CN106447676B - A kind of image partition method based on fast density clustering algorithm - Google Patents
A kind of image partition method based on fast density clustering algorithm Download PDFInfo
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Abstract
A kind of image partition method based on fast density clustering algorithm, comprising the following steps: the 1) natural image to be processed for one is pre-processed first and initialized, including filtering noise reduction, gray-level registration, area dividing and scaling etc.；2) calculating of similarity distance, obtains the correlation between pixel then carrying out data point to the subgraph for completing change of scale；3) parallel dividing processing is then carried out in each width subgraph, including decision diagram is drawn based on density clustering algorithm, is determined cluster centre based on decision diagram progress residual analysis and is compared based on similarity distance and sorts out the left point on archeus subgraph；4) then the subgraph after the completion of segmentation is merged, carries out secondary reunion class and obtains the segmentation result figure of original size size.The present invention, which provides one kind, can automatically determine segmentation classification number, and realizing segmentation, accuracy rate is higher, the image partition method to parameter robust based on fast density clustering algorithm.
Description
Technical field
The invention belongs to technical field of image processing, and in particular to a kind of image partition method.
Background technique
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, region inside has strong similitude, each interregional with strong otherness.Meanwhile image
Segmentation is also that the important step of data analysis and understanding is carried out to image, is the key that by image procossing to image analysis.It is existing
Image partition method mainly divides following a few classes: the dividing method based on boundary, the dividing method based on region and based on specific
Theoretical dividing method etc..After the completion of image segmentation, the target extracted can be used for image, semantic identification, picture search etc.
Field, so the quality of image segmentation result will directly affect the accuracy of subsequent identification or search.
Due to the ambiguity and complexity of image, all kinds of images can be generally applicable to currently without general segmentation theory
Segmentation, the partitioning algorithm proposed is greatly both for particular problem, therefore there is still a need for constantly explore new segmentation
Algorithm and segmentation theory, this is also the purpose studied herein.Dividing method based on boundary be by detection gray level or
There is person's structure the place of mutation to be split the determination on boundary, including common first order differential operator have Roberts operator,
Prewitt operator and Sobel operator, Second Order Differential Operator have Laplace operator and Kirsh operator etc..Wang Junmin is " based on micro-
The edge detection and its application of point operator " in Roberts operator, Prewitt operator, Sobel operator, Laplace operator,
The basic principle of LOG operator is analyzed, and summarizes the advantage and disadvantage of various operators.Canny proposes a kind of new edge detection
Method, it is optimal on the step change type edge influenced by white noise, but there are the discontinuous situations in boundary.Miao Jiaqing is " adaptive
Dictionary improve Canny operator CT image segmentation " in canny operator is improved using self-adapting dictionary learning algorithm.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 key is determining segmentation threshold, therefore derives global threshold, adaptive threshold, optimal threshold again
Etc..Chen Ningning is in " realization of several threshold segmentation algorithms is compared with " to histogram thresholding method, iterative method and great Jin
The common threshold value such as method determines that method is comprehensively compared, and Ma Yinghui et al. will be traditional in " color image segmentation method summary "
Grey relevant dynamic matrix be applied to color image, obtain better segmentation effect using the more color informations of color image.Region
Growth method and split degree method be two kinds of typical serial regional development and technologies, carries out growth criterion and split degree criterion is set
Meter, the processing of cutting procedure subsequent step will be judged according to the result of historical steps and be determined.As each subject is many
There are many image partition methods combined with some specific theories, method, including base in the it is proposed of new theory and new method
Image segmentation in genetic algorithm, the image segmentation based on artificial neural network, the image segmentation based on objective function optimization, base
Image segmentation in clustering, the image segmentation based on MRF, image segmentation based on fuzzy set theory etc..
With the appearance of new clustering methods various in recent years, many image segmentation sides based on clustering algorithm have been derived
Method, compared to the dividing method of other specific theories, the image partition method based on clustering provides one for image segmentation
A new thinking.Meanwhile it has recently been demonstrated that comprehensively utilizing the location 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 known as feature space clustering procedure, the key that the problem of dividing the image into is converted to clustering problem is empty using feature
Between point indicate image space in corresponding pixel, according to their aggregation results in feature space to feature space point carry out
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 novel cluster centre side of portraying
Method provides a kind of new thinking for the design of clustering algorithm, is based on the image segmentation of clustering algorithm progress herein, together
When it is huge for high time complexity of the former clustering algorithm when handling big data quantity and high spatial complexity and image data amount
Contradiction, propose a series of solution.
Summary of the invention
Have the sensitivity of cluster centre existing for the image partition method based on clustering algorithm, parameter dependence to overcome
Greatly, adaptivity is poor, the deficiency that can not accurately automatically determine of segmentation class number of clusters, can automatically determine point the present invention provides one kind
Cut that classification number, accuracy rate is higher for segmentation, the image partition method to parameter robust based on fast density clustering algorithm.
The technical solution adopted by the present invention to solve the technical problems is:
A kind of image partition method based on fast density clustering algorithm: it the described method comprises the following steps:
1) it initializes, process is as follows:
1.1) area dividing operation is carried out first, and the image to be processed for one includes the pixel of M row N column, warp
After crossing pretreatment, 2 are divided the image intoW1×2W2Width subgraph, obtained sub-graph size areBefore wherein Z [f] is
To bracket function；
1.2) change of scale operation then is carried out to image, the subgraph after the completion of piecemeal is subjected to scaling processing, i.e.,
Subgraph having a size of a*b is become into a1*b1, wherein a1=a/ksizeAnd b1=b/ksize, ksize> 1；During scaling, because
It include there are three pixel value, so the method using weak sampling carries out change of scale, by image to be processed for each pixel
Retain the important clustering information of original image while the pixel number for including is reduced as far as possible；
2) it is calculated based on the similarity of pixel value and location information distance, process is as follows:
2.1) the natural image I to be processed for one includes M row N column pixel, enables n=M*N, then pixel data
CollectionIn the characteristic information that has of each pixel include three chrominance channel component values under RGB color space, as R, G, B
Three pixel values；And be to the right Y-axis using the image upper left corner as coordinate origin, horizontal line, vertical line is downwards for the two of X-axis
Coordinate value (x, y) under dimensional plane rectangular coordinate system；
2.2) d is setpThe similarity distance of (p1, p2) between two pixels, similarity distance calculation formula are as follows:
dp(p1, p2)=θ dp_rgb(p1,p2)+(1-θ)dp_xy(p1,p2) (3)
In formula (1), r1, g1, b1 and r2, g2, b2 respectively represent the pixel value of pixel p1, p2 under RGB color space,
dp_rgbIndicate the distance between the pixel under the space；In formula (2), x1, y1 and x2, y2 respectively represent pixel p1, p2 straight
Coordinate value in angular coordinate system, dp_xyIndicate distance between pixel in the coordinate system, in formula (3), θ is weight factor, is used
To adjust the contribution that color distance and positional distance determine similarity；
3) Density Clustering for automatically determining cluster centre, operates subgraph, and process is as follows:
3.1) the similarity distance between image slices vegetarian refreshments is calculated, it is known that there are dualities for the similarity distance of pixel, i.e.,
dp(p1, p2)=dp(p2, p1), and dp(p1, p1)=0, therefore similarity distance is stored as upper three that diagonal line data are zero
Angular moment battle array { Dpij}；
3.2) density value for calculating each pixel, obtains density matrixCalculation formula is as follows:
Wherein function
In formula (4), ρiIndicate pixel piDensity value, the set of pixels of imageCorresponding index set is Is
={ 1,2 ..., M*N }, dij=dp(pi, pj) indicates the similarity distance between two pixels；
3.3) distance value for calculating each pixel, obtains distance matrixEach pixel piDistance value definition
For δi, first look for comparing piThe big pixel of density obtains set S'={ pj, then search S' in piDistance it is nearest
Pixel pj', then obtain δi=dp(pi,pj')；
3.4) it is obtained according to step 3.2) and step 3.3)WithDecision diagram is drawn, obtains indicating pixel
The discrete function δ of density and distance relationi=f (ρi)；
3.5) unitary linear fit is carried out by the discrete data point in ρ-δ relational graph, obtains matched curve yδ=kxρ+b0WithCalculate the residual values ε of each data pointδi=yδi-δiAnd ερi=xρi-ρi, draw residual error histogram εδi- h and
ερi- h carries out normal approach with bell-shaped curve respectively, obtains variance yields σδAnd σρ, it is in outside confidence interval using the determination of λ σ principle
Singular point as cluster centre, be denoted as cδAnd cρ；
3.6) discrete function γ=f of bivariate is obtained by decision diagramγ(ρ, δ) carries out the fitting on binary inclined-plane, is intended
Conjunction plane is zγ=b1+b2ρ+b3δ calculates the residual values ε of each data pointγi=yγi(ρ,δ)-γi(ρ, δ) it is straight to draw residual error
Side figure εγi- h carries out normal approach also with bell-shaped curve, obtains variance yields σγ, confidence area is in using the determination of λ σ principle
Between outer singular point as cluster centre, be denoted as cγ；
Wherein function fγIt is the binary function about variable ρ and δ, be corresponding to the coordinate value in three-dimensional space (ρ, δ,
fγ), then define bivariate discrete function are as follows:
In formula (5), take the logarithm of the product of density value and distance value as functional value；1 is added to be in order to be zero in density,
D is fallen in withoutcFormula is still set up when in radius；It indicates to correspond to original image piPoint and its four neighborhoods totally five pictures
The density value of vegetarian refreshments adds up and increases the weighted value that constituent density determines cluster centre；
3.7) cluster centre determined by step 3.5) and step 3.6) is taken into union, obtained in the final cluster of image
Heart cδργ=cδ∪cρ∪cγResidual pixel point is sorted out then according to nearest neighbouring rule for the set comprising η element,
And homogeneous region is filled with the pixel value of cluster centre point；
3.8) step 3.1) is repeated to operation 3.7) to every width subgraph, then each width subgraph is merged, obtains intermediate knot
Fruit figure；
4) secondary reunion class, process are as follows:
4.1) the intermediate result figure as obtained in step 3.8) zooms to the scale of needs, using color distance dp_rgb
The measuring similarity index of (p1, p2) as reunion class calculatesWithρ-δ relational graph is drawn, discrete function is obtained
δi=f (ρi)；
4.2) δ obtained by step 4.1)i=f (ρi) relationship calculating bivariate discrete function γ=fγ(ρ, δ) carries out two
The fitting on first inclined-plane calculates the residual values ε of each data pointγi=yγi(ρ,δ)-γi(ρ, δ) draws residual error histogram εγi- h,
Normal approach is carried out also with bell-shaped curve, obtains variance yields σγ, it is in using the determination of λ σ principle unusual outside confidence interval
Point is used as cluster centre, is denoted as cγ；
It 4.3) will be by cluster centre c that step 4.2) obtainsγScale playback is carried out in spatial domain, obtains original size
The cluster centre of intermediate result figure sorts out residual pixel point according to nearest neighbouring rule, and with the pixel value of cluster centre
Fill homogeneous region.
Further, in the step 3.2), dcIt is a positive real number, for portraying with pixel piFor the center of circle, dcFor radius
Circumference, and density value ρiAs fall in the pixel number of circumferential inner；It is cumulative with channel each under color space pixel value
With the pixel p of maximummaxWith each channel pixel value it is cumulative and minimum at pixel pminBetween similarity distance
2% is used as dcValue, calculation formula are as follows:
In formula (6),If indicating in piece image, have multiple pixels pixel value under color space cumulative and
It is equal, all in maximum or the smallest situation, to be then averaged, i.e.,
Further, in the step 3.7), finally obtained cluster centre cδργBe analyzed by cubic regression it is poly-
Class center cδ、cρ、cγIt takes union to obtain, when showing the result figure of cluster segmentation, uses the cluster obtained in the case of over-segmentation
The pixel value at center fills such cluster region.
Further, in the step 4.2), the judgment basis that the cluster centre of secondary reunion class automatically determines no longer makes
Use cδ、cρ、cγUnion, only to γ value carry out histogram analysis.
Technical concept of the invention are as follows: the image partition method based on fast density clustering algorithm, to natural image
Segmentation classification number can be automatically determined in segmentation, realizing segmentation, accuracy rate is higher, image segmentation to parameter robust.For a width
Natural image to be processed comprising M row N column pixel, is pre-processed, including filtering and noise reduction, gray-level registration etc. first；So
The piecemeal that image is carried out to region afterwards, obtains the subgraph of equidimension；In order to guarantee the rapidity of algorithm, while comprehensively considering the time
Each width subgraph is carried out the scaling of equal proportion, the subgraph after obtaining change of scale by the integrality of complexity and clustering information；So
The calculating of similarity distance, obtains the correlation between pixel carrying out data point to the subgraph for completing change of scale afterwards；Then
Parallel dividing processing is carried out in each width subgraph, including decision diagram is drawn based on density clustering algorithm, is carried out based on decision diagram
Residual analysis, which is determined cluster centre and compared based on similarity distance, sorts out the left point on archeus subgraph；Then will
Subgraph after the completion of segmentation merges, and carries out reunion class and obtains the segmentation result figure of original size size.The fusion of image includes pair
Adjacent area in subgraph on cut-off rule is merged and is merged to the adjacent area on subgraph piecemeal boundary line, thus obtains intermediate knot
Fruit figure.Finally, the intermediate result slightly merged 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: can automatically determine the segmentation classification number of image, final segmentation knot
Fruit accuracy rate is higher, reduces the sensitivity to parameter problem of image segmentation process.It is on true picture the experimental results showed that, should
Algorithm has good applicability and precision, effectively can carry out adaptivenon-uniform sampling to image, and obtains preferable segmentation effect
Fruit.
Detailed description of the invention
Fig. 1 is the flow chart that scaling is carried out to image.
Fig. 2 is the stored digital model schematic of natural image.
Fig. 3 is to carry out the flow chart that unitary linear fit searches cluster centre to subgraph according to ρ-δ relationship, is obtained in cluster
Heart cδAnd cρ, wherein (a) is to look for cluster centre cδ, (b) it is to look for cluster centre cρ。
Fig. 4 is by γ=fγ(ρ, δ) function carries out the fitting of binary inclined-plane and searches cluster centre cγFlow 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.
Referring to Fig.1~Fig. 6, a kind of image partition method based on fast density clustering algorithm, comprising the following steps:
1) it initializes, in order to accelerate the processing speed of algorithm, reduces the processing time, mainly pass through area dividing and ruler herein
Degree converts collective effect to reduce picture size, while can retain the most important information searched for cluster centre, mistake again
Journey is as follows:
1.1) area dividing operation is carried out first, and the image to be processed for one includes the pixel of M row N column, warp
After crossing the pretreatment such as noise reduction filtering, 2 are divided the image intoW1×2W2Width subgraph, obtained sub-graph size areIts
Middle Z [f] is preceding to bracket function；
1.2) in order to further decrease the pixel number that image to be processed includes, ruler is carried out to the subgraph after the completion of piecemeal
Scaling processing is spent, i.e., the subgraph having a size of a*b is become into a1*b1, wherein a1=a/ksizeAnd b1=b/ksize, ksize> 1.?
During scaling, because each pixel includes to carry out change of scale using the method for weak sampling there are three pixel value,
Retain the important clustering information of original image while pixel number to be processed is reduced as far as possible.
Specific scaling algorithm flow is as shown in Figure 1, wherein the function of imresize (I, [a1, b1]) function is using height
Image I change of scale is a1*b1 by method down-sampled again after this is fuzzy.It, can by the transformation of the piecemeal and scale in region
Data volume to be processed is reduced in tolerance interval, thus speed up processing.
2) it is calculated based on the similarity of pixel value and location information distance, process is as follows:
2.1) the natural image I to be processed for one includes M row N column pixel, enables n=M*N, then pixel data
CollectionIn the characteristic information that has of each pixel include three chrominance channel component values under RGB color space, as R is (red
Color), three pixel values of G (green), B (blue)；And be to the right Y-axis using the image upper left corner as coordinate origin, horizontal line,
Vertical line is the coordinate value (x, y) under the two-dimensional surface rectangular coordinate system of X-axis downwards.Then define the table of each pixel on image
Show that form is pi(ri,gi,bi,xi,yi), it is illustrated in figure 2 stored digital model of two pixels in natural image.
2.2) it when progress similarity distance determines, is calculated using Euclidean distance, p1, p2 represent two different pictures
Vegetarian refreshments, the then color difference and position difference obtained between two pixels can be expressed as follows with color distance and positional distance:
R1, g1, b1 and r2, g2, b2 respectively represent the pixel value of pixel p1, p2 under RGB color space in formula (1),
dp_rgbIndicate the distance between the pixel under the space；X1, y1 and x2, y2 respectively represent pixel p1, p2 at right angle in formula (2)
Coordinate value in coordinate system, dp_xyDistance between the pixel of expression in the coordinate system.Pixel value is different with the dimension of coordinate value,
Therefore internal normalization has been carried out to these two types of information in formula, has obtained the unified good results of weight.Because of this paper subsequent processing
Image each pixel value be with 8 binary storages, therefore when carrying out pixel value normalization use 28- 1 conduct
A reference value.M, it is that every row has N number of pixel that N, which represents the size of input picture, often shows M pixel.
2.3) the similarity distance d between two pixels is finally calculatedp(p1, p2), distance value is bigger to illustrate that difference is bigger, phase
Lower like spending, the calculation formula of similarity distance is as follows:
dp(p1, p2)=θ dp_rgb(p1,p2)+(1-θ)dp_xy(p1,p2) (3)
In formula (3), θ is weight factor, the contribution determined to adjust color distance and positional distance to similarity.
Similarity distance is applied not only to clustering, after determining cluster centre, also needs to arrive according to each pixel
The similarity distance of cluster centre determines that it belongs to situation, and segmentation result is obtained after the completion of all pixels point is sorted out.In phase
Like joined location information in degree distance calculating, the interaction between farther away pixel of meeting on spatial position is weaker,
Image data setData volume it is less when, it will lead to not smooth enough the problem at segmentation block edges, handed in vision
Friendly relation are not met on mutually.To solve this problem, the conversion that obtained segmentation result figure is carried out to color space, by RGB
The color space HSV is converted to, median filtering then is carried out to the V channel information for characterizing light levels under HSV model, then again
HSV is converted to RGB model to export, obtains the segmentation result figure of vision close friend.
3) Density Clustering for automatically determining cluster centre, operates subgraph, and process is as follows:
Definition 1 sets the image I for a width comprising n pixel, corresponds to two one-dimensional data matrixes,Indicate close
Matrix is spent,Indicate distance matrix, size is all 1 row n column.The i-th column data and original graph of density matrix or distance matrix
The mapping relations of Mx row Nx column pixel are as follows as in:
I=N (Mx-1)+Nx (7)
3.1) the similarity distance between image slices vegetarian refreshments is calculated, it is known that there are dualities for the similarity distance of pixel, i.e.,
dp(p1, p2)=dp(p2, p1), and dp(p1, p1)=0, therefore similarity distance is stored as upper three that diagonal line data are zero
Angular moment battle array { Dpij}；
3.2) density value for calculating each pixel, obtains density matrixCalculation formula is as follows:
Wherein function
In formula (4), ρiIndicate pixel piDensity value, the set of pixels of imageCorresponding index set is Is
={ 1,2 ..., M*N }, dij=dp(pi, pj) indicates the similarity distance between two pixels；
In order to reduce space complexity when operation, to increase regular hour complexity as cost, the present invention uses one
The improved density matrix calculation method of kind, specific density matrix algorithm steps are as follows:
3.2.1) one width of input includes the digital picture I and lookup radius d of M row N column pixelc, setting circulation initial value,
I1=j1=1, i2=j2=1, i=1, the memory space of density of distribution matrix, are denoted asN=M*N, initial value are set to 0；
3.2.2 the similarity distance for) calculating pixel (i1, j1) and point (i2, j2) in image, is denoted as dp(p(i1,j1),
p(i2,j2)), if dp(p(i1,j1),p(i2,j2)) > dc, then ρi=ρi+ 0, on the contrary ρi=ρi+1；
3.2.3) j2=j2+1, if j2≤N, return step 3.2.2), on the contrary j2=1 is enabled, execute step 3.2.4)；
3.2.4) i2=i2+1, if i2≤M, return step 3.2.2), on the contrary i2=1 is enabled, execute step 3.2.5)；
3.2.5) j1=j1+1, i=i+1, if j1≤N, return step 3.2.2), on the contrary j1=1 is enabled, execute step
3.2.6)；
3.2.6) i1=i1+1, if i1≤M, return step 3.2.2), on the contrary i1=1 is enabled, execute step 3.2.7)；
3.2.7 finally obtained density matrix) is exported
It is not to be previously stored { Dp in algorithm aboveijAnd then determine, but calculating each pixel
When density value, all similarity distance of calculated in advance time pixel and other n-1 pixel, in the density for completing the point
After calculating, the space for storing similarity distance is discharged, greatly reduces memory consumption when operation in this way.
3.3) distance value for calculating each pixel, obtains distance matrixEach pixel piDistance value definition
For δi, first look for comparing piThe big pixel of density obtains set S'={ pj, then search S' in piDistance it is nearest
Pixel pj', then obtain δi=dp(pi, pj'), specific distance matrix algorithm are as follows:
3.3.1 the density matrix in step 3.2) is ranked up from big to small), obtains orderly new density matrixArray of indexes is calculated according to the mapping relations for defining 1 simultaneouslySave new density matrixWith
The mapping relations of position between each pixel of original image, setting circulation initial value i1=j1=1, ind1=1；
3.3.2 density maxima ρ ') is calculated1Corresponding pixel pρ'1With the distance value of rest of pixels point, calculation formula is
δ _ temp (1, ind)=dp(p(i1,j1),pρ'1)；
3.3.3) j1=j1+1, ind1=ind1+1, if j1≤N, return step 3.3.2), on the contrary j1=1 is enabled, it executes
Step 3.3.4)；
3.3.4) i1=i1+1, if i1≤M, return step 3.3.2), on the contrary i1=1 is enabled, execute step 3.3.5)；
3.3.5 the maximum value of δ _ temp (1, ind)) is searched, as the similarity distance value of the maximum pixel of density, i.e.,
δ'1=MAX δ _ temp (1, i) | i ∈ (1, n) }；
3.3.6) setting circulation initial value i1=2, i2=1；
3.3.7 residual pixel point) is calculatedThe distance value of the pixel big to the density ratio point, calculation formula be δ _
Temp (1, i2)=dp(pρ'i1,pρ'i2)；
3.3.8) i2=i2+1, if i2≤i1-1, return step 3.3.7), on the contrary take its minimum value as similarity away from
From value, i.e. δ 'i1=MIN δ _ temp (1, i) | and i ∈ (1, i2) }, execute step 3.3.9)；
3.3.9) i1=i1+1, if i1≤M*N, return step 3.3.7), otherwise execute step 3.3.10)；
3.3.10) by indexingIt willIt is mapped to and original density matrixThe corresponding distance in position
Storage unitExport distance matrix
3.4) it is obtained according to step 3.2) and step 3.3)WithDecision diagram is drawn, obtains indicating pixel
The discrete function δ of density and distance relationi=f (ρi)；
3.5) unitary linear fit is carried out by the discrete data point in ρ-δ relational graph, obtains matched curve yδ=kxρ+b0WithCalculate the residual values ε of each data pointδi=yδi-δiAnd ερi=xρi-ρi, draw residual error histogram εδi- h and
ερi- h carries out normal approach with bell-shaped curve respectively, obtains variance yields σδAnd σρ, it is in outside confidence interval using the determination of λ σ principle
Singular point as cluster centre, be denoted as cδAnd cρ, algorithm flow chart is as shown in Figure 3；
It defines 2 and sets function fγIt is the binary function about variable ρ and δ, be corresponding to the coordinate value in three-dimensional space (ρ, δ,
fγ), then define bivariate discrete function are as follows:
In formula (5), take the logarithm of the product of density value and distance value as functional value；1 is added to be in order to be zero in density,
D is fallen in withoutcFormula is still set up when in radius, and there is no actual physical meanings；There are contexts between the pixel of image
Information also includes contextual information equally in corresponding density battle array, thereforeIt indicates to correspond to original image piPoint and its four
The density value of neighborhood totally five pixels it is cumulative and, increase the weighted value that constituent density determines cluster centre.
3.6) by discrete function γ=f of the bivariate in definition 2γ(ρ, δ) carries out the fitting on binary inclined-plane, is intended
Conjunction plane is zγ=b1+b2ρ+b3δ calculates the residual values ε of each data pointγi=yγi(ρ,δ)-γi(ρ, δ) it is straight to draw residual error
Side figure εγi- h carries out normal approach also with bell-shaped curve, obtains variance yields σγ, confidence area is in using the determination of λ σ principle
Between outer singular point as cluster centre, be denoted as cγ, algorithm flow chart is as shown in Figure 4；
3.7) cluster centre determined by step 3.5) and step 3.6) is taken into union, obtained in the final cluster of image
Heart cδργ=cδ∪cρ∪cγResidual pixel point is sorted out then according to nearest neighbouring rule for the set comprising η element,
Algorithm flow chart is as shown in Figure 5；
Finally obtained cluster centre cδργIt is the cluster centre c analyzed by cubic regressionδ、cρ、cγUnion is taken to obtain
, over-segmentation is easily caused in this way, i.e., can finally divide the image into many zonules.Although the segmentation result obtained in this way exists
Similarity in region is very high, i.e., internal to have strong interaction, but interregional otherness is not but high, this is not our institutes
Desired cluster result.This just needs to carry out fusion treatment in the next steps, and the high different zones of similarity are reconsolidated
Together.In order to facilitate fusion treatment, when showing the result figure of cluster segmentation, using in the cluster obtained in the case of over-segmentation
The pixel value of the heart fills such cluster region, while can possess more friendly visual effect.
3.8) step 3.1) is all repeated to every width subgraph to operation 3.7), obtains a segmentation result of every width subgraph
Figure, then the segmentation result figure of each width subgraph is merged, obtain intermediate result figure.
4) secondary reunion class, process are as follows:
4.1) the scaling method for intermediate result figure foundation Fig. 1 that step 3.8) obtains is zoomed to the scale of needs,
Using dp_rgb(p1, p2) is used as measuring similarity index, calculates according to density matrix algorithm and distance matrix algorithmWithρ-δ relational graph is drawn, discrete function δ is obtainedi=f (ρi)；
Because the detailed information that original image includes is completely capped in the intermediate result figure after primary cluster,
So the contradiction of information integrity and algorithm complexity is no longer so sharp in secondary reunion class, also there is no need to carry out area again
The piecemeal in domain need to only scale the images to the scale of needs.In secondary reunion class, used measuring similarity refers to
Mark is dp_rgb(p1, p2), because of dp(p1, p2) be added characterization location information coordinate value after, 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 color distance d is used onlyp_rgb(p1,p2)；
4.2) δ obtained by step 4.1)i=f (ρi) relationship calculate bivariate discrete function γ=fγ(ρ, δ) is carried out
The fitting on binary inclined-plane calculates the residual values ε of each data pointγi=yγi(ρ,δ)-γi(ρ, δ) draws residual error histogram εγi-
H carries out normal approach using bell-shaped curve, obtains variance yields σγ, the singular point being in outside confidence interval is determined using λ σ principle
As cluster centre, it is denoted as cγ；
4.3) position of cluster centre in step 4.2) is carried out to scale playback in spatial domain, intermediate result figure is obtained and exists
Cluster centre under original size sorts out residual pixel point, fills homogeneous region with the pixel value of cluster centre.It is secondary
Weight clustering algorithm is as follows:
4.3.1) input includes the intermediate result figure I_temp and search radius d of M row N column pixelc；
4.3.2 I_temp) is subjected to scaling according to scaling rule, obtains I_temp'；
4.3.3 it) is first depending on the density matrix that density matrix algorithm calculates I_temp', is calculated according to distance matrix algorithm
The distance matrix of I_temp' carries out histogram analysis and automatically determines singular point as cluster then according to 2 calculating γ values are defined
The position of cluster centre is finally carried out scale playback, obtains the cluster centre position under original scale, calculating at this time by center
All take dp_rgb(p1, p2) is used as measuring similarity index；
4.3.4) according to apart from nearest principle, i.e. similarity maximum principle is sorted out, by the rest of pixels point of I_temp
It is included into the class cluster nearest apart from oneself, obtains secondary reunion class as a result, and exporting 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 described method comprises the following steps:
1) it initializes, process is as follows:
1.1) area dividing operation is carried out first, and the image to be processed for one includes the pixel of M row N column, by pre-
After processing, 2 are divided the image intoW1×2W2Width subgraph, obtained sub-graph size areWherein Z [f] is preceding to taking
Integral function；
1.2) change of scale operation then is carried out to image, the subgraph after the completion of piecemeal is subjected to scaling processing, i.e., by ruler
The very little subgraph for a*b becomes a1*b1, wherein a1=a/ksizeAnd b1=b/ksize, ksize> 1；During scaling, because often
A pixel includes that there are three pixel values, so the method using weak sampling carries out change of scale, is including by image to be processed
Pixel number reduce while as far as possible retain original image important clustering information；
2) it is calculated based on the similarity of pixel value and location information distance, process is as follows:
2.1) the natural image I to be processed for one includes M row N column pixel, enables n=M*N, then pixel data setIn the characteristic information that has of each pixel include three chrominance channel component values under RGB color space, as R, G, B
Three pixel values；And be to the right Y-axis using the image upper left corner as coordinate origin, horizontal line, vertical line is downwards for the two dimension of X-axis
Coordinate value (x, y) under plane right-angle coordinate；
2.2) d is setpThe similarity distance of (p1, p2) between two pixels, similarity distance calculation formula are as follows:
dp(p1, p2)=θ dp_rgb(p1,p2)+(1-θ)dp_xy(p1,p2) (3)
In formula (1), r1, g1, b1 and r2, g2, b2 respectively represent the pixel value of pixel p1, p2 under RGB color space, dp_rgb
Indicate the distance between the pixel under the space；In formula (2), x1, y1 and x2, y2 respectively represent pixel p1, p2 and sit at right angle
Coordinate value in mark system, dp_xyDistance between the pixel of expression in the coordinate system；In formula (3), θ is weight factor, to adjust
Save the contribution that color distance and positional distance determine similarity；
3) Density Clustering for automatically determining cluster centre, operates subgraph, and process is as follows:
3.1) the similarity distance between image slices vegetarian refreshments is calculated, it is known that there are dualities, i.e. d for the similarity distance of pixelp(p1,
P2)=dp(p2, p1), and dp(p1, p1)=0, therefore similarity distance is stored as the upper triangular matrix that diagonal line data are zero
{Dpij}；
3.2) density value for calculating each pixel, obtains density matrixCalculation formula is as follows:
In formula (4), ρiIndicate pixel piDensity value, the set of pixels of imageCorresponding index set is Is=1,
2 ..., M*N }, dij=dp(pi, pj) indicates the similarity distance between two pixels；
3.3) distance value for calculating each pixel, obtains distance matrixEach pixel piDistance value be defined as δi,
It first looks for comparing piThe big pixel of density obtains set S'={ pj, then search S' in piThe nearest pixel of distance
pj', then obtain δi=dp(pi,pj')；
3.4) it is obtained according to step 3.2) and step 3.3)WithDecision diagram is drawn, obtains indicating pixel point density
With the discrete function δ of distance relationi=f (ρi)；
3.5) unitary linear fit is carried out by the discrete data point in ρ-δ relational graph, obtains matched curve yδ=kxρ+b0WithCalculate the residual values ε of each data pointδi=yδi-δiAnd ερi=xρi-ρi, draw residual error histogram εδi- h and
ερi- h carries out normal approach with bell-shaped curve respectively, obtains variance yields σδAnd σρ, it is in outside confidence interval using the determination of λ σ principle
Singular point as cluster centre, be denoted as cδAnd cρ；
3.6) discrete function γ=f of bivariate is obtained by decision diagramγ(ρ, δ) carries out the fitting on binary inclined-plane, it is flat to obtain fitting
Face is zγ=b1+b2ρ+b3δ calculates the residual values ε of each data pointγi=yγi(ρ,δ)-γi(ρ, δ) draws residual error histogram
εγi- h carries out normal approach also with bell-shaped curve, obtains variance yields σγ, it is in outside confidence interval using the determination of λ σ principle
Singular point as cluster centre, be denoted as cγ；
Wherein function fγIt is the binary function about variable ρ and δ, is (ρ, δ, f corresponding to the coordinate value in three-dimensional spaceγ), then
Define bivariate discrete function are as follows:
In formula (5), take the logarithm of the product of density value and distance value as functional value；Add 1 to be to be zero in density, that is, does not have
D is fallen in a littlecFormula is still set up when in radius；It indicates to correspond to original image piPoint and its four neighborhoods totally five pixels
Density value it is cumulative and, increase the weighted value that constituent density determines cluster centre；
3.7) cluster centre determined by step 3.5) and step 3.6) is taken into union, obtains the final cluster centre of image
cδργ=cδ∪cρ∪cγResidual pixel point is sorted out then according to nearest neighbouring rule for the set comprising η element, and
Homogeneous region is filled with the pixel value of cluster centre point；
3.8) step 3.1) is repeated to operation 3.7) to every width subgraph, then each width subgraph is merged, obtains intermediate result figure；
4) secondary reunion class, process are as follows:
4.1) the intermediate result figure as obtained in step 3.8) zooms to the scale of needs, using color distance dp_rgb(p1,
P2 it) as the measuring similarity index of reunion class, calculatesWithρ-δ relational graph is drawn, discrete function δ is obtainedi=
f(ρi)；
4.2) δ obtained by step 4.1)i=f (ρi) relationship calculating bivariate discrete function γ=fγ(ρ, δ) it is oblique to carry out binary
The fitting in face calculates the residual values ε of each data pointγi=yγi(ρ,δ)-γi(ρ, δ) draws residual error histogram εγi- h, equally
Normal approach is carried out using bell-shaped curve, obtains variance yields σγ, determine that the singular point being in outside confidence interval is made using λ σ principle
For cluster centre, it is denoted as cγ；
It 4.3) will be by cluster centre c that step 4.2) obtainsγScale playback is carried out in spatial domain, obtains the centre of original size
Residual pixel point is sorted out according to nearest neighbouring rule, and is filled with the pixel value of cluster centre by the cluster centre of result figure
Homogeneous region.
2. the image partition method as described in claim 1 based on fast density clustering algorithm, it is characterised in that: the step
3.2) in, dcIt is a positive real number, for portraying with pixel piFor the center of circle, dcFor the circumference of radius, and density value ρiAs fall
In the pixel number of circumferential inner；With the cumulative pixel p with maximum of channel each under color space pixel valuemaxWith it is each
Pixel p at a channel pixel value is cumulative and minimumminBetween similarity distance 2% be used as dcValue, calculation formula is such as
Under:
In formula (6),If indicating in piece image, there is multiple pixels pixel value under color space cumulative and phase
Deng all in maximum or the smallest situation, to be then averaged, i.e.,
3. the image partition method as claimed in claim 1 or 2 based on fast density clustering algorithm, it is characterised in that: described
In step 3.7), finally obtained cluster centre cδργIt is the cluster centre c analyzed by cubic regressionδ、cρ、cγTake union
It obtains, when showing the result figure of cluster segmentation, fills class using the pixel value of the cluster centre obtained in the case of over-segmentation
Cluster region.
4. the image partition method as claimed in claim 1 or 2 based on fast density clustering algorithm, it is characterised in that: described
In step 4.2), the judgment basis that the cluster centre of secondary reunion class automatically determines does not use cδ、cρ、cγUnion, it is only right
γ value carries out histogram analysis.
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