ 1, 2, 3... C, C is the marker The number of foreground or background pixels, σ is the variance of the image block centered on _xi , and the block size is 7×7, is the normalization factor, df( _xi ) represents the shortest Euclidean distance between the pixel point x _i and the foreground marker block, db( _xi ) represents the shortest Euclidean distance between the pixel point x _i and the background marker block, and N is the block’s size;

(2d) by the formula $\mathrm{PF}\left(x_i\right)=\frac{\mathrm{pf}\left(x_i\right)}{\mathrm{pf}\left(x_i\right)+\mathrm{pf}\left(x_i\right)},$ $\mathrm{PB}\left(x_i\right)=\frac{\mathrm{pb}\left(x_i\right)}{\mathrm{pf}\left(x_i\right)+\mathrm{pb}\left(x_i\right)}$ Obtain the similarity probability PF(xi ₎ of the foreground and the similarity probability PB(xi ₎ of the background for the pixel point x _i to be processed respectively;

Step 3: Calculate the geodesic distance d _f ( _xi ) from the pixel point x _i to be processed to the foreground. Take 1-PF( _xi ) as the weight needed to calculate the geodesic distance, and calculate the geodesic distance:

(3a) Initialize the geodesic distance from the foreground marker point to the foreground to 0, initialize the geodesic distance of the background to infinity, and use the foreground marker point as a sample point;

(3b) According to the 8-neighborhood matrix of the pixel point, search the 8-connected neighborhood pixel point of the current sample, and find out the pixel point with the smallest weight among these pixel points;

(3c) Add the pixel with the smallest weight to the path of the geodesic distance, and sort according to the size;

(3d) For other pixels on the path, perform weight correction according to the weight of the newly added pixel, and the smaller of the original weight of the pixel and the corrected weight is used as the updated weight probability of other pixels on the path ;

(3e) use the newly added pixel as a new sample, and repeat steps (3b)-(3d) until all the pixels in the image are searched;

(3f) take the updated weight probability of the pixel point x _i to be processed as the geodesic distance d _f (xi ₎ from the pixel point x _i to the foreground;

Step 4: Calculate the geodesic distance d _b ( _xi ) from the pixel point x _i to be processed to the background:

Take 1-PB( _xi ) as the weight needed to calculate the geodesic distance, and calculate the geodesic distance:

(4a) Initialize the geodesic distance from the background marker point to the background to 0, initialize the geodesic distance of the foreground to infinity, and use the background marker point as a sample point;

(4b) According to the 8-neighborhood matrix of the pixel point, search the 8-connected neighborhood pixel point of the current sample, and find out the pixel point with the smallest weight among these pixel points;

(4c) Add the pixel with the smallest weight to the path of geodesic distance, and sort according to size; (4d) For other pixels on the path, perform weight correction according to the weight of the newly added pixel, take The smaller of the original weight of the pixel and the corrected weight is used as the updated weight probability of other pixels on the path;

(4e) use the newly added pixel as a new sample, and repeat steps (4b)-(4d), until all the pixels in the image are searched;

(4f) take the updated weight probability of the pixel point x _i to be processed as the geodesic distance d _b (xi ₎ from the pixel point x _i to the background;

及属于背景的概率

Step 5: According to the geodesic distance d _f (x _i ), d _b (x _i ), it is obtained that the pixel to be processed belongs to the foreground

and the probability of belonging to the background

${\mathrm{<span\; class="notranslate">\; PB</span>}}_{{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}}<span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; b</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; )</span>}{{\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; b</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; f</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; ,</span>$

${\mathrm{<span\; class="notranslate">\; PF</span>}}_{{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}}<span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; f</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; )</span>}{{\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; b</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; f</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; .</span>$

的大小得到像素点的分割结果：若

把待处理像素点x_i判为背景像素点，若

则把待处理像素点x_i判为背景像素点。Step 6: According to the probability that the pixel to be processed belongs to the foreground Probability with background

The size of the pixel to get the segmentation result: if

Determine the pixel point x _i to be processed as the background pixel point, if

Then judge the pixel point x _i to be processed as a background pixel point.

Step 7: Repeat steps 2-6 until all pixels in the input image to be segmented are processed, and the final segmentation result of the image to be segmented is obtained.

Effect of the present invention is further illustrated by following simulation:

1. Simulation conditions:

The present invention adopts the image shown in Fig. 2 as the test image, wherein Fig. 2 (a) is the test image bird to be segmented, Fig. 2 (b) is the test image cat to be segmented, and Fig. 2 (c) is the test image vase to be segmented, The software platform is MATLAB7.0.

Mark the foreground and background pixels respectively for the test image to be segmented shown in Figure 2(a), Figure 2(b), and Figure 2(c), and Figure 3(a) is the labeled image of the test image shown in Figure 2(a) , Figure 3(b) is the labeled map of the test chart shown in Figure 2(b), and Figure 3(c) is the labeled map of the test chart shown in Figure 2(c), where the dotted lines represent foreground pixels and the solid lines represent background pixels .

2. Simulation content

Simulation 1, using the existing Gabor feature and the method of the present invention to test Figure 2 (b) simulation experiment, the experimental results as shown in Figure 4, wherein, Figure 4 (a) is an existing segmentation result figure based on Gabor feature, Fig. 4(b) is a segmentation result figure of the method of the present invention,

Simulation 2, using the existing Gabor feature and the method of the present invention to carry out the simulation experiment on the segmentation result and the ideal template diagram of the test figure 2 (b), the experimental results are as shown in Figure 5, where Figure 5 (a) is based on the existing The difference between the segmentation result of the Gabor feature and the ideal template. The white area represents the misclassified pixels. FIG.

2. Simulation results:

From Figure 4(a) and Figure 5(a), it can be seen that the method based on Gabor features is weak in the ability to obtain the foreground target of the image, the overall grasp of the image is not accurate enough, the background information of the image is relatively disturbed, and it will cause target errors. score results.

It can be seen from Fig. 4(b) and Fig. 5(b) that the method of the present invention has a relatively accurate grasp of the overall structure of the image, more accurate feature similarity analysis, better consistency of segmentation results, and low background interference.

Using the misclassification rate as the evaluation standard of the segmentation results, the methods in Figure 4(a) and Figure 4(b) are compared, and the evaluation indicators are shown in Table 1.

Table 1: Comparison of misclassification rate (%) of two segmentation methods

bird cat vase Gabor characteristics 5.1749 13.3302 21.15 The method of the present invention 3.3386 7.4799 9.8532

It can be seen from Table 1 that the traditional similarity analysis of Gabor features cannot make good use of similar information between image pixels, and the weight probability of geodesic distance is not accurate enough, resulting in unsatisfactory segmentation results. The method of the invention can effectively utilize the block information of the image to perform segmentation experiments on different images. It can be seen from the experiment that the present invention is superior to the similarity analysis based on the traditional Gabor feature method in grasping the overall information of the image and reducing the background interference.

Claims (4)

1. An interactive image segmentation method based on block similarity, comprising the steps of: (1) Assuming that the input image to be segmented obeys the Markov distribution, construct the weight probability formula p(x _i |x _j ) of the pixels in the image to be segmented and the background and foreground: $\mathrm{<span\; class="notranslate">\; p</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; |</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{{\mathrm{<span\; class="notranslate">\; Z</span>}}_{{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}}}\mathrm{<span\; class="notranslate">\; exp</span>}<span\; class="notranslate">\; (</span><span\; class="notranslate">\; -</span>\frac{{<span\; class="notranslate">\; |</span><span\; class="notranslate">\; |</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}<span\; class="notranslate">\; |</span><span\; class="notranslate">\; |</span>}_{\mathrm{<span\; class="notranslate">\; 2</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}{{{\mathrm{<span\; class="notranslate">\; 4</span>}\mathrm{<span\; class="notranslate">\; \&sigma;</span>}}_{{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ,</span>$ Among them, x _i is the pixel to be processed, x _j is the rest of the pixels in the similar window centered on x _i , is the normalization factor,

is the Euclidean distance between pixel point x _i and pixel point x _j ,

is the block variance centered on pixel x _i ; (2) Input the foreground and background labeled images of the image to be segmented, introduce the size of the image block into the obtained weight probability formula, and perform block information similarity analysis on the brightness information of the image to be segmented, and obtain the pixel point x _i to be processed that belongs to Process the weight probability pf( _xi ) of the pixel point x _i and the foreground marker point and the weight probability pb(xi ₎ of the background marker point: $\mathrm{<span\; class="notranslate">\; pf</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{{\mathrm{<span\; class="notranslate">\; Z</span>}}_{{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}}}\mathrm{<span\; class="notranslate">\; exp</span>}<span\; class="notranslate">\; (</span><span\; class="notranslate">\; -</span>\frac{\mathrm{<span\; class="notranslate">\; df</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; )</span>}{{\mathrm{<span\; class="notranslate">\; 4</span>}\mathrm{<span\; class="notranslate">\; \&sigma;</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}\mathrm{<span\; class="notranslate">\; N</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ,</span>$ $\mathrm{<span\; class="notranslate">\; pb</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{{\mathrm{<span\; class="notranslate">\; Z</span>}}_{{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}}}\mathrm{<span\; class="notranslate">\; exp</span>}<span\; class="notranslate">\; (</span><span\; class="notranslate">\; -</span>\frac{\mathrm{<span\; class="notranslate">\; db</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; )</span>}{{\mathrm{<span\; class="notranslate">\; 4</span>}\mathrm{<span\; class="notranslate">\; \&sigma;</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}\mathrm{<span\; class="notranslate">\; N</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ,</span>$ Where x _i is the pixel to be processed, i ∈ 1, 2, 3... M, M is the size of the image to be segmented, x _j is the foreground or background marker pixel, j ∈ 1, 2, 3... C, C is the marker The number of foreground or background pixels, σ is the variance of the image block centered on _xi , the block size is 7×7, df( _xi ) represents the shortest Euclidean distance between pixel _xi and the foreground marker block, db ( _xi ) represents the shortest Euclidean distance between the pixel point x _i and the background marker block, and N is the size of the block; (3) by the formula

Get the similarity probability PF( _xi ) of the pixel point x _i to be processed belonging to the foreground, by the formula Obtain the similarity probability PB( _xi ) that the pixel point x _i to be processed belongs to the background; (4) Take 1-PF(xi ₎ as the weight to calculate the geodesic distance d _f ( _xi ) to the foreground, and use Dijkstra's algorithm to find the shortest path to obtain the distance between the pixel point x _i to be processed and the foreground Geodesic distance d _f ( _xi ), using 1-PB(xi ₎ as the weight to calculate the geodesic distance d _b ( _xi ) to the background, using Dijkstra’s algorithm for finding the shortest path to get The geodesic distance d _b ( _xi ) from the pixel point x _i to the background; (5) According to the geodesic distance d _f (x _i ), d _b (x _i ), it is obtained that the pixel to be processed belongs to the foreground

and the probability of belonging to the background

${\mathrm{<span\; class="notranslate">\; PB</span>}}_{{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}}<span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; b</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; )</span>}{{\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; b</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; f</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; ,</span>$ ${\mathrm{<span\; class="notranslate">\; PF</span>}}_{{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}}<span\; class="notranslate">\; =</span>\frac{{\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; f</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; )</span>}{{\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; b</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; d</span>}}_{\mathrm{<span\; class="notranslate">\; f</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; ;</span>$ (6) According to the probability that the pixel to be processed belongs to the foreground

Probability with background

The size of the pixel to get the segmentation result: if

Determine the pixel point x _i to be processed as the background pixel point, if

Then judge the pixel point x _i to be processed as a background pixel point; (7) Steps (2)-(6) are repeated until all pixels in the input image to be segmented are processed, and the final segmentation result of the image to be segmented is obtained. 2. the method for the geodesic distance image segmentation based on block similarity according to claim 1, wherein the described construction of step (1) goes out the weight probability formula of pixel point and background and foreground in the image to be segmented, as follows Steps to proceed: (2a) In image denoising, according to the Bayesian estimation theory framework, the estimated value of the pixel

for: $\stackrel{<span\; class="notranslate">\; ^</span>}{\mathrm{<span\; class="notranslate">\; x</span>}}<span\; class="notranslate">\; =</span>\frac{\underset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{{\mathrm{<span\; class="notranslate">\; N</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}\mathrm{<span\; class="notranslate">\; p</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; |</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}<span\; class="notranslate">\; )</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}}{\underset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{{\mathrm{<span\; class="notranslate">\; N</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}\mathrm{<span\; class="notranslate">\; p</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; |</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; ,</span>$ Among them, x _i is the pixel to be estimated, x _j is the remaining pixels in the similar window centered on x _i , p( _xi | x _j ) is the weight probability of pixel x _i and pixel x _j information, N _i is the size of the search window centered on pixel x _i ; (2b) Assuming that each pixel in the image to be segmented is independent of each other and obeys the Gaussian Markov distribution, let p( _xi |x _j )=p( _xi -x _j ), then according to the Markov distribution model: $\mathrm{<span\; class="notranslate">\; p</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; |</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{{\mathrm{<span\; class="notranslate">\; Z</span>}}_{{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}}}\mathrm{<span\; class="notranslate">\; exp</span>}<span\; class="notranslate">\; (</span><span\; class="notranslate">\; -</span>\frac{{<span\; class="notranslate">\; |</span><span\; class="notranslate">\; |</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; \&mu;</span>}}_{{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; \&mu;</span>}}_{{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}}<span\; class="notranslate">\; |</span><span\; class="notranslate">\; |</span>}_{\mathrm{<span\; class="notranslate">\; 2</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}{\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; \&sigma;</span>}}_{{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; \&sigma;</span>}}_{{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ,</span>$ in,

is the block mean centered on _xi ,

is the block variance centered on _xi ,

is the block mean centered on _xj ,

block variance centered at _xj ,

is the normalization factor; (2c) Since all pixels obey the Gaussian Markov distribution, so

Then p( _xi |x _j ) in (2b) becomes: $\mathrm{<span\; class="notranslate">\; p</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; |</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{{\mathrm{<span\; class="notranslate">\; Z</span>}}_{{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}}}\mathrm{<span\; class="notranslate">\; exp</span>}<span\; class="notranslate">\; (</span><span\; class="notranslate">\; -</span>\frac{{<span\; class="notranslate">\; |</span><span\; class="notranslate">\; |</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}<span\; class="notranslate">\; |</span><span\; class="notranslate">\; |</span>}_{\mathrm{<span\; class="notranslate">\; 2</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}{{{\mathrm{<span\; class="notranslate">\; 4</span>}\mathrm{<span\; class="notranslate">\; \&sigma;</span>}}_{{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ,</span>$ in,

is the Euclidean distance between pixel point x _i and pixel point x _j . 3. the method for the geodesic distance image segmentation based on block similarity according to claim 1, wherein the algorithm that utilizes Dijkstra to seek the shortest path described in step (4) obtains the pixel point _x to be processed to the foreground The geodesic distance d _f ( _xi ) of , proceed as follows: (3a) Initialize the geodesic distance from the foreground marker point to the foreground to 0, initialize the geodesic distance of the background to infinity, and use the foreground marker point as a sample point; (3b) According to the 8-neighborhood matrix of the pixel point, search the 8-connected neighborhood pixel point of the current sample, and find out the pixel point with the smallest weight among these pixel points; (3c) Add the pixel with the smallest weight to the path of the geodesic distance, and sort according to the size; (3d) For other pixels on the path, perform weight correction according to the weight of the newly added pixel, and take the smaller of the original weight of the pixel and the corrected weight as the updated weight of other pixels on the path probability; (3e) use the newly added pixel as a new sample, and repeat steps (3b)-(3d) until all the pixels in the image are searched; (3f) Take the updated weight probability of the pixel point x _i to be processed as the geodesic distance d _f (xi ₎ from the pixel point x _i to the foreground. 4. the method for the geodesic distance image segmentation based on block similarity according to claim 1, wherein the algorithm that utilizes Dijkstra to seek the shortest path described in step (4) obtains pixel point _x to be processed to background The geodesic distance d _b ( _xi ) of , according to the following steps: (4a) Initialize the geodesic distance from the background marker point to the background to 0, initialize the geodesic distance of the foreground to infinity, and use the background marker point as a sample point; (4b) According to the 8-neighborhood matrix of the pixel point, search the 8-connected neighborhood pixel point of the current sample, and find out the pixel point with the smallest weight among these pixel points; (4c) Add the pixel with the smallest weight to the path of the geodesic distance, and sort according to the size; (4d) For other pixels on the path, perform weight correction according to the weight of the newly added pixel, and take the smaller of the original weight of the pixel and the corrected weight as the updated weight of other pixels on the path probability; (4e) use the newly added pixel as a new sample, and repeat steps (4b)-(4d), until all the pixels in the image are searched; (4f) Take the updated weight probability of the pixel point x _i to be processed as the geodesic distance d _b (xi ₎ from the pixel point x _i to the foreground.

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