CN103971355A - Digital image noise-proof categorizing technology based on geodesic distance - Google Patents

Abstract

The invention discloses a digital image noise-proof categorizing technology based on geodesic distance. The technology includes: by an algorithm, properly selecting the initial centers of k categories; in the ith iteration, calculating the similarity of an optional pixel to k centers, and categorizing the pixel to category of the center with the shortest distance; calculating the mean value of each area, and updating clustering centers; if the values of all the k clustering centers are unchanged, stopping iteration, or else continuing iteration. By the technology, the influence of noise can be eliminated effectively to obtain clear cutting effect, the color space and the physical space of an image are combined to allow the pixels of each cluster to be close in color and space, and problems of overcutting and unobvious boundary are solved effectively.

Description

Digital picture anti-noise sorting technique based on geodesic distance

(1) technical field

The present invention relates to digital picture anti-noise sorting technique, belongs to image processing field.

(2) background technology

Image is the source the most intuitively that the mankind obtain objective things information, in information transmission, can bring into play effect unique.Along with high-tech development, Digital Image Processing is applied in the industry-by-industries such as military affairs, meteorology, medical science, traffic more and more.

In order to reduce the error of image processing, need to extract area-of-interest, therefore will be to Image Segmentation Using.It is that piece image is divided into several mutually disjoint subregions that image is cut apart, and the pixel of same subregion inside has some same or analogous characteristic (as gray scale, color, texture etc.).It is a kind of important image processing techniques that image is cut apart, and it is the committed step of being processed graphical analysis by image, in theoretical research and practical operation, is all widely used.

Geodesic distance is a key concept in mathematical morphology, is used for measuring the distance between 2.Different with Euclidean distance, geodesic distance has been considered the connectedness in region.In connected graph, at least exist a circuit can connect A, B 2 points, a shortest geodesic arc being called between A, B in all these lines, the length of geodesic arc is geodesic distance.Geodesic distance utilization be the gradient of figure, along the maximum direction of gradient, 2 connections are obtained to geodesic arc.

K means clustering method (K-means algorithm) is the most classical clustering method based on dividing, and is one of ten communication classics data mining algorithm.Its basic thought is: by space K point centered by carry out cluster, to the most close they object sort out.By the method for iteration, successively upgrade the value of each cluster centre, until obtain best cluster result.

K means clustering algorithm is during successfully application image is cut apart, but also there are several shortcomings in it: the Euclidean distance of (1) original K means clustering algorithm based between pixel, whether adjacently in physical space only consider between pixel, ignored the connectedness between pixel; (2) original K mean algorithm is successfully processed isotropic images, but may occur over-segmentation phenomenon, and can not obtain zone boundary clearly for noisy image.

(3) summary of the invention

The present invention proposes a kind of digital picture anti-noise sorting technique based on geodesic distance, it has considered the physical space of pixel and the distance of color space, can be effectively to the Image Segmentation Using with noise.

For realizing segmentation effect, the present invention adopts following scheme:

Weighting K means clustering algorithm based on geodesic distance is to revise on original K mean cluster basis, each pixel is replaced with geodesic distance to the distance of cluster centre, and it is weighted to amendment, carry out cluster with amended formula, iteration, cuts apart thereby realize image.

Concrete steps of the present invention are:

1. suitably select the initial center of k class;

2. in the i time iteration, to any one pixel, ask its similarity that arrives k center, this pixel is grouped into the class apart from place, Duan center;

3. ask the average in each region, upgrade cluster centre;

4. for all k cluster centre, if value remains unchanged after 2,3, iteration finishes, otherwise continues iteration.

Step 1 looks for k bar line as cluster centre exactly in image to be split, distinguishes k region with this.If this k cluster centre is C=(C ₁, C ₂... C _k), each cluster centre region is W=(W ₁, W ₂... W _k), cluster centre C _ithe cluster at place is W _i, k is the number of cluster centre, will be divided into k region.

Step 2 be according to each pixel s in given once step computed image to the similarity of each cluster centre (comprising the distance in similarity and the physical space of color), thereby judge the cluster under each pixel.Calculate this distance and be divided into following steps:

2-1. utilizes the color value of image to carry out color cluster to its pixel, and its step is as follows:

2-1-1. calculates the probability distribution function of each cluster centre region:

P(x|W _i)，(i＝1，2......k)

2-1-2. calculates each pixel and belongs to W _iprobability:

$P_{\mathrm{Wi}}\left(x\right)=\frac{P\left(x\right|W_i)}{\underset{i=1}{\overset{k}{\mathrm{\Σ}}}P\left(x\right|W_i)},(i=\mathrm{1,2}......k)$

2-1-3. calculates P _wi(x) gradient:

$D_{\mathrm{Wi}}={\▿P}_{\mathrm{Wi}}\left(x\right),(i=\mathrm{1,2}......k)$

2-1-4. establishes C _{s1, s2}(p), p ∈ (0,1) is from a S ₁to a S ₂at the path of color space, i.e. S ₁and S ₂communication path, for pixel s, we will find s to arrive each cluster centre C _ithe path of any point c, and calculate the distance in this path by formula below:

$d(s,c)=\underset{C_{s,c}}{\min }{\∫}_0^1|D_{\mathrm{Wi}}\·C_{s,c}\left(p\right)|\mathrm{dp},c\∈C_i,(i=\mathrm{1,2}......k)$

Wherein c is C _iin pixel.This formula has been obtained s to each cluster centre C _ithe shortest color distance of each pixel of (i=1,2......k).

This step of 2-1-5. is used for judging the cluster under pixel s in color space.According to following formula obtain s to the color of each cluster apart from U _i(s):

$U_i\left(s\right)=\underset{c\∈C_i}{\min }d(s,c),(i=\mathrm{1,2}......,k)$

Find and make U _i(s) minimum C _i, we temporarily define pixel s and belong to C _iplace cluster W _i.So far we have obtained the cluster W obtaining taking C as cluster centre, and we define this cluster for (C; W).

The following content of 2-2. is the physical relation of analyzing between pixel.The cluster that color space forms can correspondingly obtain the D of cutting apart in image physical space _i, that is:

D _i＝{s|s∈U _i}，(i＝1，2......，k)

For each pixel s, we establish the neighborhood that Nr (s) is s, and this neighborhood can be the square region of r × r centered by s, can be also taking s as the center of circle, the circle that r is radius.

Suppose that the number of pixels in Nr (s) is | Nr (s) |, D _iand in Nr (s) intersecting area except the number of pixels of s is N _i(s) D, not belonging in Nr (s) _ithe number of pixel be n _i(s)=| Nr (s) |-N _i(s)-1.

Formula is below for analyzing the physical relation between pixel:

D _i(s)＝2λn _i(s)

Wherein λ is edge weights, and λ=1/r ³

2-3. comprehensive above to pixel and cluster centre in the relation of color space and physical space, draw a pixel s and cluster centre C _irange formula:

$\mathrm{dist}(s,C_i)=\sqrt{{\left(U_i\left(s\right)\right)}^2+D_i\left(s\right)}$

Make the minimum C of above distance _ithe cluster W at place _iit is the cluster under s.

Step 3 item is to ask the mean value AVG of pixel in each cluster _i(i=1,2......, k), carries out iteration with this as new cluster centre.

Step 4 item is the variation that there is no pixel value after the iteration of carrying out 2,3 steps, and algorithm finishes, otherwise proceeds 2,3 iteration.

(4) brief description of the drawings

Fig. 1 is schematic flow sheet of the present invention.

(5) embodiment

Below in conjunction with accompanying drawing, the present invention will be further described.

As shown in Fig. 1 process flow diagram, the present invention includes following steps:

1. in image to be split, look for k bar line as cluster centre, cluster centre integrates the (C as C= ₁, C ₂... C _k), cluster areas integrates the (W as W= ₁, W ₂... W _k), cluster centre C _ithe cluster at place is W _i, k is the number of cluster centre, will be divided into k region.

2. utilize the color value of image to carry out color cluster to its pixel:

2-1-1. calculates the probability distribution function of each cluster centre region:

P(x|W _i)，(i＝1，2......k)

2-1-2. calculates each pixel and belongs to cluster W _iprobability:

$P_{\mathrm{Wi}}\left(x\right)=\frac{P\left(x\right|W_i)}{\underset{i=1}{\overset{k}{\mathrm{\Σ}}}P\left(x\right|W_i)},(i=\mathrm{1,2}......k)$

2-1-3. calculates P _wi(x) gradient:

$D_{\mathrm{Wi}}={\▿P}_{\mathrm{Wi}}\left(x\right),(i=\mathrm{1,2}......k)$

2-1-4. establishes C _{s1, s2}(p), p ∈ (0,1) is from a S ₁to a S ₂at the path of color space, i.e. S ₁and S ₂communication path, for pixel s, we will find s to arrive each cluster centre C _ithe path of any point c, and calculate the distance in this path by formula below:

$d(s,c)=\underset{C_{s,c}}{\min }{\∫}_0^1|D_{\mathrm{Wi}}\·C_{s,c}\left(p\right)|\mathrm{dp},c\∈C_i,(i=\mathrm{1,2}......k)$

Wherein c is C _iin pixel.This formula has been obtained s to each cluster centre C _ithe shortest color distance of each pixel of (i=1,2......k).

This step of 2-1-5. is used for judging the cluster under pixel s in color space.According to following formula obtain s to the color of each cluster apart from U _i(s):

$U_i\left(s\right)=\underset{c\∈C_i}{\min }d(s,c),(i=\mathrm{1,2}......,k)$

Find and make U _i(s) minimum C _i, we temporarily define pixel s and belong to C _iplace cluster W _i.So far we have obtained the cluster W obtaining taking C as cluster centre, and we define this cluster for (C; W).

The following content of 2-2. is the physical relation of analyzing between pixel.The cluster that color space forms can correspondingly obtain the D of cutting apart in image physical space _i, that is:

D _i＝{s|s∈U _i}，(i＝1，2......，k)

For each pixel s, we establish the neighborhood that Nr (s) is s, and this neighborhood can be the square region of r × r centered by s, can be also taking s as the center of circle, the circle that r is radius.

Suppose that the number of pixels in Nr (s) is | Nr (s) |, in Di and Nr (s) intersecting area except the number of pixels of s is N _i(s) D, not belonging in Nr (s) _ithe number of pixel be n _i(s)=| Nr (s) |-N _i(s)-1.

Formula is below for analyzing the physical relation between pixel:

D _i(s)＝2λn _i(s)

2-3. comprehensive above to pixel and cluster centre in the relation of color space and physical space, draw a pixel s and cluster centre C _irange formula:

$\mathrm{dist}(s,C_i)=\sqrt{{\left(U_i\left(s\right)\right)}^2+D_i\left(s\right)}$

Make the minimum C of above distance _ithe cluster W at place _iit is the cluster under s.

3. ask the mean value AVG of pixel in each cluster _i(i=1,2......, k), carries out iteration with this as new cluster centre.

4. after the iteration of carrying out 2,3 steps, there is no the variation of pixel value, algorithm finishes, otherwise proceeds 2,3 iteration.In sum, the present invention combines color space and the physical space of image, has proposed a kind of digital picture anti-noise sorting technique based on geodesic distance, by the Digital Image Segmentation technology solving with noise.Advantage of the present invention: (1) can eliminate the impact of noise effectively, obtains segmentation effect more clearly; (2) effectively combine color space and the physical space of image, make the pixel in each cluster more approaching on color and space, effectively solved the not obvious problem of over-segmentation and boundary.

Claims (4)

1. the digital picture anti-noise sorting technique based on geodesic distance, has considered the physical space of pixel and the distance of color space, can be effectively to the Image Segmentation Using with noise.

2. a kind of digital picture anti-noise sorting technique based on geodesic distance as claimed in claim 1, mainly comprises following step:

Step 1 is suitably selected the initial center of k class on original image;

Step 2, in the i time iteration, to any one pixel, is asked the similarity at itself and k center, comprising the distance in similarity on color space and physical space, this pixel is grouped into the class at the most similar place, center;

Step 3 is asked the average in each region, is worth renewal cluster centre with this;

Step 4 is for all k cluster centre, if value remains unchanged after step 2,3, iteration finishes, otherwise continues iteration.

3. the digital picture anti-noise sorting technique based on geodesic distance as claimed in claim 2, is characterized in that, in step 1, selects k cluster centre for image, and each cluster centre comprises N Seed Points.

4. the digital picture anti-noise sorting technique based on geodesic distance as claimed in claim 2, is characterized in that, step 2 utilizes the color space of image and physical space information to carry out cluster, is divided into following steps:

(1) calculate image pixel to be split shortest path to each cluster centre on color space, this path distance formula is:

$d(s,c)=\underset{C_{s,c}}{\min }{\∫}_0^1|D_{\mathrm{Wi}}\·C_{s,c}\left(p\right)|\mathrm{dp},c\∈C_i,(i=\mathrm{1,2}......k)$

Wherein c is C _iin pixel, C _{s, c}(p) for some s is to a paths of a c;

Obtain after the distance of point-to-point transmission, continue to obtain s distance U to each cluster in color space _i(s), this range formula is:

$U_i\left(s\right)=\underset{c\∈C_i}{\min }d(s,c),(i=\mathrm{1,2}......,k)$

Find U _i(s) minimum value, the cluster at temporary transient defining point s place is W _i, so far we have obtained the cluster W obtaining taking C as cluster centre, and we define this cluster for (C; W).

(2) each pixel of image is further optimized, considered the distribution of each pixel in physical space.First color space and physical space are carried out to correspondence, that is: D _i={ s|s ∈ U _i, (i=1,2......, k)

Analyze the physical relation between pixel: D _i(s)=2 λ n _i(s), wherein λ is edge weights, and λ=1/r ³.

(3) cluster based under above-mentioned required point s is in color space and physical space, comprehensive color space and physical space are considered, obtain the cluster under s according to total range formula.Total cluster formula: $\mathrm{dist}(s,C_i)=\sqrt{{\left(U_i\left(s\right)\right)}^2+D_i\left(s\right)},$ This is apart from minimum C _ithe cluster W at place _iit is the cluster under s.