CN105427307B - A kind of image partition method of cube Granule Computing - Google Patents

Abstract

The invention relates to an image segmentation method for cube grain calculation, which can effectively solve the problems of slow image segmentation speed and poor effect. The technical solution is to first extract the RGB values of the pixels of the color image to be segmented, and then according to the color image to be segmented RGB value, construct the atomic cube grain set, construct the merge operator and the cube grain template between the cube grains, express the RGB value of each pixel of the image to be segmented as a cube grain, and match it with the cube grain template, and Determine the RGB value of each pixel of the segmented image, and finally save the segmented color image, so as to realize the image segmentation of cube granule calculation. The method of the invention has fast segmentation speed and good effect, makes the segmentation result more in line with human vision, is an innovation in the color image segmentation method, and has strong practical application value.

Description

An Image Segmentation Method Based on Cube Granular Computing

technical field

The invention relates to image processing, in particular to an image segmentation method for cube granule calculation.

Background technique

Image segmentation is a core issue in the field of digital image processing and computer vision, and it is also an important research direction of image understanding and analysis. Its purpose is to separate the areas that people are more interested in in the image from other areas. Disjoint, each region satisfies the region-specific consistency. Researchers have done a lot of research on image segmentation and proposed many methods, such as threshold segmentation technology, differential operator edge detection, region growth technology and clustering segmentation technology. However, due to technical problems, the segmentation speed is slow, The effect is poor and cannot meet the actual needs in image processing, so its improvement and innovation are imperative.

Contents of the invention

In view of the above situation, in order to overcome the defects of the prior art, the object of the present invention is to provide an image segmentation method based on cube granule calculation, which can effectively solve the problems of slow image segmentation speed and poor effect.

The technical scheme solved by the present invention is to first extract the pixel point RGB value of the color image to be segmented, and then according to the RGB value of the color image to be segmented, construct an atomic cube grain set, construct a merge operator and a cube grain template between cube grains, The RGB value of each pixel of the image to be segmented is expressed as a cube grain, and it is matched with the cube grain template, and the RGB value of each pixel of the segmented image is determined, and finally the segmented color image is saved to realize the cube grain calculation image segmentation.

The method of the invention has fast segmentation speed and good effect, makes the segmentation result more in line with human vision, is an innovation in the color image segmentation method, and has strong practical application value.

Description of drawings

Fig. 1 is a flowchart block diagram of the present invention.

Fig. 2 is a diagram of the result of merging between two cube grains of the present invention.

Fig. 3 is a segmented image of the present invention.

Detailed ways

The specific implementation manners of the present invention will be described in detail below in conjunction with the accompanying drawings and specific conditions.

Shown in Figure 1, the present invention comprises the following steps when concrete implementation:

(1), extract the pixel RGB value of the color image to be segmented:

Extract the pixel RGB value of the color image to be segmented, R is the red value, G is the green value, B is the blue value, (i, j) is the coordinate of the pixel point, the color is composed of R, G, B, R, The value range of G and B is [0,255];

(2), according to the RGB value of the color image to be segmented, construct the atomic cube particle set:

The RGB value of each pixel of the color image to be segmented is expressed as a cube grain, and the cube grain has the form of g=(C, r), where C=(R, G, B) is the center of the cube grain, and r is the cube grain The side length of the cube represents the size of the cube, which is called the granularity of the cube; when r=0, the cube is the smallest and cannot be divided, which is called an atomic cube. For an image with a height of N1 and a width of N2, its pixel The number is N=N1×N2, and the grain set GS composed of N cubic grains is constructed, and the grain set corresponding to the coordinates (i, j) of the pixel point is N ₁ ×(j-1)+1 cubic grains;

(3), construct the merging operator and the cube-grain template between the cube-grains, the method is:

Two cubic particles g ₁ =(C1,r1), where C1=(R ₁ ,G ₁ ,B ₁ ) is the center of g1, r1 is the particle size of g1, g ₂ =(C2,r2), where C2=(R ₂ , G ₂ , B ₂ ) is the center of g2, r2 is the granularity of g2, and the center and granularity of the cubic grain are combined, and the center of the cubic grain is calculated from the centers of g1 and g2 according to formula 1, formula 2 and formula 3 ( Ru,Gu,Bu):

Ru＝0.5(max{R1+0.5r1, R2+0.5r2}+min{R1-0.5r1, R2-0.5r2}) Formula 1

Gu＝0.5(max{G1+0.5r1, G2+0.5r2}+min{G1-0.5r1, G2-0.5r2}) Formula 2

Bu＝0.5(max{B1+0.5r1, B2+0.5r2}+min{B1-0.5r1, B2-0.5r2}) Formula 3

From the center and particle size of g1 and g2, according to formula 4, the center of the combined cube grain, ru is the granularity of the combined cube grain:

gu＝g ₁ ∨ g ₂ ＝(Cu,ru) Formula 4;

Wherein Cu=(Ru, Gu, Bu) is the center of the merged cube grain;

According to the following formula:

ru=max{max{R1+0.5r1, R2+0.5r2}-min{R1-0.5r1, R2-0.5r2}, max{G1+0.5r1, G2+0.5r2}-min{G1-0.5r1, G2-0.5r2}, max{B1+0.5r1, B2+0.5r2}-min{B1-0.5r1, B2-0.5r2}} Formula 5

Get the merged cube grain;

Set the particle size threshold ρ to build a cube-grain template, which is a set, represented by GB, and the cube-grain template in the cube-grain template is represented by gb=(Cb,rb), where Cb=(Rb,Gb,Bb) is the template cube is the center of the cube grain, and rb is the grain size of the template cube grain; add the first cube grain of the cube grain set GS to the cube grain template, and delete the first cube grain in the cube grain set GS, and use formula 1 to formula 5 to calculate The merged cube grain gu between all the cube grains in the cube grain set GS and all the cube grains in the cube grain template GB; when the grain size of the cube grain gu is less than or equal to the grain size threshold ρ, gb=gu, and in the cube grain set GS delete the cube grains participating in the merger, when the grain size of the cube grain gu is greater than the grain size threshold ρ, select the first cube grain in the cube grain set GS to join the cube grain template GB, and delete the first cube grain in the cube grain set GS Cube grains, until all the cube grains in the cube grain set GS are deleted, so that the elements in the cube grain template GB continue to increase, while the elements in the cube grain set GS continue to decrease until it is an empty set, that is, a structure containing n The cube-grain template GB of the cube-grain={gb1,gb2,...,gbn);

(4) Express the RGB value of each pixel of the image to be segmented as a cube grain set GS, and match it with the cube grain template. The matching formula is:

D(i,j)＝max{|Rj-Rbi|,|Gj-Gbi|,|Bj-Bbi|} Formula 6

Wherein (Rbi, Gbi, Bbi) is the center of the ith cube grain in the cube grain template, (Rj, Gj, Bj) is the center of the jth cube grain in the cube grain set GS;

Calculate the distance between the jth cube grain of the cube grain set GS and the ith cube grain of the cube grain template GB according to formula 6;

(5), determine the RGB value after the pixel point of the color image to be divided is divided:

According to the distance D(i, j) between the cube grain gj corresponding to the RGB value of the image pixel to be segmented and the cube grain template GB cube grain gbi, find the number of the cube grain in the cube grain template corresponding to the minimum distance id=argminD(i, j), wherein 1<i<n, the center of the id cube grain in the cube grain template is the RGB value after the pixel point division;

(6) Save the segmented color image, save the segmented color image in the corresponding folder of the computer in JPG format, so as to realize the image segmentation of cube grain calculation.

The present invention can also be provided by the following examples in the specific implementation.

The first step is to extract the RGB value of the pixel point of the color image to be segmented, for a 3×4 color image, the RGB value of the pixel point (2,1) is (10,13,34);

The second step is to construct a cube grain set according to the RGB values of the color image to be segmented, express the RGB value as an atomic cube grain, and its cube grain set is GS={g ₁ ,g ₂ ,g ₃ ,g ₄ ,g ₅ , g ₆ , g ₇ , g ₈ , g ₉ , g ₁₀ , g ₁₁ , g ₁₂ }, where

g ₁ =(0,0,0,0), g ₂ =(10,13,34,0), g ₃ =(35,20,15,0), g ₄ =(21,38,12,0 ),

g ₅ =(151,151,155,0) g ₆ =(101,155,98,0) g ₇ =(155,100,95,0) g ₈ =(102,99,155,0)

g ₉ =(255,198,197,0) g ₁₀ =(195,199,255,0) g ₁₁ =(199,255,200,0) g ₁₂ =(255,255,255,0)

The third step is to combine the cube grains to construct the cube grain template. The two cube grains g ₁ =(0,0,0,0) and g ₂ =(10,13,34,0), through formula 1, formula 2, formula 3. For formula 4 and formula 5, the combined cube grains are calculated as gu=g ₁ ∨ g ₂ =(5,6.5,17,34), and the combined results are shown in Figure 2;

Set the granularity threshold ρ, construct a cube-grain template, add the first cube-grain of the cube-grain set GS to the cube-grain template GB, delete the first cube-grain of the granule-set GS, and the second cube-grain becomes the first cube-grain , merge the first cube grain with the cube grains in the cube grain template GB respectively, when the size of the combined cube grain is less than or equal to ρ, the merged cube grain replaces the cube grain of the cube grain template GB. Repeat this process until GS does not contain any cube grains, set the grain size threshold as ρ = 200, and use a 3×4 color image to illustrate the generation process of the cube grain template:

The cube grain set formed by RGB is GS={g ₁ ,g ₂ ,g ₃ ,g ₄ ,g ₅ ,g ₆ ,g ₇ ,g ₈ ,g ₉ ,g ₁₀ ,g ₁₁ ,g ₁₂ }, firstly, the g ₁ is added to the cubic grain template GB, delete g ₁ from GS, the cubic grain template GB has 1 cubic grain GB={gb ₁ }, and gb ₁ =g ₁ , for the first cubic grain g ₂ of GS, According to formula 2 and formula 3, the cubic grain after g ₂ and gb ₁ are merged is gu=g ₂ ∨ gb ₁ =(5,6.5,17,34), because its particle size is 34 less than ρ, gb1=gu, namely gb1 =(5,6.5,17,34), at this time, the cube-grain template has 1 cube-grain, namely GB={gb ₁ };

gu=g ₃ ∨ gb ₁ ＝(11.5,9.425,16.5667,47), because its particle size is 47 less than ρ, gb1=gu,

gu=g ₄ ∨ gb ₁ ＝(12.3436, 11.9625, 16.1611, 52.075), because its granularity is smaller than ρ, gb1=gu,

gu=g ₅ ∨ gb ₁ ＝(68.6887,68.4625,72.5804,165.075), because its particle size is smaller than ρ, gb1=gu,

gu=g6∨gb ₁ ＝(69.4355,70.4625,73.1679,169.075), because its granularity is smaller than ρ, gb1=gu,

gu=g ₇ ∨ gb ₁ ＝(69.9490, 70.6398, 73.2989, 170.102), because its granularity is smaller than ρ, gb1=gu,

gu=g ₈ ∨ gb ₁ ＝(69.9490, 70.6398, 73.2989, 170.102), because its particle size is smaller than ρ, gb1=gu,

gu=g ₉ ∨ gb ₁ ＝(119.9490, 105.0520, 106.7224, 270.102), because its particle size is larger than ρ, gb2=g9,

gu=g ₁₀ ∨ gb ₁ ＝(123.2963,109.2421,113.3357,283.3286), because its particle size is larger than ρ, but gu=g ₁₀ ∨ gb ₂ =(225,198.5,226,60), because its particle size is smaller than ρ, gb2=gu ,

gu=g ₁₁ ∨ gb ₁ ＝(123.8758,112.5005,111.3559,285), because its particle size is larger than ρ, but gu=g ₁₁ ∨ gb ₂ ＝(218.9027,211.75,219.9027,86.5), because its particle size is smaller than ρ, gb2 =gu,

gu=g ₁₂ ∨ gb ₁ =(126.6575,112.5005,114.0880 285), because its particle size is 255 greater than ρ, but gu=g ₁₂ ∨ gb ₂ =(218.9027,211.75,219.9027,86.5), because its particle size is smaller than ρ, gb2=gu,

The obtained cubic grain template is GB={gb ₁ , gb ₂ };

The fourth step is to extract the RGB values of the pixels of the color image to be segmented, and the RGB values of the 3×4 color image to be segmented are

RGB(1,1)=(0,0,0) RGB(2,1)=(10,13,34) RGB(3,1)=(35,20,15)

RGB(1,2)=(21,38,12) RGB(2,2)=(151,151,155) RGB(3,2)=(101,155,98)

RGB(1,3)=(155,100,95) RGB(2,3)=(102,99,155) RGB(3,3)=(255,198,197)

RGB(1,4)=(195,199,255) RGB(2,4)=(199,255,200) RGB(3,4)=(255,255,255)

The corresponding granule set is GS, and the matching distance between it and the cubic granule template GB is

D(1,1)=73.2989, D(1,2)=59.9490, D(1,3)=58.2989, D(1,4)=61.2989, D(1,5)=81.7011, D(1,6 )=84.3602, D(1,7)=85.0510, D(1,8)=81.7011, D(1,9)=185.0510, D(1,10)=181.7011, D(1,11)=184.3602, D (1,12)=185.0510

D(2,1)＝219.9027 D(2,2)＝208.9027 D(2,3)＝204.9027 D(2,4)＝207.9027 D(2,5)＝67.9027D(2,6)＝121.9027 D( 2,7)=124.9027 D(2,8)=116.9027 D(2,9)=36.0973 D(2,10)=35.0973 D(2,11)=43.2500 D(2,12)=43.2500

The fifth step, determine the numbering of the cube grains in the cube grain template GB closest to each cube grain in the GS, and the cube grains of the nearest cube grain template GB to the 12 cube grains are 1, 1, 1, 1, 2, 1,1,1,2,2,2,2, the RGB values of the divided pixels are:

RGB(1,1)=(70,71,73) RGB(2,1)=(70,71,73) RGB(3,1)=(70,71,73)

RGB(1,2)=(70,71,73) RGB(2,2)=(219,222,220) RGB(3,2)=(70,71,73)

RGB(1,3)=(70,71,73) RGB(2,3)=(70,71,73) RGB(3,3)=(219,222,220)

RGB(1,4)=(219,222,220) RGB(2,4)=(219,222,220) RGB(3,4)=(219,222,220);

The sixth step is to save the segmented image, and save the segmented color image in the corresponding folder of the computer in JPG format.

And the experiment has achieved a very good technical effect, the specific situation is as follows:

Experiment 1: It is used to compare the speed of the image segmentation of the present invention with FCM clustering and the image segmentation of Kmeans clustering, and Experiment 2 is used to compare the GCE, VI and RI of the present invention with FCM and Kmeans segmentation.

In order to verify that the present invention has a faster speed, the 154401 (321*481) pixel image with the file name of 3096 in BSD300 is selected for segmentation. The granularity threshold ρ drops from 200 to 100 with a step size of 2, and Table 1 lists the split times for 51 runs. The number of cube grains in the cube grain template obtained by the present invention is used as the clustering number of the FCM and Kmeans methods. The average segmentation time of the present invention is 0.0272, and the average segmentation time of FCM method is 3.1595, and the average segmentation time of Kmeans is 0.3515, and the segmentation speed of the present invention is 116.1581 times of FCM method (3.1595/0.0272=116.1581) 11.5846 times (0.3151) of Kmeans method /0.0272=11.5846).

Experiment two, according to GCE, VI the smaller the better and the RI the bigger the better metric standard, choose the image that BSDS300 size is 154401 (321 * 481) pixel file name is 3096, verify the superiority of the present invention relative to FCM and Kmeans method . The granularity threshold ρ drops from 200 to 100 with a step size of 2, and Table 2 lists the split GCE, VI, and RI for 51 runs. When ρ=152, GCE and VI reach the minimum, which are 0.0094 and 0.1154 respectively, and RI reaches the maximum, which is 0.9909. The segmented image is shown in Figure 3. Figure 3(a) is the artificially segmented image, Figure 3(b) is the segmented image corresponding to the minimum GCE, Figure 3(c) is the segmented image corresponding to the minimum VI, and Figure 3(d) is the segmented image corresponding to the maximum RI. For the FCM method, the minimum GCE is 0.02, the minimum VI is 0.9641, and the maximum RI is 0.6124. Kmeans method, the minimum GCE is 0.02, the minimum VI is 0.9004, and the maximum RI is 0.6515.

Table 1 The segmentation time comparison between the present invention and Kmeans and FCM

Table 2 The present invention compares with GCE, VI and RI of FCM and Kmeans segmentation

It can be seen from the above that the present invention is a set division method for granular computing, that is, the set is divided into a set composed of subsets, and the grain is expressed in a standardized form. Since a color image is a combination of red (R), The RGB value of the image generated by fusing the three color information of green (G) and blue (B) can represent the grain as a cube in three-dimensional space, that is, cube grain. The RGB value of the image to be segmented is expressed as a cube grain, and the cube grain with a smaller granularity is merged into a cube grain with a larger granularity by using the merge operator between the cube grains, so that the RGB value of each pixel is in a unique cube in the grain. Granular computing is an effective method to achieve space conversion with different granularities, which is consistent with the degree of people's recognition of the image's thickness. Therefore, the use of granular computing to segment images reflects the objective laws of people's understanding of images. Compared with the prior art, it has the following outstanding advantages:

1, segmentation speed is fast, because the method of the present invention can finish the segmentation of image by once scanning the pixel value of known image, its computational complexity is O (N), and wherein N is the size of image;

2, segmentation effect is good, utilizes GCE (Global Consistency Error) that D.Martin proposes, VI (Variant Information) that M.Meilǎ proposes and RI (Rand Index) three methods that W.M.Rand proposes evaluate the performance of the image segmentation of the present invention , and select the image evaluation basis in BSDS300, an image segmentation data set commonly used in the world. This data set includes original images and artificially segmented images. It is an innovation in image segmentation methods and has strong practicability.

Claims (2)

1. a kind of image partition method of cube Granule Computing, which is characterized in that the pixel of the colored image to be split of extraction first Point rgb value constructs atom cube grain collection further according to the rgb value of coloured image to be split, builds the merging between cube grain The rgb value of each pixel of image to be split is expressed as cube grain by operator and cube grain template, and by itself and cube Grain template is matched, and determines the rgb value of each pixel of image after segmentation, finally preserves Segmentation of Color Images, to real The image segmentation of existing cube Granule Computing, specifically includes following steps：

(1), the pixel rgb value of the colored image to be split of extraction：

The pixel rgb value of the colored image to be split of extraction, R are red value, and G is green value, and B is blue valve, and (i, j) is pixel The coordinate of point, color are made of R, G, B, and the value range of R, G, B are [0,255]；

(2), according to the rgb value of coloured image to be split, atom cube grain collection is constructed：

The rgb value of each pixel of coloured image to be split is expressed as cube grain, cube grain has the shape of g=(C, r) Formula, wherein C=(R, G, B) are the center of cube grain, and r is the length of side of cube grain, indicates the size of cube grain, referred to as vertical The granularity of cube grain；As r=0, cube grain is minimum and cannot divide again, referred to as atom cube grain, is to a height of N1, width The image of N2, pixel number are N=N1 × N2, construct the grain collection GS being made of N number of cube grain, the coordinate (i, j) of pixel Corresponding cube grain is N₁+ 1 cube grain of × (j-1)；

(3), the combined operators between structure cube grain and cube grain template, method are：

Two cube grain g₁=(C1, r1), wherein C1=(R₁,G₁,B₁) be g1 center, r1 be g1 granularity, g₂=(C2, R2), wherein C2=(R₂,G₂,B₂) be g2 center, r2 is the granularity of g2, merges center and the granularity of cube grain, by g1 and The center of g2 calculates the center (Ru, Gu, Bu) of cube grain according to formula 1, formula 2, formula 3：

Ru=0.5 (max { R1+0.5r1, R2+0.5r2 }+min { R1-0.5r1, R2-0.5r2 }) formula 1

Gu=0.5 (max { G1+0.5r1, G2+0.5r2 }+min { G1-0.5r1, G2-0.5r2 }) formula 2

Bu=0.5 (max { B1+0.5r1, B2+0.5r2 }+min { B1-0.5r1, B2-0.5r2 }) formula 3

Center by g1 and g2 and granularity merge the center of cube grain according to formula 4, and ru is the granularity for merging cube grain：

Gu=g₁∨g₂=(Cu, ru) formulas 4；

Wherein Cu=(Ru, Gu, Bu) is the center for merging cube grain；

According to the following formula：

Ru=max { max { R1+0.5r1, R2+0.5r2 }-min { R1-0.5r1, R2-0.5r2 }, max { G1+0.5r1, G2+0.5r2 }- Min { G1-0.5r1, G2-0.5r2 }, max { B1+0.5r1, B2+0.5r2 }-min { B1-0.5r1, B2-0.5r2 } } formula 5

It obtains merging cube grain；

Granularity thresholds ρ is set, cube grain template is built, which is a set, is indicated with GB, in cube grain template Cube grain indicates that wherein Cb=(Rb, Gb, Bb) is the center of template cube grain with gb=(Cb, rb), and rb is template cube The granularity of body grain；First cube grain of cube grain collection GS is added in cube grain template, and is deleted in cube grain collection GS First cube grain is removed, the same all cube grains and cube grain template calculated with formula 1 to formula 5 in cube grain collection GS Merging cube grain gu in GB between all cube grains；When the granularity of cube grain gu is less than or equal to granularity thresholds ρ, Gb=gu, and leave out in cube grain collection GS and participate in combined cube grain, when the granularity of cube grain gu is more than granularity When threshold value ρ, cube grain template GB is added in first cube grain for choosing cube grain collection GS, and in cube grain collection GS In leave out first cube grain, until cube grain all in cube grain collection GS is all left out, such cube grain Element in template GB is continuously increased, and cube grain integrates the element in GS and constantly reduces until as empty set, that is, constructs containing n A cube grain cube grain template GB=gb1, gb2 ..., gbn)；

(4), the rgb value of each pixel of image to be split is expressed as cube grain collection GS, and by itself and cube grain template It is matched, matching formula is：

D (i, j)=max | Rj-Rbi |, | Gj-Gbi |, | Bj-Bbi | } formula 6

The center of i-th of cube grain wherein in (Rbi, Gbi, Bbi) cube grain template, (Rj, Gj, Bj) are cube grain collection The center of j-th of cube grain of GS；

According to formula 6 calculate between j-th of cube grain of cube grain collection GS and cube grain template i-th of cube grain of GB away from From；

(5), the rgb value after color image pixel point segmentation to be split is determined：

According to the corresponding cube grain gj of the rgb value of image slices vegetarian refreshments to be split and cube grain template GB cube grains gbi it Between distance D (i, j), find out the number id=of the cube grain in the cube grain template corresponding to minimum distance ArgminD (i, j), wherein 1<i<N, after the center of i-th d cube grain is pixel segmentation in cube grain template Rgb value；

(6), Segmentation of Color Images is preserved, the coloured image after segmentation is saved in the corresponding file of computer with JPG formats In, to realize the image segmentation of cube Granule Computing.

2. the image partition method of cube Granule Computing according to claim 1, which is characterized in that include the following steps：

The rgb value of the first step, extraction color image pixel point to be split, 3 × 4 coloured image, the RGB of pixel (2,1) Value is (10,13,34)；

Second step, according to the rgb value of coloured image to be split, construct cube grain collection, rgb value be expressed as atom cube Grain, cube grain integrate as GS={ g₁,g₂,g₃,g₄,g₅,g₆,g₇,g₈,g₉,g₁₀,g₁₁,g₁₂, wherein

g₁=(0,0,0,0), g₂=(10,13,34,0), g₃=(35,20,15,0), g₄=(21,38,12,0),

g₅=(151,151,155,0) g₆=(101,155,98,0) g₇=(155,100,95,0) g₈=(102,99,155, 0)

g₉=(255,198,197,0) g₁₀=(195,199,255,0) g₁₁=(199,255,200,0) g₁₂=(255,255, 255,0)

Third step merges cube grain, constructs cube grain template, two cube grain g₁=(0,0,0,0) and g₂=(10,13, 34,0) it, by formula 1, formula 2, formula 3, formula 4 and formula 5, calculates and merges cube grain for gu=g₁∨g₂=(5,6.5,17,34)；

Granularity thresholds ρ is set, cube grain template is constructed, cube grain mould is added in first cube grain of cube grain collection GS In plate GB, leave out first cube grain of grain collection GS, second cube grain becomes first cube grain, vertical by first Cube grain merges respectively at the cube grain in cube grain template GB, when the granularity for merging cube grain is less than or equal to ρ, Merge the cube grain that cube grain replaces cube grain template GB, repeats this process, until GS is free of any cube grain, If granularity thresholds are ρ=200, the generating process of cube grain template is illustrated with 3 × 4 coloured images：

The cube grain that RGB is formed integrates as GS={ g₁,g₂,g₃,g₄,g₅,g₆,g₇,g₈,g₉,g₁₀,g₁₁,g₁₂, first by g₁It is added In cube grain template GB, g is left out from GS₁, cube grain template GB has 1 cube grain GB={ gb₁, and gb₁=g₁, For first cube grain g of GS₂, according to formula 2 and formula 3, g₂With gb₁Cube grain after merging is gu=g₂∨gb₁=(5, 6.5,17,34), since its granularity is 34 to be less than ρ, gb1=gu, i.e. gb1=(5,6.5,17,34), at this time cube grain template There are 1 cube grain, i.e. GB={ gb₁}；

Gu=g₃∨gb₁=(11.5,9.425,16.5667,47), since its granularity is less than ρ, gb1=gu for 47,

Gu=g₄∨gb₁=(12.3436,11.9625,16.1611,52.075), since its granularity is less than ρ, gb1=gu,

Gu=g₅∨gb₁=(68.6887,68.4625,72.5804,165.075), since its granularity is less than ρ, gb1=gu,

Gu=g6 ∨ gb₁=(69.4355,70.4625,73.1679,169.075), since its granularity is less than ρ, gb1=gu,

Gu=g₇∨gb₁=(69.9490,70.6398,73.2989,170.102), since its granularity is less than ρ, gb1=gu,

Gu=g₈∨gb₁=(69.9490,70.6398,73.2989,170.102), since its granularity is less than ρ, gb1=gu,

Gu=g₉∨gb₁=(119.9490,105.0520,106.7224,270.102), since its granularity is more than ρ, gb2=g9,

Gu=g₁₀∨gb₁=(123.2963,109.2421,113.3357,283.3286), since its granularity is more than ρ, but gu =g₁₀∨gb₂=(225,198.5,226,60), since its granularity is less than ρ, gb2=gu,

Gu=g₁₁∨gb₁=(123.8758,112.5005,111.3559,285), since its granularity is more than ρ, but gu=g₁₁ ∨gb₂=(218.9027,211.75,219.9027,86.5), since its granularity is less than ρ, gb2=gu,

Gu=g₁₂∨gb₁=(126.6575,112.5005,114.0880 285), since its granularity is 255 to be more than ρ, but gu =g₁₂∨gb₂=(218.9027,211.75,219.9027,86.5), since its granularity is less than ρ, gb2=gu,

Obtained cube grain template is GB={ gb₁, gb₂}；

The rgb value of 4th step, extraction color image pixel point to be split, 3 × 4 coloured image to be split its rgb value are followed successively by：

RGB (1,1)=(0,0,0) RGB (2,1)=(10,13,34) RGB (3,1)=(35,20,15)

RGB (1,2)=(21,38,12) RGB (2,2)=(151,151,155) RGB (3,2)=(101,155,98)

RGB (1,3)=(155,100,95) RGB (2,3)=(102,99,155) RGB (3,3)=(255,198,197)

RGB (1,4)=(195,199,255) RGB (2,4)=(199,255,200) RGB (3,4)=(255,255,255)

Its corresponding grain integrates as GS, and the matching distance between cube grain template GB is：

D (1,1)=73.2989, D (1,2)=59.9490, D (1,3)=58.2989, D (1,4)=61.2989, D (1, 5)=81.7011, D (1,6)=84.3602, D (1,7)=85.0510, D (1,8)=81.7011, D (1,9)= 185.0510, D (1,10)=181.7011, D (1,11)=184.3602, D (1,12)=185.0510

D (2,1)=219.9027 D (2,2)=208.9027 D (2,3)=204.9027 D (2,4)=207.9027 D (2, 5)=67.9027 D (2,6)=121.9027 D (2,7)=124.9027 D (2,8)=116.9027 D (2,9)= 36.0973 D (2,10)=35.0973 D (2,11)=43.2500 D (2,12)=43.2500；

5th step determines the number away from cube grain in the nearest cube grain template GB of each cube grain in GS, vertical away from 12 The number of the cube grain of the nearest cube grain template GB of cube grain is 1,1,1,1,2,1,1,1,2,2,2,2, after segmentation The rgb value of pixel is：

RGB (1,1)=(70,71,73) RGB (2,1)=(70,71,73) RGB (3,1)=(70,71,73)

RGB (1,2)=(70,71,73) RGB (2,2)=(219,222,220) RGB (3,2)=(70,71,73)

RGB (1,3)=(70,71,73) RGB (2,3)=(70,71,73) RGB (3,3)=(219,222,220)

RGB (1,4)=(219,222,220) RGB (2,4)=(219,222,220) RGB (3,4)=(219,222,220)；

6th step preserves the image after segmentation, and the coloured image after segmentation is saved in the corresponding file of computer with JPG formats In folder, to realize the image segmentation of cube Granule Computing.