JP6080740B2 - Image area dividing apparatus, image area dividing method, and image area dividing program - Google Patents

Description

  The present invention relates to a clustering method, and more particularly, to an image region dividing device, an image region dividing method, and an image region dividing program for dividing an image into non-overlapping regions.

  Conventionally, as a method of dividing an image region, there is a method called connected component labeling as shown in Non-Patent Document 1. In connected component labeling, a binary image such as an edge image extracted from a line drawing or a general image is input, and continuous regions separated by boundaries such as lines and edges are extracted.

  The binary image input to the connected component labeling has the following format.

ここで、１≦ｙ≦ｍ、１≦ｘ≦ｎであり、ｍは高さ、ｎは幅を表す。

Here, 1 ≦ y ≦ m, 1 ≦ x ≦ n, m represents height, and n represents width.

  An example of the connected component labeling algorithm is shown in Table 1 below. The connected component labeling is performed, for example, in steps 1 to 36 of “Algorithm 1 connected component labeling” shown in Table 1 below.

  For example, it is assumed that the image data (image 1) shown in FIG. 3 is input to the connected component labeling algorithm shown in Table 1. In FIG. 3, white pixels represent areas, and black pixels represent boundaries. A border forming a rectangle separates the region into an inner side and an outer side.

  In this case, the result of the connected component labeling is a result (result 1) as shown in FIG. A label of 0 is given to the boundary portion, 1 to the outer region, and 2 to the inner region.

  On the other hand, various methods are known as image processing methods. For example, as a technique for thinning an image, a Zhang-Suen Thinning method as shown in Non-Patent Document 2 is known. As a clustering method, k-means clustering as shown in Non-Patent Document 3 is known.

Edited by Hideyuki Tamura, “Computer Image Processing”, 1st Edition, Ohm Co., Ltd., December 2002, p.149-151 T.Y.Zhang and C.Y.Suen, “A Fast Parallel Algorithm for Thinning Digital Patterns”, Communication of the ACM, March 1984, Volume 27, Number 3, pp.236-239 C. M.M. Bishop, “Pattern Recognition and Machine Learning,” First Edition, Springer Japan, Inc., August 2008, p.140-143

  In the above-described connected component labeling, pixels connected in the vicinity of 4 are used as one region. Therefore, there is a problem that the regions cannot be separated unless the boundary is completely connected.

  For example, if the boundary is broken as in the image data (image 2) shown in FIG. 5, the outer and inner areas are connected, and appropriate area division cannot be performed. The result (result 2) of the connected component labeling in this case is shown in FIG.

  Therefore, an object of the present invention made in view of such a point is that a boundary line that is not completely connected, such as a line drawing by a dotted line, a line drawing having a gap that is not closed, an edge extraction result of a noisy image or a blurred image, and the like. An object of the present invention is to provide an image area dividing apparatus, an image area dividing method, and an image area dividing program capable of appropriately dividing an area of an image.

  In order to solve the above problems, an image region dividing device according to the present invention is an image region dividing device that divides input data by a specified number of regions, and a transition matrix that calculates a transition matrix from an adjacency relationship of the input data A calculation means, a random walk feature quantity calculation means for calculating a random walk feature quantity from the transition matrix, a similarity calculation means for calculating a similarity degree between candidates from the random walk feature quantity, an adjacency relationship between the input data and Deviation information calculation means for calculating divergence information between candidates from the random walk feature quantity, candidate feature quantity calculation means for calculating feature values of candidates from similarity between the candidates and divergence information between candidates, and the candidates Candidate clustering means for clustering feature quantities of the random walk feature quantity, the random walk feature quantity, and the candidate clustering means. In which and a region number calculating means for calculating a region number from the clustering results.

  In order to solve the above-mentioned problem, an image region dividing method according to the present invention is an image region dividing method for dividing input data by a specified number of regions, and the adjacency relationship of the input data is determined by a transition matrix calculating means. A transition matrix calculating step for calculating a transition matrix from the random matrix, a random walk feature amount calculating step for calculating a random walk feature amount from the transition matrix by a random walk feature amount calculating unit, and a randomness calculating unit for calculating the random walk feature amount. A similarity calculation step for calculating a similarity between candidates from a candidate, a divergence information calculation step for calculating divergence information between candidates from the adjacent relation of the input data and the random walk feature amount by a divergence information calculation means, and a candidate feature From the similarity between the candidates and the divergence information between the candidates, a quantity calculation means A candidate feature amount calculating step for calculating a collection amount; a candidate clustering step for clustering the candidate feature amount by candidate clustering means; and a clustering by the random walk feature amount and the candidate clustering step by region number calculating means. And an area number calculating step for calculating an area number from the result.

  In order to solve the above problem, an image region dividing program according to the present invention is an image region dividing program that divides input data by a specified number of regions. A transition matrix calculation step for calculating a random walk feature amount for calculating a random walk feature amount from the transition matrix, a similarity calculation step for calculating a similarity between candidates from the random walk feature amount, and the input A divergence information calculation step for calculating divergence information between candidates from data adjacency and the random walk feature amount, and a candidate feature amount calculation for calculating a candidate feature amount from similarity between the candidates and divergence information between candidates A candidate clustering step for clustering the candidate feature quantities, and the run Muwoku feature amount, and is intended to execute the region number calculating step of calculating an area number from the clustering result by the candidate clustering step.

  According to the present invention, an area of image input data can be appropriately divided. Appropriately divide the region even for images with borders that are not completely connected, such as line drawings with dotted lines, line drawings with gaps that are not closed, edge extraction results of images containing noise and blurry images, etc. Can do.

1 is a diagram illustrating a schematic configuration of an image region dividing device according to an embodiment of the present invention. It is a flowchart which shows operation | movement of the image area division | segmentation apparatus which concerns on one Embodiment of this invention. It is a figure which shows the image data (image 1) in which the boundary is connected completely. It is a figure which shows the result (result 1) which performed the connected component labeling to the image 1. FIG. It is a figure which shows the image data (image 2) where the boundary is interrupted. It is a figure which shows the result (result 2) which performed the connected component labeling to the image 2. FIG. It is a figure which shows the result of having thinned the image. It is a figure which shows a mode that the candidate point was acquired from the data shown in FIG. It is a figure which shows the result clustered with respect to the feature-value. It is a figure which shows the result of having calculated the area number of the image. It is a figure which shows the result of having divided | segmented the area | region of the image. FIG. 3 is a diagram illustrating an example of a shortest path between a node 1 and a node 2. It is a figure which shows an example of the shortest path | route between the node 1 and the node 2 when there exists a boundary. It is a figure explaining a random walk feature-value. It is a figure explaining the random walk feature-value when there exists a boundary.

  Hereinafter, embodiments according to the present invention will be described with reference to the drawings.

FIG. 1 is a diagram showing a schematic configuration of an image area dividing device 100 according to an embodiment of the present invention. Image area dividing device 100, a binary image _I mage (y, x), the image size (m, n), the number of clusters _{N r,} the number of candidates _{N c,} the candidate likelihood threshold eta, feature dimensions number dim, recursion The probability c, the weight coefficient τ of the distance between candidates, and the weight coefficient δ of the divergence information are input, and the region number divided into Nr regions is output. The image region dividing device 100 includes an input unit 110, a storage unit 120, a calculation unit 130, and an output unit 140.

Input unit 110, and the like network or file, binary image _{I mage,} image size (m, n), the number of clusters _{N r,} the number of candidates _{N c,} the candidate likelihood threshold eta, feature dimensions number dim, recursion probability c, a weighting factor τ for distance between candidates and a weighting factor δ for divergence information are input and stored in the storage unit 120.

  The storage unit 120 stores data input to the input unit 110 and data calculated by the calculation unit 130. Data stored in the storage unit 120 is referred to by the calculation unit 130.

  The calculation unit 130 includes a transition matrix calculation unit 131 as a transition matrix calculation unit, a random walk feature amount calculation unit 132 as a random walk feature amount calculation unit, a similarity calculation unit 133 as a similarity calculation unit, and a divergence information calculation unit. Divergence information calculation section 134, candidate feature quantity calculation section 135 as candidate feature quantity calculation means, candidate clustering section 136 as candidate clustering means, and area number calculation section 137 as area number calculation means. The calculation unit 130 reads and processes data from the storage unit 120 and outputs the data to the output unit 140.

The transition matrix calculation unit 131 _{thins the} binary image I image input to the input unit 110. There are various methods for thinning. For example, Non-Patent Document 2 introduces the Zhang-Suen Thinning method. The Zhang-Suen Thinning method is executed by an algorithm such as steps 1 to 30 of “Algorithm 2 Zhang-Suen Thinning” shown in Table 2 below, for example.

Next, the transition matrix calculation unit 131 creates an adjacency matrix A: N _p × N _p , N _p = m · n as follows.

ここで、ｉ、ｊはノード番号である。また、ノード番号と座標（ｙ、ｘ）との関係は下記のようになる。

Here, i and j are node numbers. The relationship between the node number and the coordinates (y, x) is as follows.

ここで、記号「÷」は整数除算を表し、記号「ｍｏｄ」は剰余を表す。

Here, the symbol “÷” represents integer division, and the symbol “mod” represents a remainder.

  Moreover, B in Formula (2) is a boundary set, and the boundary set B is represented as follows.

The transition matrix calculation unit 131 calculates the transition matrix P: N _p × N _p from the adjacency matrix A as follows.

ここで、

here,

であり、また、

And also

である。

It is.

First, the random walk feature quantity calculation unit 132 acquires N _c grid points from the image, and creates a candidate point set σ as follows.

Next, the random walk feature quantity calculation unit 132 calculates a random walk feature quantity by a random walk with restart starting from each candidate point. A random walk with restart starting from σ _j is expressed by the following equation.

ここで、

here,

であり、また、

And also

である。ここで、式（１０）におけるｃは、再帰確率（０＜ｃ＜１）である。

It is. Here, c in equation (10) is a recursive probability (0 <c <1).

Z _j in equation (10) can be obtained by solving the following simultaneous equations.

ここで、Ｉ_ＮｐはＮ_ｐ次元の単位行列である。

_{Here, I Np} is a unit matrix of _{N p} dimensions.

  Further, the random walk feature value Z is obtained as follows.

  As described above, the random walk feature amount calculation unit 132 according to the present embodiment can appropriately evaluate the distance between the region pixels by calculating the degree to which the traffic between the region pixels is hindered by the boundary.

  For example, in the shortest distance (city distance) in the vicinity of 4, the shortest path between node 1 and node 2 is as shown in FIG. Hereinafter, in FIGS. 12 to 15, the nodes 1 and 2 are represented by encircled numbers. Even if there is a boundary between the node 1 and the node 2, if the detour can be made as shown in FIG. 13, the distance does not change, so the influence of the boundary cannot be evaluated.

  On the other hand, the random walk feature quantity calculation unit 132 according to the present embodiment considers all routes connecting the node 1 and the node 2 as shown in FIG. For this reason, if there is a boundary as shown in FIG. 15, some paths are hindered, so the random walk feature quantity calculation unit 132 can evaluate the influence of the boundary.

  The similarity calculation unit 133 calculates a candidate similarity matrix K from the random walk feature amount Z as follows.

ここで、

here,

である。また、式（１４）のｅｘｐは指数関数、式（１５）のｌｎは自然対数を表す。また、

It is. Further, exp in equation (14) represents an exponential function, and ln in equation (15) represents a natural logarithm. Also,

である。

It is.

The divergence information calculation unit 134 calculates divergence information g _ij between candidates from the boundary set B and the random walk feature amount Z. The deviation information calculation unit 134 first calculates a candidate likelihood matrix from the random walk feature amount Z as follows.

Next, the divergence information calculation unit 134 calculates the divergence information g _ij according to the algorithm procedure shown in Tables 3 to 6 below.

  As described above, the divergence information calculation unit 134 according to the present embodiment can appropriately evaluate the degree to which two candidates should be separated by calculating the correlation between candidates at the boundary.

  The candidate feature amount calculation unit 135 maps the random walk feature amount of the candidate point to a high-dimensional space by nonlinear transformation ψ (•), and projects it to the partial space where the variance is maximum. At this time, the candidate feature quantity calculation unit 135 simultaneously minimizes the correlation of the candidates across the boundary.

  The projection onto the subspace is given by

ここで、ｗはψ（・）と同次元のベクトルであり、ｂはスカラー定数である。また、分散の値は下記の式で求められる。

Here, w is a vector of the same dimension as ψ (•), and b is a scalar constant. Further, the value of dispersion is obtained by the following equation.

ここで、

here,

である。

It is.

  In addition, the correlation of candidates across the boundary can be obtained by the following formula.

  From the above, the objective function is as follows.

ここで、

here,

である。

It is.

  Further, in equation (22), δ is a weighting factor of divergence information, and in equation (21), γ is a regularization parameter.

  Here, the similarity and non-linear conversion have the following relationship.

  Therefore, equation (21) is

の固有値問題を解くことで得られる。ここで、

Can be obtained by solving the eigenvalue problem of. here,

である。また、

It is. Also,

である。固有値λ_ｌの順番は実部の降順とする。すなわち、

It is. The order of the eigenvalue λ _l is the descending order of the real part. That is,

とする。また、λ_ｌに対応する固有ベクトルをｘ_ｌとすると、候補集合の特徴量Ｆは、

And If the eigenvector corresponding to λ _l is x _l , the feature amount F of the candidate set is

となる。ここで、

It becomes. here,

である。

It is.

  As described above, the candidate feature amount calculation unit 135 according to the present embodiment makes it possible to easily perform candidate clustering by appropriately integrating a plurality of pieces of information such as similarity between candidates and deviation information.

Candidate clustering unit 136 designates the feature F and the number of regions N _r candidate, clustering candidate hierarchical clustering (nearest neighbor method). The algorithm is shown in Table 7 and Table 8 below.

The region number calculation unit 137 first calculates a contribution coefficient matrix C (N _c × N _r ). The contribution coefficient matrix can be obtained by solving the following simultaneous equations.

ここで、Ｚ′は下記に示すような縮小滞在確率行列である。

Here, Z ′ is a reduced stay probability matrix as shown below.

  Q is a candidate correspondence matrix as shown below.

  Also, the area number of node number i, region (i) is

となる。ここで、

It becomes. here,

である。

It is.

  The output unit 140 restores the boundary deleted by thinning to the area number region, creates an area division result, and outputs the result to a network or a file.

  Next, the operation of the image region dividing device 100 according to an embodiment of the present invention will be described with reference to the flowchart shown in FIG.

  The input unit 110 inputs data and parameters from a network or a file (step S101).

  The transition matrix calculation unit 131 calculates a transition matrix from the adjacency relationship of data (step S102).

  The random walk feature quantity calculation unit 132 calculates a random walk feature quantity from the transition matrix (step S103).

  The similarity calculation unit 133 compares the distribution of random walk feature amounts starting from each candidate point, and calculates the similarity between candidates (step S104).

The divergence information calculation unit 134 calculates divergence information between candidates from the adjacent relationship of data and the random walk feature amount (step S105). At this time, when two regions (for example, the region a and the region b) are separated by the boundary, on the other hand, the likelihood of the region a (random walk feature amount) is large and the likelihood of the region b is small. On the other side of the boundary, the likelihood of the region a is small and the likelihood of the region b is large. Using this property, the divergence information is obtained for the two candidates a and b as follows, and the information is integrated for all the boundaries.
The likelihood of the two candidates a and b across the boundary is large.
-On the same side of the boundary, the likelihood of a is large and the likelihood of b is small.
・ The same candidate across the boundary has a low likelihood.

  Candidate feature amount calculation unit 135 calculates the feature amount of a candidate such that a candidate with a high similarity is closer and a candidate with a large difference information is placed farther from the similarity and divergence information between candidates. (Step S106).

  The candidate clustering unit 136 clusters candidate feature amounts (step S107).

  The region number calculation unit 137 calculates a region number from the random walk feature amount and the candidate clustering result (step S108).

  The output unit 140 outputs the area number to a network or a file (step S109).

  Subsequently, the operation of the image region dividing device 100 according to the present embodiment will be described with a specific operation example.

In this operation example, the image data (image 2: m = 11, n = 11) shown in FIG. 5 and _Nr = 2, _Nc = 9, η = 0.05, dim = Assume that 2, c = 0.05, τ = 2, and δ = 1 are input.

  The transition matrix calculation unit 131 first thins the image data (image 2) shown in FIG. FIG. 7 shows the thinning result of the image 2. As shown in FIG. 7, the boundary set B is

となる。

It becomes.

  Subsequently, the transition matrix calculation unit 131 creates an adjacency matrix A by Expression (2) and calculates the transition matrix P by Expression (6).

Next, the transition matrix calculation unit 131 acquires N _c candidate points as illustrated in FIG. 8 from the lattice points. The acquired candidate points are as follows.

The random walk feature quantity calculation unit 132 calculates z _j , j = 1,..., N _c from Expression (12) using a Gaussian elimination method or the like.

  The similarity calculation unit 133 calculates the similarity between candidates from Expression (14), and obtains a similarity matrix as shown in Table 9 below.

The deviation information calculation unit 134 calculates the deviation information g _ij according to the procedure of “Algorithm 3: deviation information calculation” shown in Table 3. The calculated divergence information g _ij is shown in Table 10 below.

  Candidate feature amount calculator 135 calculates a candidate feature amount from Expression (28). The calculated candidate feature amounts are shown in Table 11 below.

The candidate clustering unit 136 clusters the feature amounts shown in Table 11 calculated by the candidate feature amount calculation unit 135 by “Algorithm 7: Hierarchical clustering (shortest distance method)” shown in Table 7. The result of clustering by the candidate clustering unit 136 is shown in FIG. Since the number of clusters N _r = 2 is designated, the clustering results are candidate 5 and other candidates. The cluster index is as follows.

  The area number calculation unit 137 calculates the area number from Expression (32). The calculated region numbers are shown in FIG.

  The output unit 140 outputs a region division result as shown in FIG.

(Modification)
Hereinafter, modifications of the present embodiment will be described.

The transition matrix calculation unit 131 may randomly select N _c nodes as a candidate point set creation method.

  The similarity calculation unit 133 may calculate a candidate similarity matrix as follows.

  Alternatively, the similarity calculation unit 133 may calculate a candidate similarity matrix as follows.

  The candidate clustering unit 136 may cluster candidate feature amounts by k-means clustering. The k-means clustering is introduced in Non-Patent Document 3, for example.

  As described above, according to the present embodiment, for an image having a boundary that is not completely connected, such as a line drawing by a dotted line, a line drawing having a gap that is not closed, or an edge extraction result of a noisy image or a blurred image. However, the area can be appropriately divided.

  The present embodiment can also be applied to data that can define an adjacency matrix, and can also cluster data other than images.

  Furthermore, this embodiment can integrate a plurality of pieces of information such as candidate similarity and deviation information, and can perform clustering that integrates a plurality of pieces of data.

  Although the present invention has been described based on the drawings and examples, it should be noted that those skilled in the art can easily make various modifications and corrections based on the present disclosure. Therefore, it should be noted that these variations and modifications are included in the scope of the present invention. For example, the functions included in each component, each step, etc. can be rearranged so that there is no logical contradiction, and multiple components, steps, etc. can be combined or divided into one It is. Further, although the present invention has been described mainly with respect to the apparatus, the present invention can also be realized as a method, a program, or a storage medium recording the program, which is executed by a processor included in the apparatus, and falls within the scope of the present invention. It should be understood that these are also included.

DESCRIPTION OF SYMBOLS 100 Image area | region dividing device 110 Input part 120 Storage part 130 Calculation part 131 Transition matrix calculation part 132 Random walk feature-value calculation part 133 Similarity degree calculation part 134 Deviation information calculation part 135 Candidate feature-value calculation part 136 Candidate clustering part 137 Area number calculation Part 140 Output part

Claims (3)

An image region dividing device that divides input data by a specified number of regions,
A transition matrix calculating means for calculating a transition matrix from the adjacency relation of the input data;
Random walk feature quantity calculating means for calculating a random walk feature quantity from the transition matrix;
Similarity calculation means for calculating the similarity between candidates from the random walk feature amount;
Deviation information calculation means for calculating deviation information between candidates from the adjacency relationship of the input data and the random walk feature amount;
Candidate feature amount calculating means for calculating a feature amount of a candidate from similarity between the candidates and divergence information between the candidates;
Candidate clustering means for clustering the candidate feature quantities;
An image area dividing device comprising: the random walk feature quantity; and an area number calculating means for calculating an area number from a clustering result by the candidate clustering means. An image region dividing method for dividing input data by a specified number of regions,
A transition matrix calculating step of calculating a transition matrix from the adjacency relation of the input data by a transition matrix calculating means;
A random walk feature amount calculating step of calculating a random walk feature amount from the transition matrix by a random walk feature amount calculating means;
A similarity calculation step of calculating a similarity between candidates from the random walk feature quantity by a similarity calculation means;
A divergence information calculation step of calculating divergence information between candidates from the adjacent relation of the input data and the random walk feature amount by a divergence information calculation means;
A candidate feature amount calculating step of calculating a candidate feature amount from the similarity between the candidates and the deviation information between the candidates by a candidate feature amount calculating means;
A candidate clustering step of clustering the candidate features by candidate clustering means;
An image region dividing method comprising: an area number calculating step of calculating an area number from the random walk feature quantity and a clustering result obtained by the candidate clustering step by an area number calculating means. An image area dividing program that divides input data by a specified number of areas.
A transition matrix calculation step of calculating a transition matrix from the adjacency relationship of the input data;
A random walk feature amount calculating step for calculating a random walk feature amount from the transition matrix;
A similarity calculation step of calculating a similarity between candidates from the random walk feature,
A divergence information calculation step of calculating divergence information between candidates from the adjacent relationship of the input data and the random walk feature amount;
A candidate feature amount calculating step of calculating a candidate feature amount from similarity between the candidates and divergence information between the candidates; and
A candidate clustering step of clustering the candidate feature quantities;
An image region division program for executing the random walk feature amount and a region number calculation step of calculating a region number from the clustering result of the candidate clustering step.

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