JP2008084035A - Multipeak histogram peak classification method, data processor, and program - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To classify data for each peak by correct clustering, even if the number of peaks is unknown in analysis of a histogram. <P>SOLUTION: The similarity of each data in the histogram is redefined by calculation by a predetermined calculation equation, and the maximum value of the clustered histogram is obtained by use of the redefined similarity. The maximum value of the clustered histogram is compared with a preset threshold for the maximum value of the whole histogram, and when it is determined to be the threshold or more, each component of the similarity matrix is weighted to obtain the maximum value of the clustered histogram using the similarity obtained by the weighting result. When the maximum value is determined not to be the threshold or more, data contained in the last cluster and data not clustered are classified into closest clusters, respectively, to obtain the result of classification to each cluster. <P>COPYRIGHT: (C)2008,JPO&INPIT

Description

  The present invention, for example, represents various data such as image data as a histogram, the histogram value is divided for each peak, and is suitable for application to classify data, and a multimodal histogram branching method, and The present invention relates to a data processing apparatus to which the branching method is applied, and a program.

Conventionally, when various types of data are classified, by representing them as histogram values, it is possible to perform favorable processing when performing data classification. In this case, as a histogram value, in a unimodal histogram composed of only one peak centered on a certain peak, by extracting the maximum value of the histogram and applying a Gaussian distribution centering on the maximum value, It is easy to extract the entire peak.
However, in a histogram having a plurality of peaks, a plurality of peaks cannot be extracted by simply applying the above method.

  Therefore, in order to extract a plurality of peaks, a method has been proposed in which the number of peaks in the histogram is set in advance and a plurality of peaks are extracted based on the EM algorithm. However, this method is based on the premise that the number of peaks is known in advance, and when the number of peaks is unknown, it is difficult to extract the peaks well. The EM algorithm consists of two parts: E-step (Expectation step) and M-step (Maximization step). By updating these parameters alternately, the maximum likelihood estimator or the maximum point of the likelihood function is obtained. Is what you get.

  By the way, among the clustering methods for extracting similar data as “groups” of classes, a method called weighted sequential fuzzy clustering has been proposed. This method is characterized in that the clusters are extracted in order of clusters with the highest degree of aggregation because the clusters are sequentially extracted according to the degree of aggregation between the dakes, and noise data is also robust. Details of the weighted sequential fuzzy clustering will be described later in the embodiment.

Japanese Patent Application Laid-Open No. 2004-228561 discloses a weighted sequential fuzzy clustering.
Transactions of the Institute of Electronics, Information and Communication Engineers VOL.J84-A No.3 Pages 351-359 "Fuzzy cluster extraction from weighted graphs" by Soji Hotta, Kohei Inoue, Kiichi Urahama Published in March 2001

  As described above, in the weighted sequential fuzzy clustering method, it is necessary to set the number of peaks in the histogram in advance, and it is assumed that the number of peaks is known in advance, and the number of peaks is unknown However, it is difficult to extract the peaks well.

  The present invention has been made in view of such points, and it is an object of the present invention to correctly classify data for each peak by correctly clustering even when the number of peaks is unknown when analyzing a histogram. .

The present invention re-defines the similarity of each data in the histogram for the histogram obtained based on the data value and the frequency of each value, and uses the redefined similarity. When the maximum value of the clustered histogram is obtained, the maximum value of the clustered histogram is compared with the preset threshold value with respect to the maximum value of the entire histogram, and the comparison is determined to be equal to or greater than the threshold value, Each component of the similarity matrix is weighted, and the process returns to the process of obtaining the maximum value of the clustered histogram using the similarity obtained from the weighting result.
Then, when it is determined that the comparison does not exceed the threshold, the data included in the last cluster and the non-clustered data are each assigned to the nearest cluster, and the histogram is divided into clusters. To get.

  According to the present invention, even when the number of peaks in the histogram is unknown, data can be clustered for each peak in the histogram, and good peak processing can be performed.

  In this case, by applying weighted sequential fuzzy clustering processing as the processing for obtaining the maximum value of the clustered histogram using the redefined similarity, each maximum value can be detected well, and as a result, It becomes possible to branch to each cluster well.

  In addition, for example, by applying the brightness value of the image data as data constituting the histogram to the brightness value of the image data, the brightness value of the image data is clustered from the histogram, and the region of the image is divided based on the result of branching to each cluster. It becomes possible. Therefore, it is possible to perform image data segmentation that greatly varies depending on the image content and the histogram largely varies using the histogram branching method, and the region segmentation based on the luminance value of the image data is satisfactory. It became possible to do.

  Hereinafter, an embodiment of the present invention will be described with reference to the accompanying drawings.

  In the example of the present embodiment, input data or stored data is used as a histogram based on the frequency of the value of the data, and applied to a process of classifying each peak of the histogram. First, the data processing method will be described. In the example of the present embodiment, weighted sequential fuzzy clustering is applied.

First, a method of weighted sequential fuzzy clustering will be described.
Here, an overview of the fuzzy clustering method based on the similarity matrix as the similarity matrix that is the basis of the weighted sequential fuzzy clustering method will be described, and then an overview of the weighted sequential fuzzy clustering method will be described.

[Fuzzy clustering based on similarity matrix]
When there are n D-dimensional vector data v, the similarity between the i-th data v _i and the j-th data v _j is expressed by the following equation (1).

However, v _i ^(d) and v _j ^(d) are d-th elements of v _i and v _j , respectively.
Here, S _ij is large, that is, similar data are grouped. First, consider extracting one of the most important clusters. The degree to which each data i belongs to this cluster is assumed to be _xi, and the degree of cluster aggregation is evaluated by the following equation (2).

Here, S = [s _ij ] is a similarity matrix, and x = [x ₁ ,..., X _n ] ^T. X which maximizes the degree of aggregation is determined. However, it is constrained as || x || ² = x ^T x = 1. X of the cluster having the highest degree of aggregation is a solution of the following equation (3).

  The solution of this optimization problem can be reduced to an eigenvalue problem by the Lagrange multiplier method. When Expression (3) is expressed by a matrix S and a vector x, the following Expression (4) is obtained, and the Lagrange function is Expression (5).

λ is a Lagrange multiplier.
The solution of equation (3) satisfies equation (6).

  From equation (6), equation (7) is obtained.

The optimization problem solution of equation (3) can be reduced to an eigenvalue problem. The value of the degree of aggregation of each data is given by the eigenvalue of equation (7). Further, the degree of belonging x to the first cluster is an eigenvector of the maximum eigenvalue of the matrix S. Here, it is assumed that the data i ^* with the largest x _i is the representative data of the cluster, and normalization is performed such that m _i = x _i / x _i ^* so that the degree of membership of the representative data is 1. In this case, it will be referred to as the m _i and membership.

[Weighted Fuzzy Cluster Extraction Method]
Next, the weighted sequential fuzzy cluster extraction method will be described. Here, consider a case where each data has a weight. In this case, Expression (3) becomes the following Expression (8).

However, v _i and v _j represent weights for x _i and x _j , respectively.
Here, if Y _i = {√ (v _i )} · (X _i ), Expression (8) becomes the following Expression (9).

The solution to this optimization problem can also be reduced to an eigenvalue problem by the Lagrange multiplier method.
The optimal solution Y = [y ₁ ,..., Y _n ] of equation (9) is
Matrix S = [s _ij ]: s = {√ (v _i )} {√ (v _j )} (s _ij ) is an eigenvector, and the solution x in equation (8) is x _i = y _i / {√ (v _i )}.
{√ (v _i )} {√ (v _j )} (s _ij ) (y _i ) (y _n ) = (v _i ) (v _j ) (s _ij ) (x _i ) (x _n ) , The eigenvalues of the matrix S give the cohesion. Assuming that _i having the largest x _i is representative data i ^* , m _i = x _i / x _i ^* is the membership value of data i. If v _i = 0, this data is removed and processed. However, if v _i = 0, y _i = 0. Therefore, if x _i = 0, v _i may be included.

Next, a technique for successively extracting clusters while removing data contained in the extracted clusters using a weighted sequential fuzzy cluster extraction method will be described.
First, the first cluster is extracted by the above method. Next, when extracting the second class, the same processing is performed by removing the data belonging to the first cluster.
If the membership of each data i belonging to the first cluster is m _1i , the remaining rate of the data i is 1−m _1i , and this is the data weight v _i in the second cluster extraction. Therefore, v _i = 1−m _1i is set, and the second cluster extraction process is performed.
Matrix S ₂ = [s _2ij ]: s _2ij = {√ (1-m _1i )} {√ (1-m _ij )} (s _ij ), the first eigenvector, Y ₂ = [y _{21 ,.} , Y _2n ], x _2i = y _2i / {√ (1-m _1i )}.
However, the representative data _i ^{1 *} in the first cluster, v ₁ ^* = Since the _1-m ¹ⁱ¹ * = _0, and ^{_{x 2i (1) * = 0}} .

The data i ₂ ^* with the maximum x _2i is representative data in the second cluster, and m _2i = x _2i / x _{2i (2)} ^* is the membership value of each data i to the second cluster. Become. Similarly, the membership value for the kth cluster of each data i is as follows:
Matrix S _k = [s _kij ]: s _kij = Π _{1 = 1} ^k−1 {√ (1-m _1i )} {√ (1-m _ij )} (s _ij )
If eigenvector Y _k is obtained, x _ki = y _ki / {√ [Π _{1 = 1} ^k−1 (1−m _1i )]}, so that m _ki = x _ki / x _ki ^* . Since the degree of condensation of the extracted cluster decreases monotonously as k increases, the cluster extraction process ends when the degree of aggregation becomes equal to or less than the threshold.

  In the present embodiment, the weighted sequential fuzzy cluster extraction method described so far is applied to analyze a multimodal histogram in which the number of peaks is unknown.

Hereinafter, the outline of the method will be described. In the present embodiment, the similarity s _ij between the data i and j is redefined as the following equation (10) in order to obtain the aggregation degree of the histogram.

Then, using the redefined similarity s _ij , clustering is performed for each peak of the histogram by a weighted sequential fuzzy clustering method. Finally, the histograms clustered in addition to the main peaks belong to the main peaks to complete the branching of the entire histogram.

  In the following, with reference to FIG. 1 and FIG. 2, a specific branching process according to the present embodiment, to which the weighted sequential fuzzy clustering method is applied, will be described with respect to the algorithm of the proposed method.

  FIG. 1 is a diagram showing an example of a histogram. When the input or stored data is represented as a histogram, it is assumed that the histogram has a plurality of peaks as shown in FIG. The horizontal axis of FIG. 1A is a data value, and the vertical axis is a histogram value. Processing for dividing the histogram data of FIG. 1A for each peak is performed.

  The flowchart of FIG. 2 is a diagram showing a flow of processing. Explaining based on FIG. 2, first, the re-similarity calculation is performed on the histogram using the equation (10) (step S1). Then, the weighted sequential fuzzy clustering process described above is performed using the redefined similarity (step S2). Then, a threshold value is set in which the value is reduced at a certain ratio with respect to the maximum value of the entire histogram. For example, the threshold value is about 20% of the maximum value of the entire histogram.

  The threshold value thus set is compared with the maximum value of the clustered histogram (step S3). In this comparison, when the maximum value of the clustered histogram is equal to or larger than the threshold value, each component of the similarity matrix is weighted (step S4), and the weighted sequential fuzzy clustering process of step S2 is performed again. By repeating the weighted sequential fuzzy clustering process of step S2, the comparison process of step S3, and the weighting process of each component of the similarity matrix of step S4, as shown in FIG. The maximum value of the peaks is detected in order, and the data belonging to the detected peak cluster is divided to obtain a clustered histogram.

  If the maximum value of the clustered histogram is not greater than or equal to the threshold value in the comparison in step S3, the data included in the last cluster and the data that has not yet been clustered in the histogram are A process of belonging to a neighboring cluster is performed (step S5), and a branching result of the histogram is obtained (step S6).

  A detailed example of the processing shown in this flowchart will be described below by using mathematical expressions. ~ 8. The procedure will be described in order. Here, it is assumed that a histogram value h (i) for 0 ≦ i ≦ n is given.

1. k: = 1, l (i): = 0 (1 ≦ i ≦ n), and the maximum value of the histogram is h _max .
2. The similarity s _ij is defined as the following equation (11).

  If k = 1, the setting is made as shown in equation (12).

  If k> 1, it is set as shown in equation (13).

The similarity is set as in the equation (13), and the membership value m _ki of each data i with respect to the k-th cluster is obtained by weighted sequential fuzzy clustering.

3. m _ki ^(max) = argmax _{1 ≦ i ≦ n, l (i) = 0} m _ki and i in m _ki ^(max) is max _ki . For each membership values, performs the operation of formula (14), calculates a new membership value m _i.

4). The histogram of _i satisfying 0.5 ≦ mi is labeled as the k-th cluster (l (i): = k).
5. _{hk max = argmax 1 ≦ i ≦} n, and _{l (i) = 0 h i} , hk max / h max is determined whether or larger than the threshold _{Th end The.}
5.1 Here, if it is equal to or greater than the threshold value Th _end , k: = k + 1. Return to the process.
5.2 If it is not equal to or greater than the threshold Th _end , l (i) satisfying l (i) = k is set to 0; Proceed to
6). i: = 1.
7). Is l (i) = 0?
7.1 If l (i) = 0, j ^* satisfying the condition of Expression (15) is extracted and set to l (i): = l (j ^* ).

7.2 If l (i) = 0 is not satisfied, i: = i + 1 is set. Return to Judgment.
8). Is i = n?
8.1 If i = n, exit.
8.2 If i = n, i: = i + 1 and 7. Return to Judgment.

  By performing processing in this way, each peak is detected and clustered at that peak as shown in FIGS. 1B and 1C, and finally all the data in the histogram are collected. Are clustered in each peak.

  FIG. 3 is a diagram showing a configuration example of a data processing apparatus that performs such histogram branching processing. Here, the data processing device is constituted by, for example, a computer device and its peripheral devices, and an image is captured by the image capturing unit 11 configured by a camera or a scanner connected to the computer device. Is displayed on the display 21. The computer device has installed therein software (program) for converting the luminance value of the image data into a histogram and performing the peak split processing of the histogram. The software executes the processing shown in the flowchart of FIG. For the operation, for example, a keyboard 17 connected to a computer device is used.

  The image data captured by the image capturing unit 11 is sent to the data processing unit 12 and converted into histogram data under the control of the control unit 15. The histogram data is stored in the data memory 13. The histogram data stored in the data memory 13 is subjected to branching processing according to the instructions of the program stored in the program memory 16 and the result is displayed on the display 21. Although FIG. 3 is an example in which image data is input, other various types of data that can be formed into a histogram are input or stored, the data is converted into a histogram, and then the branching process is performed with the same configuration. It may be.

Next, an example of splitting an artificially generated histogram using such a processing configuration will be described with reference to FIGS. 4 and 5.
In the example of FIG. 4, a histogram having three peaks satisfying the condition of the following equation (16) is generated as shown in FIG. 4A, and noise satisfying the equation (16) is added to the histogram value. I let you.

The parameters of Am in Formula (16) at each peak were Am ₁ = 1.5 × 10 ³ , Am ₂ = 1.0 × 10 ³ , and Am ₃ = 2.0 × 10 ³ , respectively. The parameters of σ were σ ₁ = 4.0, σ ₂ = 3.0, and σ ₃ = 5.0. The parameters of μ were μ ₁ = 60.0, μ ₂ = 30.0, and μ ₃ = 90.0. Further, the parameters Am, σ, and μ in the added noise parameter formula (16) are Am _n = 30.0, σ _n = 1.0, and μ _n = 1.0, respectively. Here, α in the equation (11) is 0.5, and the threshold Th _end is 0.2. The histogram generated with these parameters is shown in FIG.

  FIG. 4B shows the result of dividing this histogram by the processing of this example. In FIG. 4B, symbols ◯, ×, and □ are assigned to each label value l (i), and are shown as divided data. As shown in FIG. 4B, it can be seen that the three peaks are well divided.

  In the example of FIG. 5, a histogram having six peaks satisfying the condition of Expression (16) is generated as shown in FIG. 5A, and noise satisfying Expression (16) is added to the histogram value. It is an example.

The parameters of Am in Formula (16) at each peak were Am ₁ = 1.5 × 10 ³ , Am ₂ = 1.0 × 10 ³ , and Am ₃ = 2.0 × 10 ³ , respectively. The parameters of σ were σ ₁ = 4.0, σ ₂ = 3.0, and σ ₃ = 5.0. The parameters of μ were μ ₁ = 60.0, μ ₂ = 30.0, and μ ₃ = 90.0. Further, the parameters Am, σ, and μ in the added noise parameter formula (16) are Am _n = 30.0, σ _n = 1.0, and μ _n = 1.0, respectively. Here, α in the equation (11) is 0.5, and the threshold Th _end is 0.2. The histogram generated with these parameters is shown in FIG.

  The result of dividing this histogram by the processing of this example is shown in FIG. In FIG. 5 (b), symbols ◯, ×, □, +, ◇, * are given for each label value l (i), and are shown as divided data. As shown in FIG. 5B, it can be seen that the six peaks are well divided.

Next, an example in which the histogram branching process of the present embodiment is applied to the image data area dividing process will be described.
As an area division processing configuration of image data, for example, as shown in FIG. 6, image data input to an image data storage unit (or input unit) 1 is sent to the data processing unit 2 every frame, and the data processing unit 2, the luminance value of each color of the data of each frame is sent to the histogram generation unit 3 to form a histogram, and the result of the histogram formation is sent to the branch processing unit 4. The branching processing unit 4 is a functional unit that executes the histogram branching processing of this example.

  Then, the branching result in the branching processing unit 4 is returned to the data processing unit 2, and the region division processing of the image data is performed based on the branching result, and the resulting data is sent from the region splitting image output unit 5 It is set as the structure to output.

  FIG. 7 shows an example of processing with such a configuration. The image shown in FIG. 7A is, for example, an 8-bit grayscale image with an image size of 256 pixels × 256 pixels and a quantization level per pixel. The brightness value of the image in FIG. 7A is histogrammed on the right side. In this histogram, the horizontal axis represents the luminance value, and the vertical axis represents the frequency of each luminance value.

  The result of branching the histogram of the image shown in FIG. 7A is shown on the right side of FIG. 7B. The image shown in FIG. 7B shows the data divided into clusters by the branching processing in different regions in the image. As can be seen from the image in FIG. 7B, the region is well divided for each luminance value of the image. For example, it can be seen that the edge portion of the object (person) in the image is well separated as a region different from the surroundings. If the image is a color image, for example, after adding the luminance values of the primary color signals of each color, the luminance value at each pixel position is obtained by １ ／, and the luminance value is histogrammed. Good.

In the example of FIGS. 6 and 7, the example applied to the image processing has been described. However, the histogram peaking processing of the present embodiment can be applied to other various data processing. For example, the present invention may be applied to processing when analyzing a voice signal (audio signal).
Or you may use for the data analysis for performing personal identification. As data for performing this personal identification, for example, data of an image obtained by photographing a person to be identified or various types of biological data for personal identification are obtained, and these data are processed by the branching processing of the histogram of the present embodiment. The clustered data may be collated with clustered data for personal authentication registered in a database or the like, and personal identification (personal authentication) may be performed based on the degree of coincidence.

It is explanatory drawing which showed the outline | summary of the branching process by one embodiment of this invention. It is a flowchart which shows the branching process by one embodiment of this invention. It is a block diagram which shows the process structural example by one embodiment of this invention. It is explanatory drawing which shows the example (Example 1) of the branching of the histogram by one embodiment of this invention. It is explanatory drawing which shows the branching example (example 2) of the histogram by one embodiment of this invention. It is a block diagram which shows the structural example which applied one embodiment of this invention to image processing. It is explanatory drawing which showed the image processing example by one embodiment of this invention.

Explanation of symbols

  DESCRIPTION OF SYMBOLS 1 ... Image data memory | storage part, 2 ... Data processing part, 3 ... Histogram production | generation part, 4 ... Dividend processing part, 5 ... Area division | segmentation image output part, 11 ... Image capture part, 12 ... Data processing part, 13 ... Data memory , 15 ... control unit, 16 ... program memory, 17 ... keyboard, 18 ... display control unit, 19 ... display

Claims (5)

For the histogram obtained based on the value of the data and the frequency of each value, the similarity of each data in the histogram is redefined by a calculation using a predetermined calculation formula,
Using the redefined similarity measure, obtain the maximum value of the clustered histogram,
The maximum value of the clustered histogram is compared with a preset threshold value with respect to the maximum value of the entire histogram,
When it is determined that the comparison is greater than or equal to the threshold, each component of the similarity matrix is weighted, and the similarity obtained by the weighting result is used to return to the process of obtaining the maximum value of the clustered histogram.
When it is determined that the comparison does not exceed the threshold value, the data included in the last cluster and the non-clustered data are each assigned to the nearest cluster,
A multimodal histogram branching method characterized by obtaining a result of splitting a histogram into clusters. The multimodal histogram branching method according to claim 1,
The multi-modal histogram branching method characterized in that the process of obtaining the maximum value of the clustered histogram using the re-defined similarity is a weighted sequential fuzzy clustering process. The multimodal histogram branching method according to claim 1,
The data constituting the histogram is the luminance value of the image data,
A multi-peak histogram branching method characterized in that luminance values of image data are clustered from histograms and divided into regions based on the result of splitting into clusters. In a data processing device that splits a multimodal histogram,
Re-definition processing means for re-defining the similarity of each data in the histogram with respect to the histogram obtained based on the value of the data and the frequency of each value by an operation according to a predetermined arithmetic expression;
Maximum value calculation means for obtaining the maximum value of the clustered histogram using the similarity redefined by the redefinition processing means,
Comparison means for comparing the maximum value of the clustered histogram with a preset threshold value with respect to the maximum value of the whole histogram obtained by the maximum value calculation means;
Weighting means for weighting each component of the similarity matrix when the comparison means determines that the comparison is greater than or equal to a threshold, and supplying the similarity obtained by the weighting result to the maximum value computing means;
When it is determined that the comparison by the comparison means is not equal to or greater than the threshold, the data included in the last cluster and the non-clustered data are provided with auxiliary processing means that belong to the nearest cluster, respectively,
A data processing apparatus characterized by obtaining a result obtained by dividing a histogram into clusters. In a program that executes a process of splitting a multimodal histogram,
Re-defining the similarity of each data in the histogram with respect to the histogram obtained based on the value of the data and the frequency of each value by an operation according to a predetermined arithmetic expression;
Obtaining a maximum value of a clustered histogram using the redefined similarity;
Comparing the maximum value of the clustered histogram with a preset threshold for the maximum value of the entire histogram;
Returning to the process of obtaining the maximum value of the clustered histogram using the similarity obtained by weighting each component of the similarity matrix when the comparison is determined to be equal to or greater than the threshold; ,
When it is determined that the comparison is not greater than or equal to the threshold value, the process includes the step of causing the data included in the last cluster and the data that is not clustered to belong to the nearest cluster, respectively,
A program characterized by obtaining a result of dividing a histogram into clusters.