CN104376329A - Clustering assessment method based on spatial autocorrelation and watershed algorithm - Google Patents
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Abstract
The invention provides a clustering assessment method based on a watershed algorithm and spatial autocorrelation. The method comprises the steps that an image is preprocessed so that a feature marking image can be obtained; the watershed algorithm is used for segmentation, and the barycentric coordinates and the area of each polygonal area are calculated; the numerical values of the adjacent matrixes of the polygonal areas and the numerical value of local Moran's I are calculated, and a scatter diagram is drawn; the polygonal areas belonging to different quadrants of the scatter diagram are marked in different modes, and the clustering state is visually displayed; relevant parameters are calculated, and the clustering state is estimated. According to the clustering assessment method, the watershed algorithm is used for accurately reflecting the location information and the dimensional information of target objects; through spatial autocorrelation analysis, an initial clustering central point does not need to be provided, and the method has the advantages of being high in efficiency, accuracy and credibility, and the distribution behaviors of targets can be analyzed and estimated in the aspects of the scatter area and the number of scattered targets.
Description
Technical Field
The invention relates to a distribution image sparseness and confidentiality evaluation method, in particular to a clustering evaluation algorithm based on a watershed algorithm and spatial autocorrelation, which can be used for sparseness and denseness evaluation analysis including micro-nano particle distribution, metallographic analysis, defect detection distribution and cell biological morphology distribution.
Background
The density is an indispensable important link in detection means such as image analysis, metallographic detection and particle distribution detection, and is an important index for researching the aggregation or dispersion behavior of a target object in an image in an integral area and the dispersion or aggregation degree of the target object. The distribution image is converted into the binary image, the target area in the image is converted into the connected domain in the binary image, and the connected domain and the related position and distance distribution of the connected domain can be analyzed accurately and conveniently.
The evaluation of the density of the image exists as an evaluation means for the bias and directionality of the dispersion or aggregation behavior of the target objects in the image, and the analysis result is significant for knowing the behavior of the target objects distributed in the spatial direction and the reason of the behavior. The mainstream cluster analysis or cluster analysis is to divide similar objects into different groups or more subsets by a static classification method. Similar subsets all have similar properties, such as spatial distance, etc. Conventional cluster analysis, such as the K-means algorithm (MacQueen J. methods for classification and analysis of multiple observations, etc. [ C ]// Proceedings, oft fine Berkeley system characterization and probability, 1967,1(281, 297):14.), uses K points in space as input, performs cluster analysis with the K points as the center, and divides the other points of the population into different subsets of clusters in the K points according to the distance between the points as the characteristic. The algorithm has the greatest advantages of simplicity and quickness, but the application range is narrow, a plurality of results cannot be well matched, and the selection requirement of the clustering analysis result on input k points is very high.
Disclosure of Invention
Aiming at the defects in the prior art, the invention aims to provide a clustering evaluation method based on a watershed algorithm and spatial autocorrelation.
The conventional clustering algorithm first gives the program several initial focus points, which may be given randomly or according to the coordinates of the points of the dense area seen by the naked eye. The initial point is different and the effect is different. If the initial point is a dense region seen by naked eyes, the overall distribution is more grasped after the clustering algorithm is used for processing, and if the initial point is given randomly, the calculation amount is too large, and the analysis effect is not good. Generally, if the random giving is not performed, the intelligence of the algorithm is poor.
The spatial autocorrelation analysis refers to the phenomena of potential interdependency, spatial interaction and diffusion of some variables among observed data in the same distribution area. Spatial correlation refers to the effect that a phenomenon occurring in one place affects other locations related to it, which is generally related to distance and direction.
Since the clustering and clustering behaviors of the target distributions are closely related to the areas of the polygon regions after watershed segmentation (Meyer F, Beucher S. simulation segmentation [ J ]. journal visual communication and image representation,1990,1(1):21-46.), the denser regions have smaller polygon areas and the more scattered regions have larger polygon areas, the measurement of the sizes of the polygon areas can be used as an important parameter for the spatial autocorrelation analysis to evaluate the clustering or clustering behaviors of the targets.
Moran proposed a local Moran's I metric (Moran P. the interpretation of Statistical maps J. Journal of the Royal Statistical society B (methodological),1948,10(2): 243-251) that can be used to measure the correlation of different sub-regions of the same region at a parameter. Moran's I is greater than 0, then positive correlation is obtained; less than 0, negative correlation; equal to 0, indicating no correlation. And through the analysis of the parameters and the adjacent matrix, the distribution of the image can be divided into areas with different aggregation or dispersion states, so that the method has higher value for knowing the distribution state and density degree of the image and has high operability.
Therefore, the cluster evaluation is shifted to solve the following problems: how to combine the segmentation of the image by the watershed algorithm, the area calculation of the segmented polygonal region, the processing of the adjacent matrix in the spatial autocorrelation and the local Moran's I index, analyze the dispersion or aggregation behaviors in the image and the degree of the dispersion or aggregation behaviors, and how to use the parameters to evaluate the density degree of the distribution in the image.
The clustering evaluation method based on the watershed algorithm and the spatial autocorrelation, provided by the invention, comprises the steps of segmenting an image by adopting the watershed algorithm, taking the area of the segmented polygon as a parameter for spatial autocorrelation analysis, taking the centroid distance of the polygon as the basis of an adjacency matrix for the spatial autocorrelation analysis, calculating a local Moran's I index, analyzing the dispersion and aggregation behaviors of target distribution in the image, searching the polygons in a high aggregation region and a low aggregation region, and evaluating the aggregation and dispersion degrees of the image distribution by calculating relevant parameters.
The clustering evaluation method based on the watershed algorithm and the spatial autocorrelation, provided by the invention, can accurately mark the aggregation and dispersion areas in the image, has high efficiency, is visual and reliable, and can better analyze and evaluate the stability of the distribution in the dispersion and aggregation areas.
The specific technical scheme of the invention is as follows: the method comprises the steps of firstly carrying out gray level processing on an original image, carrying out median filtering, eliminating noise points and interference information, and obtaining a filtered image. On the basis, the OTSU Otsu method is used for binarization processing, then a watershed algorithm is used for segmenting the graph, and the area of the segmented polygonal area and the distance between the centroids are calculated. Constructing an adjacency matrix on the basis of the centroid matrix, calculating the numerical value of local Moran' sI of each polygonal area, and performing scatter plot representation on the polygonal areas and the average adjacency values thereof. And dividing areas with different aggregation states on the basis of the scatter diagram, calculating related parameters of polygonal areas belonging to the areas with the aggregation states, and analyzing and evaluating the aggregation and dispersion states of the distribution image.
The invention provides a clustering evaluation method based on a watershed algorithm and spatial autocorrelation, which comprises the following steps:
(1) carrying out gray level processing on the image, carrying out median filtering, and obtaining a binary image by using an OTSU Otsu method on the filtered image;
(2) performing morphological processing on the binary image, deleting boundary interference, and eliminating obviously too small non-target features to obtain a feature labeled image;
(3) segmenting the feature marker image by using a watershed algorithm, and calculating the centroid coordinate and the area of each polygonal area according to the segmented image;
(4) calculating an adjacency matrix of the polygonal area according to the centroid coordinates of the polygonal area, and calculating an average adjacency value of the polygonal area; calculating the numerical value of local Moran's I of each polygonal region by using the area of the polygonal region of the image segmented by the watershed algorithm as a parameter of spatial autocorrelation analysis, and calculating the standardized value of the numerical value of local Moran' sI; drawing a scatter diagram by taking the normalized value of the numerical value of the local Moran's I as an abscissa and the average adjacent value of the polygonal area as an ordinate;
(5) the four quadrants of the scatter diagram represent different clustering states, wherein the first quadrant of the scatter diagram is a low-dispersion area, the third quadrant of the scatter diagram is a high-density area, and the polygonal area belonging to the first quadrant of the scatter diagram and the polygonal area belonging to the third quadrant of the scatter diagram are marked in different modes so as to visually display the clustering states;
(6) and calculating related parameters of the low-dispersion area and the high-density area, and evaluating the clustering state.
According to the clustering evaluation method based on the watershed algorithm and the spatial autocorrelation, the watershed algorithm is adopted, the image can be accurately segmented according to the size of the original target object and the distribution distance, the segmented polygonal area can well represent the size and the distribution characteristics of the original target object, and accurate adjacency matrix information and spatial autocorrelation characteristics are provided for subsequent spatial autocorrelation analysis.
The clustering evaluation method based on the watershed algorithm and the spatial autocorrelation, provided by the invention, adopts the spatial autocorrelation analysis, is a method established on the basis of the adjacent interrelation provided by the watershed algorithm, has high calculation efficiency and good accuracy, and can accurately describe the sparse and dense attributes of the distribution among different regions in the distribution image, thereby better describing the distribution behavior characteristics of the target object in the distribution image.
The clustering evaluation method based on the watershed algorithm and the spatial autocorrelation, provided by the invention, can accurately mark the aggregation and dispersion areas in the image, has high efficiency, is visual and reliable, and can better analyze and evaluate the stability of the distribution in the dispersion and aggregation areas.
Further, the method for segmenting the feature marker image by using a watershed algorithm in the step (3) and calculating the centroid coordinate and the area of each polygonal area according to the segmented image comprises the following steps:
(31) calculating the vertex coordinates of the boundary of each polygonal area according to the ridge lines divided by the watershed algorithm, and calculating the arithmetic mean of the vertex coordinates as the centroid coordinates of the polygonal areas;
(32) the area of the polygonal region is calculated from the vertex coordinates of the boundary of the polygonal region.
Further, the adjacency matrix of the polygon area in step (4) includes the following steps:
(41) computing adjacency matrix WijThe method comprises the following steps:
Wij＝[dij]k·[βij]b
wherein d isijIs the centroid distance between the polygon area i and the polygon area j, k is the index of the polygon centroid distance, βijFor the shared boundary length between two adjacent polygon areas i and jThe ratio of the boundary lengths of the regions i, b, is 1.
Further, the method for calculating the value of local Moran's I of each polygon region in step (4) includes the following steps:
(42) calculating the standard deviation S of the area of the polygonal area:
wherein, yiIs the area of the polygonal area i,taking the area average value of all polygonal areas and n as the number of all polygonal areas;
(43) calculate the value I of the local Moran's I for each polygon regioni：
Where j ≠ i.
Further, the method for calculating the normalized value of the local Moran's I value in step (4) is as follows:
(44) computing adjacency matrix WijRow and matrix WiMean value of E (I)i)：
Wherein WiIs a contiguous matrix WijA row and matrix; the rows and matrix are n rows and 1 column matrix, and the elements of each row are adjacent matrix WijThe sum of all elements of the respective columns of each row.
(45) Calculation of Var (I)i)：
Wherein,
(46) calculating the normalized value Z (I) of the value of the local Moran's Ii)：
Wherein IiIs the value of the local Moran's I of the polygon area i.
Further, the step (4) of calculating the average adjacency value of the polygon region includes the steps of:
(47) average adjacent value W of polygonal areazThe method comprises the following steps:
Wz＝Z(Ii)*Wij
wherein Z (I)i) Is a normalized value of the value of local Moran's I, WijIs a contiguous matrix.
Further, the step (6) calculates the related parameters of the low-dispersion area and the high-density area, and the method for evaluating the clustering state comprises the following steps:
(61) calculating the ratio RHH of the area of the polygonal area belonging to the low dispersion area to the total area;
(62) calculating the ratio RLL of the area of the polygonal area belonging to the high aggregation area to the total area;
(63) performing clustering evaluation, wherein the larger the RHH is, the smaller the RLL is, and the dispersion is dominant; the smaller the RHH, the larger the RLL, indicating dense dominated.
Further, the step (6) calculates the related parameters of the low-dispersion area and the high-density area, and the method for evaluating the clustering state comprises the following steps:
(64) calculating an average value Rhh _ s of areas of polygonal regions belonging to the low dispersion region;
(65) calculating an average Rll _ s of areas of the polygonal regions belonging to the high dense region;
(66) calculating the ratio Rc of Rhh _ s to Rll _ s for comparing the clustering states of different images, wherein the larger Rc indicates that the area difference between a low-dispersion region and a high-concentration region is larger, which indicates that the distribution is in a locally-concentrated and wholly-sparse state; the smaller Rc indicates that the difference in area average between the low dispersion region and the high concentration region is small, and the distribution is more uniform.
Rhh _ s denotes the average area of the polygonal region of the dispersed region, and Rll _ s denotes the average area of the polygonal region of the dense region. Typically Rhh _ s is greater than Rll _ s, meaning that the average area of the polygon occupied by each particle in the dispersed region is greater than the area of the polygon occupied by the particles in the dense region, and Rc is typically greater than 1. Therefore, the larger Rc indicates that the larger the difference in the average area occupied by each particle in the dispersed region with respect to the average area occupied by the dense region, indicating that the difference between the dispersed region and the dense region in the distribution is large, that is, the distribution is not uniform.
Further, the step (6) calculates the related parameters of the low-dispersion area and the high-density area, and the method for evaluating the clustering state comprises the following steps:
(67) calculating a target object density D for low scatter regionshh；
(68) Calculating a target object density D for a high concentration regionll；
(69) Performing cluster evaluation to obtain target object density DhhLarger indicates a more sparsely distributed state; target object density DllLarger indicates a more densely distributed state.
Target object density D of low scatter regionhhRepresenting the ratio of the number of particles in the dispersed region to the total number, the density D of the target object in the high-concentration regionllRepresenting the ratio of the number of particles to the total number in the dense area. DhhLarge indicates that the number of particles contained in the dispersion region in the whole distribution accounts for a large total number, indicates that the whole distribution is biased toward dispersion, otherwise DllLarge indicates that the overall distribution is biased to be dense.
Compared with the prior art, the clustering evaluation method based on the watershed algorithm and the spatial autocorrelation has the following beneficial effects:
(1) the watershed algorithm is used as a basis, the dispersion characteristics of the distribution image and the differences of the target objects in size and dispersion distance are well considered, the position information and the size information of the target objects are accurately reflected, and high-reliability information is provided for the subsequent aggregation and dispersion behavior research;
(2) generally, a clustering algorithm needs to provide coordinates of a clustering center point as an initial value, the clustering center points with different coordinates are selected, and results obtained by the clustering algorithm are different, so that final distribution analysis can be greatly influenced, and the distribution analysis is inaccurate; the algorithm utilizes the spatial autocorrelation analysis, an initial clustering center point is not required to be provided, a reliable adjacency matrix can be provided on the basis of providing spatial information based on the watershed algorithm, the distribution behavior of the target object can be described, and the algorithm has the characteristics of high efficiency, good accuracy and high reliability, and can analyze and evaluate the distribution behavior of the target from a plurality of angles such as scattered areas and scattered target numbers.
Drawings
FIG. 1 is a flow chart of a clustering assessment method based on spatial autocorrelation and watershed algorithms according to an embodiment of the present invention;
FIG. 2 is a distribution artwork A;
FIG. 3 is a distribution original B;
FIG. 4 is a scatter plot corresponding to a spatial autocorrelation analysis of the distribution artwork A shown in FIG. 2;
FIG. 5 is a scatter plot corresponding to the spatial autocorrelation analysis of the distribution artwork B shown in FIG. 3;
FIG. 6 is a color fill map corresponding to the high aggregation areas and the low dispersion areas of the distribution original A shown in FIG. 2;
fig. 7 is a color fill map corresponding to the high aggregation area and the low dispersion area of the distribution original image B shown in fig. 3.
Detailed Description
FIG. 1 is a flow chart of a clustering assessment method based on spatial autocorrelation and watershed algorithms according to an embodiment of the present invention; the implementation process of the clustering evaluation method based on the spatial autocorrelation and the watershed algorithm in the embodiment is as follows:
(1) firstly, carrying out gray level processing on an input image to obtain a distribution original image A shown in figure 2 and a distribution original image B shown in figure 3; secondly, performing median filtering on the gray level images in the images in; adopting a window of 2x2, moving line by line from left to right, from top to bottom, arranging pixels contained in the field of the target in ascending or descending order of gray level, and taking the radian of the pixel with the middle gray level as the gray level of the point pixel in the field; then, the filtered image is binarized by OTSU tsu method.
(2) The method comprises the following steps of carrying out simple morphological processing on a binary image, wherein the specific steps comprise:
(21) and filling holes in the binary image. Whether holes exist in the connected domain is judged by checking whether a certain background pixel in the binary image can reach by filling the background from the edge of the image.
(22) And deleting the pixels at the boundary in the binary image. And deleting the separated and broken pixel points which are divided by the image segmentation at the boundary by judging the highlighted pixel points at the boundary.
(23) And judging the total area of the connected domain pixels in the binary image through connected domain operation, deleting small connected domains or pixel points which are obviously smaller than the area of the target object connected domain pixels in the image, and eliminating noise point interference which is not eliminated in the binary process.
(3) Carrying out watershed segmentation on the processed binary image, firstly carrying out distance transformation, then segmenting the image into polygonal areas with different sizes, and calculating the centroid coordinate, the centroid distance matrix and the area of the polygonal areas, wherein the specific steps are as follows:
(31) calculating vertex coordinates of the boundary of each polygonal area according to ridge lines divided by a watershed algorithm, and calculating an arithmetic mean of the vertex coordinates as centroid coordinates of the polygonal areas;
the distance transformation of watershed segmentation is carried out based on Euler distance, the distance between each pixel point of the image and the adjacent nearest non-0 pixel point is calculated, and finally the whole image is converted into a distance matrix; carrying out gray level transformation based on distance transformation on the image, wherein the value of the distance change is the basis of a watershed algorithm; in the water injection of the continuous watershed, the boundary of the highlighted connected domain is expanded to the adjacent connected domain, and finally, a boundary, namely a ridge line of the watershed, is formed between the highlighted connected domain and the adjacent connected domain; reading the coordinate information of the watershed ridge line, and calculating the centroid coordinate of a polygon divided by the ridge line, wherein the centroid coordinate is calculated as follows:
wherein, XiIs the abscissa, Y, of the center of mass of a certain polygoniIs ordinate, xciAnd yciRespectively, the abscissa and ordinate of the points constituting the polygon, and Ci is the number of points constituting the polygon.
Calculating a centroid distance matrix dij：
(32) And calculating the area of the polygonal area according to the vertex coordinates of the boundary of the polygonal area.
(4) Calculating an adjacency matrix of the polygonal area according to the centroid coordinates of the polygonal area, and calculating an average adjacency value of the polygonal area; calculating the numerical value of local Moran's I of each polygonal region by using the area of the polygonal region of the image segmented by the watershed algorithm as a parameter of spatial autocorrelation analysis, and calculating the standardized value of the numerical value of local Moran's I; drawing a scatter diagram by taking the normalized value of the numerical value of the local Moran's I as an abscissa and the average adjacent value of the polygonal area as an ordinate; the method comprises the following specific steps:
(41) computing adjacency matrix WijThe method comprises the following steps:
Wij＝[dij]k·[βij]b
wherein d isijIs the centroid distance between the polygon area i and the polygon area j, k is the index of the polygon centroid distance, βijB is the ratio of the boundary length shared between two adjacent polygon areas i and j to the boundary length of the polygon area i, and is equal to 1.
k the size of the index is determined according to the descriptive effect on dispersion and aggregation, where k is 3 in this embodiment, and the adjacency matrix is constructed on the basis of the inverse of the 3 rd power of the distance between the centroids of the two polygons.
Other ways of constructing the adjacency matrix are possible, and the invention is not limited in this regard.
The method for calculating the value of the local Moran's I of each polygon region in the step (4) includes the following steps:
(42) calculating the standard deviation S of the area of the polygonal area:
wherein, yiIs the area of the polygonal area i,taking the area average value of all polygonal areas and n as the number of all polygonal areas;
(43) calculate the value I of the local Moran's I for each polygon regioni：
Where j ≠ i.
The method for calculating the normalized value of the local Moran's I value in step (4) is as follows:
(44) computing adjacency matrix WijRow and matrix WiMean value of E (I)i)：
Wherein WiIs a contiguous matrix WijA row and matrix;
(45) calculation of Var (I)i)：
Wherein,
(46) calculating the normalized value Z (I) of the value of the local Moran's Ii)：
Wherein IiIs the value of the local Moran's I of the polygon area i.
The step (4) of calculating the average adjacency value of the polygon region comprises the following steps:
(47) average adjacent value W of polygonal areazThe method comprises the following steps:
Wz＝Z(Ii)*Wij
wherein Z (I)i) Is a normalized value of the value of local Moran's I, WijIs a contiguous matrix.
(48) Normalized value Z (I) of the value of local Moran's Ii) As the abscissa, the average adjacent value W of the polygonal areazDrawing a scatter diagram as a vertical coordinate, as shown in fig. 4 and 5;
normalized value Z (I) according to the value of local Moran's Ii) And average adjacent value W of polygonal areazThe case where the value is greater than 0 and less than 0 is different, and the four quadrants can be divided. The first quadrant is HH, which represents that the z value is large and the periphery is adjacently distributed, namely a low dispersion area; the second quadrant is HL, the representation z value is small, but the surrounding distribution is sparse, namely, the dense polygon is surrounded by a more dispersed area; the third quadrant is LL, and represents a high-density area with a small z value and dense distribution around; the fourth quadrant, LH, characterizes the large z-value but the dense distribution around, i.e. the scattered area is densely surrounded.
(5) The four quadrants of the scatter diagram represent different clustering states, wherein the first quadrant of the scatter diagram is a low-dispersion area, the third quadrant of the scatter diagram is a high-density area, and the polygonal area belonging to the first quadrant of the scatter diagram and the polygonal area belonging to the third quadrant of the scatter diagram are marked in different modes so as to visually display the clustering states;
in this embodiment, different gray marks are used, and different colors or other marks may be used as long as different areas can be visually distinguished.
And (6) calculating related parameters of the low-dispersion area and the high-density area, and evaluating the clustering state.
The clustering status can be evaluated as follows:
(61) calculating the ratio RHH of the area of the polygonal area belonging to the low dispersion area to the total area;
(62) calculating the ratio RLL of the area of the polygonal area belonging to the high aggregation area to the total area;
(63) performing clustering evaluation, wherein the larger the RHH is, the smaller the RLL is, and the dispersion is dominant; the smaller the RHH, the larger the RLL, indicating dense dominated.
By comparing RHH and RLL, it can be known whether the dispersion predominates or the aggregation predominates. The greater the RHH, the more dominant the dispersion, and the greater the RLL, the more dominant the population.
RHH and RLL are area ratios less than 1, with RHH greater than RLL indicating that the particles occupy more than half of the total area in the dispersed state, whereas RLL less than RHH indicates a dense state. These two parameters are used to compare the difference between the two distributions.
With respect to fig. 2 and 3, RHH is 0.447 and 0.404, and RLL is 0.245 and 0.297, respectively, and thus it can be seen that fig. 2 is larger in the low dispersion area than fig. 3, fig. 2 is smaller in the high dense area than fig. 3, and fig. 2 occupies more area and dispersion is more dominant than fig. 3.
The following method can also be used to evaluate the clustering status:
(64) calculating an average value Rhh _ s of areas of polygonal regions belonging to the low dispersion region;
(65) calculating an average Rll _ s of areas of the polygonal regions belonging to the high dense region;
(66) calculating a ratio Rc of Rhh _ s to Rll _ s for comparing clustering states of different images, wherein the larger Rc indicates that the area difference between a low-dispersion region and a high-concentration region is larger, which indicates that the distribution is in a locally dense and overall sparse state, and the larger the average area of the dispersion region is than that of the concentration region on the average area, which indicates that the polygonal area of the dispersion region is very large and the polygonal area of the concentration region is very small, which indicates that the dispersion is very sparse and the concentration is very dense, which indicates that the difference between the two states is very large, which indicates that the distribution is locally different and is unevenly distributed; the smaller Rc indicates that the area average difference between the low dispersion region and the high dense region is small, and the distribution uniformity is good, and for fig. 2 and 3, the corresponding values are: rhh _ s, 0.00139 and 0.0011, Rll _ s, 0.000534 and 0.0004; comparing the values of Rc, fig. 2 and 3 are 2.603 and 2.75, respectively, and it can be seen that Rc in fig. 2 is small and the distribution uniformity is good.
The clustering status can also be evaluated as follows:
(67) calculating a target object density D for low scatter regionshh；
(68) Calculating a target object density D for a high concentration regionll；
(69) Performing cluster evaluation to obtain target object density DhhAnd DllThe ratio of the number of particles to the total number in the dispersed state and the dense state, respectively, and the target object density DhhLarger means more dispersed particles in the distribution and thus more dispersed state; target object density DllThe larger the number of dense particles in the distribution and thus the more dense state, the correlation values of fig. 2 and 3 are: dhh0.289 and 0.240, Dll0.411 and 0.483, and in FIGS. 2 and 3, DllNumerical ratio of (D)hhLarge, indicating that in both fig. 2 and fig. 3, the number of particles in the distribution is more densely distributed.
Comparing D in respective distributionshhAnd DllIf the two are close, the numbers of the particles contained in the dispersion and the aggregation are also close, the balance is favored, and the uniformity of the distribution is good; if the difference is large, it indicates that there are too many grainsIf the distribution is dispersed or mostly aggregated, the distribution is biased to one of the aspects, which will appear unbalanced, and the local difference of the distribution is large, and the distribution is not uniform, D in FIG. 2hhAnd DllMore closely, it can be seen that in terms of particle number statistics, fig. 2 is biased toward equilibrium and the uniformity of distribution is good, while fig. 3 is biased toward imbalance, the local difference of distribution is large, and the distribution is not uniform.
According to the clustering evaluation method based on the watershed algorithm and the spatial autocorrelation, the watershed algorithm is used as a basis, the dispersion characteristic of a distribution image and the difference between target objects in size and dispersion distance are well taken care of, the position information and the size information of the target objects are accurately reflected, and high-reliability information is provided for the subsequent clustering and dispersion behavior research; by utilizing the spatial autocorrelation analysis, an initial clustering center point is not required to be provided, a reliable adjacency matrix can be provided on the basis of providing spatial information based on a watershed algorithm, the distribution behavior of a target object can be described, and the method has the characteristics of high efficiency, good accuracy and high reliability, and can analyze and evaluate the distribution behavior of the target from a plurality of angles such as scattered area, scattered target number and the like.
The foregoing detailed description of the preferred embodiments of the invention has been presented. It should be understood that numerous modifications and variations could be devised by those skilled in the art in light of the present teachings without departing from the inventive concepts. Therefore, the technical solutions available to those skilled in the art through logic analysis, reasoning and limited experiments based on the prior art according to the concept of the present invention should be within the scope of protection defined by the claims.
Claims (9)
1. A clustering evaluation method based on spatial autocorrelation and watershed algorithm is characterized by comprising the following steps:
(1) carrying out gray level processing on the image, carrying out median filtering, and obtaining a binary image by using an OTSU Otsu method on the filtered image;
(2) performing morphological processing on the binary image, deleting boundary interference, and eliminating obviously too small non-target features to obtain a feature labeled image;
(3) segmenting the feature marker image by using a watershed algorithm, and calculating the centroid coordinate and the area of each polygonal area according to the segmented image;
(4) calculating an adjacency matrix of the polygonal area according to the centroid coordinates of the polygonal area, and calculating an average adjacency value of the polygonal area; calculating the numerical value of local Moran's I of each polygonal region by using the area of the polygonal region of the image segmented by the watershed algorithm as a parameter of spatial autocorrelation analysis, and calculating the standardized value of the numerical value of the local Moran's I; drawing a scatter diagram by taking the normalized value of the numerical value of the local Moran's I as an abscissa and the average adjacent value of the polygonal area as an ordinate;
(5) the four quadrants of the scatter diagram represent different clustering states, wherein the first quadrant of the scatter diagram is a low-scattering area, the third quadrant of the scatter diagram is a high-density area, and the polygonal area belonging to the first quadrant of the scatter diagram and the polygonal area belonging to the third quadrant of the scatter diagram are marked in different modes so as to visually display the clustering states;
(6) and calculating related parameters of the low-dispersion area and the high-density area, and evaluating the clustering state.
2. The method for cluster estimation of spatial autocorrelation and watershed algorithm as claimed in claim 1, wherein the step (3) of segmenting the feature marker image by using the watershed algorithm, and the method of calculating the centroid coordinates and area of each polygon region from the segmented image comprises:
(31) calculating vertex coordinates of the boundary of each polygonal area according to ridge lines divided by a watershed algorithm, and calculating an arithmetic mean of the vertex coordinates as centroid coordinates of the polygonal areas;
(32) and calculating the area of the polygonal area according to the vertex coordinates of the boundary of the polygonal area.
3. The method for cluster estimation of spatial autocorrelation and watershed algorithm as claimed in claim 1, wherein the adjacency matrix of the polygonal region in step (4) comprises the following steps:
(41) computing adjacency matrix WijThe method comprises the following steps:
Wij＝[dij]k·[βij]b
wherein d isijIs the centroid distance between the polygon area i and the polygon area j, k is the index of the polygon centroid distance, βijB is the ratio of the boundary length shared between two adjacent polygon areas i and j to the boundary length of the polygon area i, and is equal to 1.
4. The method for cluster estimation of spatial autocorrelation and watershed algorithm as claimed in claim 3, wherein the method for calculating the value of local Moran's I of each polygon region in step (4) comprises the following steps:
(42) calculating the standard deviation S of the area of the polygonal area:
wherein, yiIs the area of the polygonal area i,taking the area average value of all polygonal areas and n as the number of all polygonal areas;
(43) calculate the value I of the local Moran's I for each polygon regioni：
Where j ≠ i.
5. The method for cluster estimation of spatial autocorrelation and watershed algorithm as claimed in claim 4, wherein the method for calculating the normalized value of the local Moran's I in step (4) is:
(44) computing adjacency matrix WijRow and matrix WiMean value of E (I)i)：
Wherein WiIs a contiguous matrix WijA row and matrix;
(45) calculation of Var (I)i)：
Wherein,
(46) calculating a normalized value Z (I) of the value of said local Moran's Ii)：
Wherein IiIs the value of the local Moran's I of the polygon area i.
6. The method for cluster estimation of spatial autocorrelation and watershed algorithm as claimed in claim 5, wherein the step (4) of calculating the average neighboring value of the polygon region comprises the steps of:
(47) average adjacent value W of the polygonal areazThe method comprises the following steps:
Wz＝Z(Ii)*Wij
wherein Z (I)i) Is a normalized value of the value of local Moran's I, WijIs a contiguous matrix.
7. The method for cluster evaluation of spatial autocorrelation and watershed algorithm as claimed in claim 1, wherein the step (6) calculates the correlation parameters of the low-dispersion region and the high-density region, and the method for evaluating the cluster state comprises:
(61) calculating the ratio RHH of the area of the polygonal area belonging to the low dispersion area to the total area;
(62) calculating the ratio RLL of the area of the polygonal area belonging to the high aggregation area to the total area;
(63) performing clustering evaluation, wherein the larger the RHH is, the smaller the RLL is, and the dispersion is dominant; the smaller the RHH, the larger the RLL, indicating dense dominated.
8. The method for cluster evaluation of spatial autocorrelation and watershed algorithm as claimed in claim 1, wherein the step (6) calculates the correlation parameters of the low-dispersion region and the high-density region, and the method for evaluating the cluster state comprises:
(64) calculating an average value Rhh _ s of areas of polygonal regions belonging to the low dispersion region;
(65) calculating an average Rll _ s of areas of polygonal regions belonging to the high dense region;
(66) calculating a ratio Rc of Rhh _ s to Rll _ s for comparing clustering states among different images, wherein the larger Rc indicates that the area difference between the low-dispersion region and the high-concentration region is larger, which indicates that the distribution is in a locally concentrated and overall sparse state; smaller Rc means that the area average difference between the low dispersion region and the high concentration region is small, indicating that the distribution is more uniform.
9. The method for cluster evaluation of spatial autocorrelation and watershed algorithm as claimed in claim 1, wherein the step (6) calculates the correlation parameters of the low-dispersion region and the high-density region, and the method for evaluating the cluster state comprises:
(67) calculating a target object density D of the low scatter regionhh；
(68) Calculating a target object density D for the high concentration regionll；
(69) Performing cluster evaluation, the target object density DhhLarger indicates a more sparsely distributed state; the target object density DllLarger indicates a more densely distributed state.
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