CN106447676A - Image segmentation method based on rapid density clustering algorithm - Google Patents

Abstract

The invention discloses an image segmentation method based on a rapid density clustering algorithm. The image segmentation method comprises the following steps: 1) for a natural image to be processed, firstly carrying out preprocessing and initialization, comprising filtering noise reduction, gray-level registration, area dividing, scale zooming and the like; 2) then carrying out calculation of similarity distance between data points on sub-graphs completing scale variation, and obtaining correlation between pixel points; 3) then carrying out concurrent segmentation processing in each sub-graph, comprising drawing a decision graph based on the density clustering algorithm, carrying out residual analysis to determine a clustering center based on the decision graph and comparing based on the similarity distance to classify remaining points on an original scale sub-graph; and 4) then merging the sub-graphs after the segmentation is completed, and carrying out secondary re-clustering to obtain a segmentation result graph with original size dimensions. The image segmentation method based on the rapid density clustering algorithm for parameter robust provided by the invention can automatically determine the number of segmented classes to realize relatively high segmentation accuracy rate.

Description

A kind of image partition method based on fast density clustering algorithm

Technical field

The invention belongs to technical field of image processing, and in particular to a kind of image partition method.

Background technology

Image segmentation is one of key technology of image procossing, is widely used, and main task is to divide the image into several Specifically, region with unique properties, intra-zone has strong similarity, each interregional with strong diversity.Meanwhile, image Segmentation is also to carry out the important step of data analysiss understanding to image, be by the key of image procossing to graphical analyses.Existing Image partition method mainly divides following a few classes：Based on the dividing method on border, the dividing method based on region and based on specific Theoretical dividing method etc..After the completion of image segmentation, the target for extracting can be used for image, semantic identification, picture search etc. Field, so the quality of image segmentation result will directly affect the accuracy of follow-up identification or search.

Due to polysemy and the complexity of image, all kinds of images can be generally applicable to currently without general segmentation theory Segmentation, the partitioning algorithm for having proposed is both for greatly particular problem, therefore there is still a need for constantly exploring new segmentation Algorithm and segmentation theory, this is also the purpose that studies herein.Based on the dividing method on border be by detect gray level or Person's structure carries out the determination of partitioning boundary where having mutation, the first order differential operator including commonly using have Roberts operator, Prewitt operator and Sobel operator, Second Order Differential Operator has Laplace operator and Kirsh operator etc..Wang Junmin exists《Based on micro- Divide rim detection and its application of operator》In to Roberts operator, Prewitt operator, Sobel operator, Laplace operator, The ultimate principle of LOG operator is analyzed, and summarizes the pluses and minuses of various operators.Canny proposes a kind of new rim detection , on the step change type edge optimum for being affected by white noise, but there is the discontinuous situation in border in method.Miao Jiaqing exists《Self adaptation Dictionary improves Canny operator CT image segmentation》Middle utilization self-adapting dictionary learning algorithm is improved to canny operator.Base Dividing method in region includes Parallel Regional Partition technology and serial domain decomposition technique.Most typical Parallel Regional Partition skill Art is thresholding method, and its key is to determine segmentation threshold, therefore derives global threshold, adaptive threshold, optimal threshold again Etc..Chen Ningning exists《The realization of several threshold segmentation algorithms with compare》In to histogram thresholding method, iterative method and great Jin The conventional threshold value such as method determines that method has carried out Integrated comparative, and Ma Yinghui et al. exists《Color image segmentation method is summarized》Middle by tradition Grey relevant dynamic matrix be applied to coloured image, obtain more preferable segmentation effect using the more color informations of coloured image.Region Growth method and split degree method are two kinds of typical serial regional development and technology, need to carry out growing setting for criterion and split degree criterion Meter, the process of its cutting procedure subsequent step will be judged according to the result of historical steps and be determined.With each subject many New theory and the proposition of new method, occur in that the image partition method that many is combined with some particular theory, method, including base Image segmentation in genetic algorithm, based on the image segmentation of artificial neural network, based on the image segmentation of objective function optimization, base Image segmentation in cluster analyses, based on the image segmentation of MRF, image segmentation based on fuzzy set theory etc..

With the appearance of various in recent years new clustering methods, many image segmentation sides based on clustering algorithm have been derived Method, compared to the dividing method of other particular theory, the image partition method based on cluster analyses provides one for image segmentation Individual new thinking.Meanwhile, it has recently been demonstrated that comprehensively utilizing the positional information between the colouring information of image, pixel, office The texture information in portion region and the contextual information of pixel, can greatly promote segmentation result.Figure based on clustering algorithm As dividing method is also called feature space clustering procedure, it is empty using feature that the problem of dividing the image into is converted to the key of clustering problem Between point represent corresponding pixel in image space, the aggregation result according to them in feature space carried out to feature space point Segmentation, then maps them into original image space, obtains final segmentation result.Classical clustering algorithm has Fuzzy C-means, K-means, Ncut, SLIC, Mean-shift etc..Alex et al. proposes a kind of cluster centre side of portraying of novelty Method, is that the design of clustering algorithm provides a kind of new thinking, is based on the image segmentation that the clustering algorithm is carried out herein, with When high time complexity for former clustering algorithm when big data quantity is processed and high spatial complexity huge with image data amount Contradiction, it is proposed that a series of solution.

Content of the invention

In order to overcome cluster centre sensitivity, the parameter dependence of image partition method presence based on clustering algorithm Greatly, adaptivity is poor, the segmentation deficiency that accurately cannot automatically determine of class number of clusters, the invention provides one kind can be automatically determined point Cut classification number, split the higher image partition method based on fast density clustering algorithm to parameter robust of accuracy rate.

The technical solution adopted for the present invention to solve the technical problems is：

A kind of image partition method based on fast density clustering algorithm,：The method comprising the steps of：

1) initialize, process is as follows：

1.1) carry out area dividing operation first, for a pending image, include the pixel of M row N row, warp After crossing pretreatment, image is divided into 2^W1×2^W2Width subgraph, the sub-graph size for obtaining isWherein Z [f] is front To bracket function；

1.2) and then to image change of scale operation is carried out, the subgraph after the completion of piecemeal is carried out scaling process, i.e., The a size of subimage of a*b is changed into a₁*b₁, wherein a₁=a/k_sizeAnd b₁=b/k_size, k_size＞ 1；During scaling, because Include three pixel values for each pixel, so change of scale is carried out using the method for weak sampling, by pending image Comprising pixel number reduce while retain the important clustering information of original image as far as possible；

2) the similarity distance based on pixel value and positional information is calculated, and process is as follows：

2.1) for a pending natural image I, include M row N row pixel, n=M*N is made, then pixel data CollectionIn the trichroism channel components value that includes under RGB color space of the characteristic information that has of each pixel, as R, G, B Three pixel values；And with the image upper left corner as zero, horizontal line to the right as Y-axis, vertical curve downwards as X-axis two Coordinate figure (x, y) under dimensional plane rectangular coordinate system；

2.2) d is set_p(p1, p2) is the similarity distance between two pixels, and similarity is as follows apart from computing formula：

d_p(p1, p2)=θ d_{p_rgb}(p1,p2)+(1-θ)d_{p_xy}(p1,p2) (3)

In formula (1), r1, g1, b1 and r2, g2, b2 represent the pixel value of pixel p1, p2 under RGB color space respectively, d_{p_rgb}Represent pixel interval under the space from；In formula (2), x1, y1 and x2, y2 represent pixel p1, p2 respectively straight Coordinate figure in angular coordinate system, d_{p_xy}Represent pixel interval in the coordinate system from, in formula (3), θ is weight factor, to use To adjust the contribution that color distance and positional distance determine to similarity；

3) Density Clustering of cluster centre is automatically determined, subgraph is operated, process is as follows：

3.1) the similarity distance between image slices vegetarian refreshments is calculated, it is known that the similarity distance of pixel has duality, i.e., d_p(p1, p2)=d_p(p2, p1), and d_p(p1, p1)=0, therefore similarity distance is stored as that diagonal data are zero upper three Angular moment battle array { Dp_ij}；

3.2) density value of each pixel is calculated, obtains density matrixComputing formula is as follows：

Wherein function

In formula (4), ρ_iRepresent pixel p_iDensity value, the set of pixels of imageCorresponding index set is I_s ={ 1,2 ..., M*N }, d_ij=d_p(pi, pj) represents the similarity distance between two pixels；

3.3) distance value of each pixel is calculated, obtains distance matrixEach pixel p_iDistance value definition For δ_i, first look for comparing p_iThe big pixel of density, obtains set S'={ p_j, then look up in S' with p_iClosest Pixel p_j', then obtain δ_i=d_p(pi,pj')；

3.4) according to step 3.2) and step 3.3) obtainWithDecision diagram is drawn, obtains representing pixel The discrete function δ of density and distance relation_i=f (ρ_i)；

3.5) unitary linear fit is carried out by the discrete data point on ρ-δ graph of a relation, obtains matched curve y_δ=kx_ρ+b₀WithCalculate residual values ε of each data point_δi=y_δi-δ_iAnd ε_ρi=x_ρi-ρ_i, draw residual error rectangular histogram ε_δi- h and ε_ρi- h, carries out normal approach with bell-shaped curve respectively, obtains variance yields σ_δAnd σ_ρ, determined using λ σ principle and be in outside confidence interval Singular point as cluster centre, be designated as c_δAnd c_ρ；

3.6) bivariant discrete function γ=f is obtained by decision diagram_γ(ρ, δ), carries out the fitting on binary inclined-plane, is intended Conjunction plane is z_γ=b₁+b₂ρ+b₃δ, calculates residual values ε of each data point_γi=y_γi(ρ,δ)-γ_i(ρ, δ), draws residual error straight Side figure ε_γi- h, carries out normal approach also with bell-shaped curve, obtains variance yields σ_γ, determined using λ σ principle and be in confidence area Between outer singular point as cluster centre, be designated as c_γ；

Wherein function f_γIt is the binary function with regard to variable ρ and δ, corresponding to the coordinate figure in three dimensions be (ρ, δ, f_γ), then defining bivariate discrete function is：

In formula (5), the logarithm value of product of density value and distance value is taken as functional value；Plus 1 and be to be zero in density, Do not put to fall in d_cWhen in radius, formula is still set up；Represent corresponding to artwork p_iPoint and its four neighborhoods totally five pictures The density value of vegetarian refreshments adds up and increases the weighted value that constituent density is judged to cluster centre；

3.7) will be by step 3.5) and step 3.6) determined by cluster centre take union, obtain in the final cluster of image Heart c_δργ=c_δ∪c_ρ∪c_γIt is the set comprising η element, then according to nearest neighbouring rule, residual pixel point is sorted out, And homogeneous region is filled with the pixel value of cluster centre point；

3.8) to per width subgraph repeat step 3.1) to 3.7) operation, then each width subgraph is merged, obtains middle knot Fruit is schemed；

4) secondary reunion class, process is as follows：

4.1) by by step 3.8) in the intermediate result figure that obtains zoom to the yardstick of needs, using color distance d_{p_rgb} (p1, p2) is calculated as the measuring similarity index of reunion classWithρ-δ graph of a relation is drawn, obtains discrete function δ_i=f (ρ_i)；

4.2) by step 4.1) δ that obtains_i=f (ρ_i) relation calculating bivariate discrete function γ=f_γ(ρ, δ), carries out two The fitting on first inclined-plane, calculates residual values ε of each data point_γi=y_γi(ρ,δ)-γ_i(ρ, δ), draws residual error rectangular histogram ε_γi- h, Normal approach is carried out also with bell-shaped curve, obtain variance yields σ_γ, it is in using the determination of λ σ principle unusual outside confidence interval Point is designated as c as cluster centre_γ；

4.3) will be by step 4.2) the cluster centre c that obtains_γYardstick playback is carried out in spatial domain, obtain original size The cluster centre of intermediate result figure, residual pixel point is sorted out according to nearest neighbouring rule, and the pixel value with cluster centre Filling homogeneous region.

Further, the step 3.2) in, d_cIt is an arithmetic number, for portraying with pixel p_iFor the center of circle, d_cFor radius Circumference, and density value ρ_iThe pixel number for being in circumferential inner；Cumulative with each passage pixel value under color space Pixel p with maximum_maxPixel p at and minimum cumulative with each passage pixel value_minBetween similarity distance 2% used as d_cValue, computing formula is as follows：

In formula (6),If representing in piece image, there is multiple pixels pixel value under color space cumulative and equal, In the case of being all maximum or minimum, then it is averaged, i.e.,

Further, the step 3.7) in, the cluster centre c that finally gives_δργBe by cubic regression analysis obtain poly- Class center c_δ、c_ρ、c_γTake what union was obtained, when the result figure of cluster segmentation is shown, using the cluster for obtaining in the case of over-segmentation The pixel value at center fills such cluster region.

Further, the step 4.2) in, the judgment basis that the cluster centre of secondary reunion class is automatically determined no longer make Use c_δ、c_ρ、c_γUnion, only histogram analysis are carried out to γ-value.

The technology design of the present invention is：Based on the image partition method of fast density clustering algorithm, to natural image Segmentation classification number can be automatically determined in segmentation, realize the higher image segmentation to parameter robust of segmentation accuracy rate.For a width Pending natural image comprising M row N row pixel, carries out pretreatment, first including filtering and noise reduction, gray-level registration etc.；So Image is carried out the piecemeal in region afterwards, obtains the subgraph of equidimension；In order to ensure the rapidity of algorithm, while considering the time Complexity and the integrity of clustering information, each width subgraph are carried out the scaling of equal proportion, obtain the subgraph after change of scale；So Carry out the calculating of similarity distance between data point afterwards the subgraph for completing change of scale, obtain the dependency between pixel；Then Parallel dividing processing being carried out in each width subgraph, including decision diagram being drawn based on density clustering algorithm, is carried out based on decision diagram Residual analysis is determined cluster centre and compared based on similarity distance to be sorted out the left point on archeus subgraph；Then will Subgraph after the completion of segmentation merges, and carries out the segmentation result figure that reunion class obtains original size size.It is right that the fusion of image includes Adjacent area in subgraph on cut-off rule merges and to the adjacent area fusion on subgraph piecemeal boundary line, thus obtains middle knot Fruit is schemed.Finally, the intermediate result of thick fusion is carried out secondary reunion class, non-conterminous homogeneous region is merged, is obtained final Result figure.

Beneficial effects of the present invention are mainly manifested in：The segmentation classification number of image can be automatically determined, final segmentation is tied Fruit accuracy rate is higher, reduces the parameter sensitivity sex chromosome mosaicism of image segmentation process.On true picture test result indicate that, should Algorithm has the good suitability and precision, effectively can carry out adaptivenon-uniform sampling to image, and obtain preferable segmentation effect Really.

Description of the drawings

Fig. 1 is the flow chart for carrying out scaling to image.

Fig. 2 is the stored digital model schematic of natural image.

Fig. 3 is to carry out, according to ρ-δ relation pair subgraph, the flow chart that unitary linear fit searches cluster centre, in being clustered Heart c_δAnd c_ρ, wherein (a) be to look for cluster centre c_δ, (b) is to look for cluster centre c_ρ.

Fig. 4 be by γ=f_γ(ρ, δ) function carries out the fitting of binary inclined-plane and searches cluster centre c_γFlow chart.

Fig. 5 is the flow chart for automatically determining final cluster centre.

Fig. 6 is the flow chart of the image partition method based on fast density clustering algorithm.

Specific embodiment

The invention will be further described below in conjunction with the accompanying drawings.

With reference to Fig. 1～Fig. 6, a kind of image partition method based on fast density clustering algorithm, comprise the following steps：

1) initialize, in order to accelerate the processing speed of algorithm, reduce process time, herein mainly by area dividing and chi Degree converts collective effect to reduce picture size, while can retain the topmost information for cluster centre lookup, mistake again Journey is as follows：

1.1) carry out area dividing operation first, for a pending image, include the pixel of M row N row, warp After crossing the pretreatment such as noise reduction filtering, image is divided into 2^W1×2^W2Width subgraph, the sub-graph size for obtaining isIts Middle Z [f] is front to bracket function；

1.2) in order to reduce the pixel number that pending image includes further, chi is carried out to the subgraph after the completion of piecemeal Degree scaling process, will a size of subimage of a*b be changed into a₁*b₁, wherein a₁=a/k_sizeAnd b₁=b/k_size, k_size＞ 1.? During scaling, because each pixel includes three pixel values, change of scale is carried out using the method for weak sampling, Retain the important clustering information of original image while pending pixel number is reduced as far as possible.

Specific scaling algorithm flow is as shown in figure 1, the function of wherein imresize (I, [a1, b1]) function is using high After this is fuzzy, image I change of scale is a1*b1 by method down-sampled again.By the piecemeal in region and the conversion of yardstick, can Pending data volume is reduced in tolerance interval, so as to speed up processing.

2) the similarity distance based on pixel value and positional information is calculated, and process is as follows：

2.1) for a pending natural image I, include M row N row pixel, n=M*N is made, then pixel data CollectionIn the trichroism channel components value that includes under RGB color space of the characteristic information that has of each pixel, as R is (red Color), G (green), three pixel values of B (blueness)；And with the image upper left corner as zero, horizontal line to the right as Y-axis, Vertical curve is the coordinate figure (x, y) under the two dimensional surface rectangular coordinate system of X-axis downwards.The table of image on each pixel is then defined Show form for p_i(r_i,g_i,b_i,x_i,y_i), it is illustrated in figure 2 stored digital model of two pixels in natural image.

2.2) when similarity distance determination is carried out, calculated using Euclidean distance, p1, p2 represent different two picture Vegetarian refreshments, then obtain the color distortion between two pixels and position difference can be expressed as follows with color distance and positional distance：

In formula (1), r1, g1, b1 and r2, g2, b2 represent the pixel value of pixel p1, p2 under RGB color space respectively, d_{p_rgb}Represent pixel interval under the space from；In formula (2), x1, y1 and x2, y2 represent pixel p1, p2 respectively at right angle Coordinate figure in coordinate system, d_{p_xy}Represent pixel interval in the coordinate system from.Pixel value is different with the dimension of coordinate figure, Therefore in formula, internal normalization has been carried out to this two category information, has obtained the unified good results of weight.Because this paper subsequent treatment Image each pixel value be with 8 binary storage, therefore when pixel value normalization is carried out using 2⁸- 1 conduct Reference value.It is that every row has N number of pixel that M, N represent the size of input picture, often shows M pixel.

2.3) similarity between two pixels is finally calculated apart from d_p(p1, p2), the bigger explanation difference of distance value is bigger, phase Lower like degree, the computing formula of similarity distance is as follows：

d_p(p1, p2)=θ d_{p_rgb}(p1,p2)+(1-θ)d_{p_xy}(p1,p2) (3)

In formula (3), θ is weight factor, in order to adjust the contribution that color distance and positional distance determine to similarity.

Similarity distance is applied not only to cluster analyses, after cluster centre is determined, needs also exist for arriving according to each pixel The similarity distance of cluster centre determines its ownership situation, obtains segmentation result after the completion of all pixels point is sorted out.In phase Positional information is added in calculating like degree distance, the interaction between the pixel that meets on locus farther out is weaker, Image data setData volume less when, it will cause not smooth enough problem at the segmentation block edges, hand in vision Friendly relation are not met on mutually.The segmentation result figure for obtaining, for this problem is solved, is carried out the conversion of color space, by RGB HSV color space is converted to, and then medium filtering is carried out to the V channel information that light levels are characterized under HSV model, then again HSV is converted to RGB model exported, obtains the segmentation result figure of vision close friend.

3) Density Clustering of cluster centre is automatically determined, subgraph is operated, process is as follows：

Define 1 and the image I comprising n pixel for a width set, two one-dimensional data matrixes are corresponded to,Represent close Degree matrix,Represent distance matrix, size is all 1 row n row.I-th column data and original graph of density matrix or distance matrix In picture, the mapping relations of Mx row Nx row pixel are as follows：

I=N (Mx-1)+Nx (7)

3.1) the similarity distance between image slices vegetarian refreshments is calculated, it is known that the similarity distance of pixel has duality, i.e., d_p(p1, p2)=d_p(p2, p1), and d_p(p1, p1)=0, therefore similarity distance is stored as that diagonal data are zero upper three Angular moment battle array { Dp_ij}；

3.2) density value of each pixel is calculated, obtains density matrixComputing formula is as follows：

Wherein function

In formula (4), ρ_iRepresent pixel p_iDensity value, the set of pixels of imageCorresponding index set is I_s ={ 1,2 ..., M*N }, d_ij=d_p(pi, pj) represents the similarity distance between two pixels；

In order to reduce space complexity during operation, to increase regular hour complexity as cost, the present invention adopts one Improved density matrix computational methods are planted, specific density matrix algorithm steps are as follows：

3.2.1) digital picture I of one width of input comprising M row N row pixel and lookup radius d_c, circulation initial value is set, I1=j1=1, i2=j2=1, i=1, the memory space of density of distribution matrix, it is designated asN=M*N, initial value is set to 0；

3.2.2 pixel (i1, j1) and the similarity distance of point (i2, j2) in image) is calculated, is designated as d_p(p_(i1,j1), p_(i2,j2)), if d_p(p_(i1,j1),p_(i2,j2)) ＞ d_c, then ρ_i=ρ_i+ 0, on the contrary ρ_i=ρ_i+1；

3.2.3) j2=j2+1, if j2≤N, return to step 3.2.2), otherwise j2=1 is made, execution step 3.2.4)；

3.2.4) i2=i2+1, if i2≤M, return to step 3.2.2), otherwise i2=1 is made, execution step 3.2.5)；

3.2.5) j1=j1+1, i=i+1, if j1≤N, return to step 3.2.2), otherwise j1=1 is made, execution step 3.2.6)；

3.2.6) i1=i1+1, if i1≤M, return to step 3.2.2), otherwise i1=1 is made, execution step 3.2.7)；

3.2.7) density matrix for finally giving is exported

It is not to be previously stored { Dp in algorithm above_ijAnd then determine, but calculating each pixel During density value, the similarity distance of all time pixel of calculated in advance and other n-1 pixel, in the density for completing the point After calculating, the space release of storage similarity distance so greatly reduces memory consumption during operation.

3.3) distance value of each pixel is calculated, obtains distance matrixEach pixel p_iDistance value definition For δ_i, first look for comparing p_iThe big pixel of density, obtains set S'={ p_j, then look up in S' with p_iClosest Pixel p_j', then obtain δ_i=d_p(pi, pj'), specific distance matrix algorithm is as follows：

3.3.1) by step 3.2) in density matrix be ranked up from big to small, obtain orderly new density matrixWhile being calculated array of indexes according to the mapping relations for defining 1Preserve new density matrixWith The mapping relations of position between each pixel of original image, arrange circulation initial value i1=j1=1, ind1=1；

3.3.2) density maxima ρ ' is calculated₁Corresponding pixel p_ρ'1With the distance value of rest of pixels point, computing formula is δ _ temp (1, ind)=d_p(p_(i1,j1),p_ρ'1)；

3.3.3) j1=j1+1, ind1=ind1+1, if j1≤N, return to step 3.3.2), otherwise j1=1 is made, execute Step 3.3.4)；

3.3.4) i1=i1+1, if i1≤M, return to step 3.3.2), otherwise i1=1 is made, execution step 3.3.5)；

3.3.5) search δ _ temp (1, ind) maximum, as density maximum pixel similarity distance value, i.e., δ'₁=MAX δ _ temp (1, i) | i ∈ (1, n) }；

3.3.6) circulation initial value i1=2, i2=1 are set；

3.3.7) residual pixel point is calculatedTo the distance value of the big pixel of the density ratio point, computing formula be δ _ Temp (1, i2)=d_p(p_ρ'i1,p_ρ'i2)；

3.3.8) i2=i2+1, if i2≤i1-1, return to step 3.3.7), on the contrary take its minima as similarity away from From value, i.e. δ '_i1=MIN δ _ temp (1, i) | i ∈ (1, i2) }, execution step 3.3.9)；

3.3.9) i1=i1+1, if i1≤M*N, return to step 3.3.7), otherwise execution step 3.3.10)；

3.3.10) by indexingWillIt is mapped to and original density matrixThe corresponding distance in position Memory elementOutput distance matrix

3.4) according to step 3.2) and step 3.3) obtainWithDecision diagram is drawn, obtains representing pixel The discrete function δ of density and distance relation_i=f (ρ_i)；

3.5) unitary linear fit is carried out by the discrete data point on ρ-δ graph of a relation, obtains matched curve y_δ=kx_ρ+b₀WithCalculate residual values ε of each data point_δi=y_δi-δ_iAnd ε_ρi=x_ρi-ρ_i, draw residual error rectangular histogram ε_δi- h and ε_ρi- h, carries out normal approach with bell-shaped curve respectively, obtains variance yields σ_δAnd σ_ρ, determined using λ σ principle and be in outside confidence interval Singular point as cluster centre, be designated as c_δAnd c_ρ, algorithm flow chart is as shown in Figure 3；

Define 2 and set function f_γIt is the binary function with regard to variable ρ and δ, corresponding to the coordinate figure in three dimensions be (ρ, δ, f_γ), then defining bivariate discrete function is：

In formula (5), the logarithm value of product of density value and distance value is taken as functional value；Plus 1 and be to be zero in density, Do not put to fall in d_cWhen in radius, formula is still set up, not actual physical meaning；There is context between the pixel of image Also include contextual information in information, equally corresponding density battle array, thereforeRepresent corresponding to artwork p_iPoint and its neighbours The density value of domain totally five pixels cumulative and, increase the weighted value that constituent density judges to cluster centre.

3.6) by the bivariant discrete function γ=f for defining in 2_γ(ρ, δ), carries out the fitting on binary inclined-plane, is intended Conjunction plane is z_γ=b₁+b₂ρ+b₃δ, calculates residual values ε of each data point_γi=y_γi(ρ,δ)-γ_i(ρ, δ), draws residual error straight Side figure ε_γi- h, carries out normal approach also with bell-shaped curve, obtains variance yields σ_γ, determined using λ σ principle and be in confidence area Between outer singular point as cluster centre, be designated as c_γ, algorithm flow chart is as shown in Figure 4；

3.7) will be by step 3.5) and step 3.6) determined by cluster centre take union, obtain in the final cluster of image Heart c_δργ=c_δ∪c_ρ∪c_γIt is the set comprising η element, then according to nearest neighbouring rule, residual pixel point is sorted out, Algorithm flow chart is as shown in Figure 5；

The cluster centre c for finally giving_δργIt is the cluster centre c for being obtained by cubic regression analysis_δ、c_ρ、c_γTake union to obtain , over-segmentation is so easily caused, i.e., can finally divide the image into into many zonules.Although the segmentation result for so obtaining exists Similarity in region is very high, i.e., internal have strong interaction, but interregional diversity is not but high, and this is not our institutes Desired cluster result.This is accomplished by carrying out fusion treatment in subsequent step, and zones of different high for similarity is reconsolidated Together.Fusion treatment for convenience, when the result figure of cluster segmentation is shown, using in the cluster for obtaining in the case of over-segmentation The pixel value of the heart fills such cluster region, while more friendly visual effect can be had.

3.8) to all repeat step 3.1 per width subgraph) to 3.7) operation, obtain a segmentation result per width subgraph Then the segmentation result figure of each width subgraph is merged, obtains intermediate result figure by figure.

4) secondary reunion class, process is as follows：

4.1) by step 3.8) the intermediate result figure that obtains zooms to the yardstick of needs according to the scaling method of Fig. 1, Using d_{p_rgb}(p1, p2) is calculated according to density matrix algorithm and distance matrix algorithm as measuring similarity indexWithρ-δ graph of a relation is drawn, obtains discrete function δ_i=f (ρ_i)；

Because the intermediate result in figure after once clustering, the detailed information that original image includes is capped completely, So information integrity is no longer so sharp with the contradiction of algorithm complex in secondary reunion class, also avoid the need for carrying out area again The piecemeal in domain, need to only scale the images to the yardstick of needs.In secondary reunion class, the measuring similarity for being adopted refers to Mark is d_{p_rgb}(p1, p2), because d_pAfter (p1, p2) characterizes the coordinate figure of positional information in addition, remote picture in spatial domain Interaction force between vegetarian refreshments just dies down, and the purpose of secondary reunion class is exactly to merge non-adjacent homogeneous region, So only using color distance d_{p_rgb}(p1,p2)；

4.2) by step 4.1) δ that obtains_i=f (ρ_i) the bivariant discrete function γ=f of relation calculating_γ(ρ, δ), is carried out The fitting on binary inclined-plane, calculates residual values ε of each data point_γi=y_γi(ρ,δ)-γ_i(ρ, δ), draws residual error rectangular histogram ε_γi- H, carries out normal approach using bell-shaped curve, obtains variance yields σ_γ, the singular point being in outside confidence interval is determined using λ σ principle As cluster centre, c is designated as_γ；

4.3) by step 4.2) in the position of cluster centre carry out yardstick playback in spatial domain, obtain intermediate result figure and exist Cluster centre under original size, residual pixel point is sorted out, and fills homogeneous region with the pixel value of cluster centre.Secondary Weight clustering algorithm is as follows：

4.3.1) intermediate result figure I_temp and search radius d comprising M row N row pixel are input into_c；

4.3.2) I_temp is carried out scaling according to scaling rule, obtains I_temp'；

4.3.3 the density matrix that density matrix algorithm calculates I_temp') is first depending on, is calculated according to distance matrix algorithm The distance matrix of I_temp', then according to 2 calculating γ-value are defined, carries out histogram analysis and automatically determines singular point as cluster The position of cluster centre is finally carried out yardstick playback by center, obtains the cluster centre position under original scale, calculating now D is all taken_{p_rgb}(p1, p2) is used as measuring similarity index；

4.3.4) according to closest principle, i.e., similarity maximum principle is sorted out, by the rest of pixels point of I_temp It is included in the class cluster nearest apart from oneself, secondary heavy cluster result is obtained, and exports final result figure I_result.

Claims (4)

1. a kind of image partition method based on fast density clustering algorithm, it is characterised in that：The method comprising the steps of：

1) initialize, process is as follows：

1.1) carry out area dividing operation first, for a pending image, include the pixel of M row N row, through pre- After process, image is divided into 2^W1×2^W2Width subgraph, the sub-graph size for obtaining isWherein Z [f] is for front to taking Integral function；

1.2) and then to image change of scale operation is carried out, the subgraph after the completion of piecemeal is carried out scaling process, will chi The very little subimage for a*b is changed into a₁*b₁, wherein a₁=a/k_sizeAnd b₁=b/k_size, k_size＞ 1；During scaling, because per Individual pixel includes three pixel values, so carrying out change of scale using the method for weak sampling, pending image is being included Pixel number retain the important clustering information of original image as far as possible while reduce；

2) the similarity distance based on pixel value and positional information is calculated, and process is as follows：

2.1) for a pending natural image I, include M row N row pixel, n=M*N is made, then pixel data setIn the characteristic information that has of each pixel trichroism channel components value that includes under RGB color space, as R, G, B Three pixel values；And with the image upper left corner as zero, horizontal line to the right as Y-axis, vertical curve two dimension downwards as X-axis Coordinate figure (x, y) under plane right-angle coordinate；

2.2) d is set_p(p1, p2) is the similarity distance between two pixels, and similarity is as follows apart from computing formula：

$\begin{array}{cc}{d}_{p\_rgb}(p1,p2)=\sqrt{{\left(\frac{r1-r2}{255}\right)}^2+{\left(\frac{g1-g2}{255}\right)}^2+{\left(\frac{b1-b2}{255}\right)}^2}& \left(1\right)\\ d_{p\_xy}(p1,p2)=\sqrt{{\left(\frac{x1-x2}{M}\right)}^2+{\left(\frac{y1-y2}{N}\right)}^2}& \left(2\right)\end{array}$

d_p(p1, p2)=θ d_{p_rgb}(p1,p2)+(1-θ)d_{p_xy}(p1,p2) (3)

In formula (1), r1, g1, b1 and r2, g2, b2 represent the pixel value of pixel p1, p2 under RGB color space, d respectively_{p_rgb} Represent pixel interval under the space from；In formula (2), x1, y1 and x2, y2 represent pixel p1, p2 respectively and sit at right angle Coordinate figure in mark system, d_{p_xy}Represent pixel interval in the coordinate system from；In formula (3), θ is weight factor, in order to adjust The contribution that section color distance and positional distance are determined to similarity；

3) Density Clustering of cluster centre is automatically determined, subgraph is operated, process is as follows：

3.1) the similarity distance between image slices vegetarian refreshments is calculated, it is known that the similarity distance of pixel has duality, i.e. d_p(p1, P2)=d_p(p2, p1), and d_pTherefore similarity distance is stored as the upper triangular matrix that diagonal data are zero by (p1, p1)=0 {Dp_ij}；

3.2) density value of each pixel is calculated, obtains density matrixComputing formula is as follows：

Wherein function

In formula (4), ρ_iRepresent pixel p_iDensity value, the set of pixels of imageCorresponding index set is I_s=1, 2 ..., M*N }, d_ij=d_p(pi, pj) represents the similarity distance between two pixels；

3.3) distance value of each pixel is calculated, obtains distance matrixEach pixel p_iDistance value be defined as δ_i, First look for comparing p_iThe big pixel of density, obtains set S'={ p_j, then look up in S' with p_iClosest pixel p_j', then obtain δ_i=d_p(pi,pj')；

3.4) according to step 3.2) and step 3.3) obtainWithDecision diagram is drawn, obtains representing pixel point density Discrete function δ with distance relation_i=f (ρ_i)；

3.5) unitary linear fit is carried out by the discrete data point on ρ-δ graph of a relation, obtains matched curve y_δ=kx_ρ+b₀WithCalculate residual values ε of each data point_δi=y_δi-δ_iAnd ε_ρi=x_ρi-ρ_i, draw residual error rectangular histogram ε_δi- h and ε_ρi- h, carries out normal approach with bell-shaped curve respectively, obtains variance yields σ_δAnd σ_ρ, determined using λ σ principle and be in outside confidence interval Singular point as cluster centre, be designated as c_δAnd c_ρ；

3.6) bivariant discrete function γ=f is obtained by decision diagram_γ(ρ, δ), carries out the fitting on binary inclined-plane, obtains fitting flat Face is z_γ=b₁+b₂ρ+b₃δ, calculates residual values ε of each data point_γi=y_γi(ρ,δ)-γ_i(ρ, δ), draws residual error rectangular histogram ε_γi- h, carries out normal approach also with bell-shaped curve, obtains variance yields σ_γ, determined using λ σ principle and be in outside confidence interval Singular point as cluster centre, be designated as c_γ；

Wherein function f_γIt is the binary function with regard to variable ρ and δ, is (ρ, δ, f corresponding to the coordinate figure in three dimensions_γ), then Defining bivariate discrete function is：

${\mathrm{\γ}}_i{|}_{i\∈(1,n)}=f_{\mathrm{\γ}i}({\mathrm{\ρ}}_i,{\mathrm{\δ}}_i)=log\left(\right(\underset{pos=1}{\overset{5}{\Σ}}{\mathrm{\ρ}}_{i\_pos})\×{\mathrm{\δ}}_i+1)---\left(5\right)$

In formula (5), the logarithm value of product of density value and distance value is taken as functional value；It is to be zero in density plus 1, that is, do not have Fall in d a little_cWhen in radius, formula is still set up；Represent corresponding to artwork p_iPoint and its four neighborhoods totally five pixels Density value cumulative and, increase the weighted value that constituent density judges to cluster centre；

3.7) will be by step 3.5) and step 3.6) determined by cluster centre take union, obtain the final cluster centre of image c_δργ=c_δ∪c_ρ∪c_γIt is the set comprising η element, then according to nearest neighbouring rule, residual pixel point is sorted out, and Homogeneous region is filled with the pixel value of cluster centre point；

3.8) to per width subgraph repeat step 3.1) to 3.7) operation, then each width subgraph is merged, obtains intermediate result figure；

4) secondary reunion class, process is as follows：

4.1) by by step 3.8) in the intermediate result figure that obtains zoom to the yardstick of needs, using color distance d_{p_rgb}(p1, P2) as the measuring similarity index of reunion class, calculateWithρ-δ graph of a relation is drawn, obtains discrete function δ_i= f(ρ_i)；

4.2) by step 4.1) δ that obtains_i=f (ρ_i) relation calculating bivariate discrete function γ=f_γ(ρ, δ), carries out binary oblique The fitting in face, calculates residual values ε of each data point_γi=y_γi(ρ,δ)-γ_i(ρ, δ), draws residual error rectangular histogram ε_γi- h, equally Normal approach is carried out using bell-shaped curve, obtain variance yields σ_γ, determine that using λ σ principle the singular point being in outside confidence interval is made For cluster centre, c is designated as_γ；

4.3) will be by step 4.2) the cluster centre c that obtains_γYardstick playback is carried out in spatial domain, obtains the centre of original size The cluster centre of result figure, residual pixel point is sorted out according to nearest neighbouring rule, and is filled with the pixel value of cluster centre Homogeneous region.

2. the image partition method based on fast density clustering algorithm as claimed in claim 1, it is characterised in that：The step 3.2) in, d_cIt is an arithmetic number, for portraying with pixel p_iFor the center of circle, d_cFor the circumference of radius, and density value ρ_iIt is Pixel number in circumferential inner；Pixel p with the cumulative and maximum of each passage pixel value under color space_maxWith each Pixel p at the cumulative and minimum of individual passage pixel value_minBetween similarity distance 2% as d_cValue, computing formula is such as Under：

$d_c=0.02*d_p({\stackrel{\‾}{p}}_{max},{\stackrel{\‾}{p}}_{\min })---\left(6\right)$

In formula (6),If representing in piece image, there is multiple pixels pixel value under color space cumulative and equal, all for most In the case of big or minimum, then it is averaged, i.e.,

3. the image partition method based on fast density clustering algorithm as claimed in claim 1 or 2, it is characterised in that：Described Step 3.7) in, the cluster centre c that finally gives_δργIt is the cluster centre c for being obtained by cubic regression analysis_δ、c_ρ、c_γTake union Obtain, when the result figure of cluster segmentation is shown, should using the pixel value filling of the cluster centre for obtaining in the case of over-segmentation Class cluster region.

4. the image partition method based on fast density clustering algorithm as claimed in claim 1 or 2, it is characterised in that：Described Step 4.2) in, the judgment basis that the cluster centre of secondary reunion class is automatically determined do not use c_δ、c_ρ、c_γUnion, only right γ-value carries out histogram analysis.