JP6661196B2 - Image processing apparatus, method, and program - Google Patents

Description

  The present invention relates to an image processing device, a method, and a program, and more particularly, to an image processing device, a method, and a program for extracting an area of a subject.

  The process of recognizing a figure from a digital image using a computer is called segmentation. If the SN of the target figure is low and the shape fluctuates statistically, accurate segmentation becomes extremely difficult.

  Graph cuts (eg, Boykov, Y., Veksler, O., Zabih, R., “Fast approximate energy minimization via graph cuts.”, Pattern Analysis and Machine Intelligence, IEEE Transactions on 23 (11), 2001, p. 1222 Segmentation algorithms based on optimization theory such as -1239.) Are superior to conventional algorithms in that they can truly optimize the objective function, and often exhibit very high performance even at low SN. Was. However, even when the shape fluctuates, it is often impossible to accurately recognize the shape.

  Therefore, recently, methods using shape information of a figure in an algorithm based on an optimization theory have become mainstream, but they are roughly divided into the following three types.

The first method is to use a single shape template. For example, as a general shape template, an elliptical template (for example, Slabaugh, G., Unal, G., Sept, “Graph cuts segmentation using an elliptical shape prior.”, In: IEEE International Conference on Image Processing, 2005, Vol. 2. p.II-1222-5.), Or a template of a massive figure (for example, Funka-Lea, G., Boykov, Y., Florin, C., Jolly, M.- P., Moreau-Gobard, R., Ramaraj, R., Rinck, D., 2006. “Automatic heart isolation for CT coronary visualization using graph-cuts.”, In: Biomedical Imaging: Nano to Macro, 3rd IEEE International Symposium on. IEEE, 2006, pp. 614-617.).
In addition, as a specific shape template, a user-defined arbitrary shape (for example, Freedman, D., Zhang, T., “Interactive graph cut based segmentation with shape priors.”, In: IEEE Computer Society Conference on Computer Vision and Pattern Recognition) Vol. 1. IEEE, 2005, pp. 755-762.) And shapes selected from statistical models (eg, Grosgeorge, D., Petitjean, C., Dacher, J.-N. , Ruan, S., “Graph cut segmentation with a statistical shape model in cardiac mri.”, Computer Vision and Image Understanding 117 (9), 2013, pp. 1027-1035., Akinobu Shimizu, Keita Nakagomi, Takuya Narihira, Hidefumi Kobatake, Shigeru Nawano, Kenji Shinozaki, Koich Ishizu, and Kaori Togashi, “Automated Segmentation of 3D CT Images based on Statistical Atlas and Graph Cuts”, Proc. Of MICCAI workshop MCV, 2010, p.129-138., Malcolm, J ., Rathi, Y., Tannenbaum, A., “Graph cut segmentation with nonlinear shape priors.”, In: Image Processing, 2007. A method using ICIP 2007. IEEE International Conference on Vol. 4. IEEE, 2007, p.IV-365.) Is known.

  A second method is to use a plurality of (several) shape templates or stochastic expressions of shapes. For example, a plurality of shapes selected from a statistical model (for example, Nakagomi, K., Shimizu, A., Kobatake, H., Yakami, M., Fujimoto, K., Togashi, K., “Multi-shape graph cuts with neighbor prior constraints and its application to lung segmentation from a chest CT volume. ”, Medical image analysis 17 (1), 2013, p.62-77.), and stochastic expression of shapes (for example, Linguraru , MG, Pura, JA, Pamulapati, V., Summers, RM, “Statistical 4d graphs for multi-organ abdominal segmentation from multiphase CT.”, Medical image analysis 16 (4), 2012, p.904-914. ) Is known.

A third method is to use a large number (several tens or more) of shape templates. For example, for specific problems (eg, Kohli, P., Rihan, J., Bray, M., Torr, PH, “Simultaneous segmentation and pose estimation of humans using dynamic graph cuts.”, International Journal of Computer Vision 79 ( 3), 2008, pp. 285-298.) And a method using an arbitrary large number of graphic shapes (for example, see US Pat. No. 8,249,349). .

  The above-described conventional technique can handle a graphic that fluctuates statistically in order from the first technique to the third technique. The most advanced method is the arbitrarily large number of graphic shapes of the third method (U.S. Pat. No. 8,249,349). However, in all methods including this method, it is necessary to prepare a shape set in advance by selecting a shape in advance. Therefore, unless the optimal shape is originally included in the shape set selected in advance, the optimality of the segmentation is not guaranteed, and the performance is reduced.

On the other hand, since a digital image is a set of a finite number of pixels, a method of preparing all possible shape patterns can be considered in principle, and in that case, optimality is guaranteed. However, the number of shapes that must be prepared for that purpose is enormous, and it is not realistic from the viewpoint of the memory required for the entire processing including preprocessing and the calculation time. For example, even in a conventional best it has been the U.S. Patent No. 8249349 Pat algorithms that handle ¹⁰⁷ or so the number of shape template with the two-dimensional image was limited. However, the number of possible shapes pattern statistical model may be generated in many cases there 10 ⁹ or more, it is very difficult in terms of computational cost in the conventional algorithm. Furthermore, three-dimensional images are mainly used for medical images, but in that case, the required memory increases by more than two orders of magnitude, and it is impossible to execute the processing in a practically time and memory size using almost conventional algorithms. Was.

  One embodiment of the present invention has been made in view of the above circumstances.

  In order to achieve the above object, an image processing apparatus according to a first aspect is an image processing apparatus that extracts an area of a subject from an input image representing a subject that is a specific object, and that receives an input image. Means, and (A) a plurality of learning images representing the subject, wherein the subject region is an eigenspace based on eigenvectors calculated in advance based on the plurality of images obtained in advance. And (B) a point on the eigenspace indicates a shape parameter of a statistical shape model representing a statistical variation of the shape of the specific object in the eigenspace based on the input image. A predetermined objective function representing a value corresponding to the likelihood of the shape of the specific object represented by the shape parameter indicated by a point and a pixel value difference between adjacent pixels in the input image is optimized. Estimating the shape parameter representing the shape of the subject represented by the input image, and extracting the area of the subject from the input image using the shape of the specific object represented by the estimated shape parameter as prior knowledge. And a segmentation means for performing the segmentation.

  An image processing method according to a second aspect is an image processing method in an image processing apparatus that includes a receiving unit and a segmentation unit, and extracts an area of the subject from an input image representing the subject as a specific object. Wherein the accepting means accepts the input image; and wherein the segmentation means includes: (A) a plurality of learning images representing the subject, wherein the region of the subject is obtained in advance; (B) a point on the eigenspace indicates a shape parameter of a statistical shape model representing a statistical variation of the shape of the specific object, based on an eigenvector calculated in advance based on the eigenvector. In the eigenspace, based on the input image, the likelihood of the shape of the specific object represented by the shape parameter indicated by a point on the eigenspace and the Estimating the shape parameter representing the shape of the subject represented by the input image, so as to optimize a predetermined objective function representing a value corresponding to a pixel value difference between adjacent pixels in the force image, Extracting the region of the subject from the input image, using the shape of the specific object represented by the estimated shape parameter as prior knowledge.

  In the third aspect, the segmentation unit estimates the shape parameter representing the shape of the subject represented by the input image in the eigenspace based on the input image so as to optimize the objective function. At the same time, the region of the subject can be extracted from the input image using the shape of the specific object represented by the estimated shape parameter as prior knowledge.

  Further, the segmentation means of the fourth aspect is configured to repeatedly divide the convex multivesicular body on the eigenspace representing a shape set including a shape of the specific object represented by a point indicating an optimal shape parameter to obtain an optimal shape parameter. Estimating the shape parameters representing the shape of the subject represented by the input image so as to optimize the objective function, according to a search algorithm for searching for convex polyvesicles on the eigenspace including points indicating The region of the subject may be extracted from the input image using the shape of the specific object represented by the obtained shape parameter as prior knowledge.

  Further, the segmentation means of the fifth aspect, in the search algorithm, by examining each vertex of the convex polycyst, by calculating the lower bound of the objective function for the shape set included in the convex polycyst, A search is made for convex polyvesicles on the eigenspace including points indicating the optimal shape parameters to estimate the shape parameters representing the shape of the subject represented by the input image, and the identification represented by the estimated shape parameters. The region of the subject may be extracted from the input image using the shape of the object as prior knowledge.

  In the sixth aspect, the segmentation means divides the convex polyvesicles in the eigenspace so that the volumes of the two convex polyvesicles after division correspond to each other, and sets a point indicating an optimal shape parameter. Iterating the search for the convex multivesicular body on the eigenspace including, estimating the shape parameter representing the shape of the subject represented by the input image, the shape of the specific object represented by the estimated shape parameter May be extracted as the prior knowledge from the input image.

  In the seventh aspect, the segmentation means sets a sampling point on the eigenspace, and divides the convex polymorph using a hyperplane determined from the sampling points set on the eigenspace. Iteratively searching for convex polyvesicles on the eigenspace including points indicating the optimal shape parameters, estimates the shape parameters representing the shape of the subject represented by the input image, and estimates the shape parameters The area of the subject may be extracted from the input image using the shape of the specific object represented by as the prior knowledge.

  Further, the segmentation means of the eighth aspect may arbitrarily set a sampling point on the eigenspace.

  Further, the objective function of the ninth aspect includes a monotonic function that monotonically changes as a likelihood of the shape of the specific object with respect to a value of a shape label in a pixel corresponding to the shape of the specific object represented by the shape parameter. You can do so.

  Further, the search algorithm according to the tenth aspect can use a Branch and bound method and a graph cut method.

  Further, a program according to an eleventh aspect is a program for causing a computer to function as each unit of the image processing apparatus.

  According to the image processing apparatus, method, and program according to the embodiment, (A) the eigenspace based on the eigenvector calculated in advance based on a plurality of images obtained in advance, B) In the eigenspace in which the point on the eigenspace indicates the shape parameter of the statistical shape model representing the shape of the specific object, the likelihood and input of the shape of the specific object represented by the shape parameter indicated by the point on the eigenspace A shape parameter representing a shape of a subject represented by the input image is estimated so as to optimize a predetermined objective function representing a value corresponding to a pixel value difference between adjacent pixels in the image. The region of the subject is extracted from the input image using the shape of the specific object represented by the estimated shape parameter as prior knowledge. As a result, it is possible to obtain an effect of suppressing an increase in the amount of calculation and extracting a region of a subject with high accuracy.

1 is a block diagram illustrating a configuration of a statistical shape model generation device according to an embodiment. FIG. 2 is a block diagram illustrating a computer configuration example of a statistical shape model generation device and an image processing device according to the embodiment. It is explanatory drawing which shows the three-dimensional image example of a liver. FIG. 9 is a diagram illustrating statistical variations in the shape of the liver along the first principal component when principal component analysis is performed on an image of the shape of the liver. FIG. 4 is an explanatory diagram illustrating an example of a statistical shape model. FIG. 4 is an explanatory diagram illustrating a relationship between an eigenspace and a shape space. FIG. 1 is a block diagram illustrating a configuration of an image processing device according to an embodiment. FIG. 4 is an explanatory diagram for describing a method of dividing an eigenspace. 9 is a flowchart illustrating a learning processing routine according to the embodiment. 5 is a flowchart illustrating an image processing routine according to the embodiment. 9 is a flowchart illustrating a segmentation processing routine according to the embodiment. FIG. 9 is a diagram for explaining an approximate solution method when setting sampling points in a grid. It is a figure showing the recognition result of 140 cases of pancreas in a 2nd embodiment. FIG. 14 is a diagram illustrating a comparison result of calculation time according to the second embodiment. FIG. 9 is a diagram for explaining an approximate solution method in a case where sampling points are set at random. It is a figure which shows the relationship where the lower bound of an objective function satisfies monotonicity. Is a diagram illustrating an example of a lower bound of the objective function satisfies the monotonicity ^h _F p and (y) and ^h _B p (y). FIG. 14 is a diagram illustrating an example of a case where LogOdds is used as a statistical shape model. It is explanatory drawing which shows a prior art.

  Hereinafter, embodiments will be described in detail with reference to the drawings. In the embodiment, the statistical shape model generation device 10 that generates a statistical model (hereinafter, referred to as a statistical shape model) of the shape of a figure representing the statistical variation of a specific object, and the specific object. An image processing apparatus 100 that extracts a subject area from an input image representing the subject will be described. In the embodiment, a case will be described as an example where a three-dimensional abdominal CT image is used as an input image and a pancreas region is extracted from the input image.

<Overview>
In the present embodiment, a segmentation algorithm using a statistical shape model is proposed. This algorithm has the following five features.

1. In the course of the segmentation are possible considering all three-dimensional shape can be generated using a statistical shape model (10 ⁹ or more), it is possible to select the optimal shape in terms of the objective function segmentation.

2. The conventional method using a large number of shape templates is indispensable, and preprocessing (generation and selection of shapes and clustering), which is particularly expensive, is unnecessary.

3. The algorithm is not limited to the combination of the branch and bound method and the graph cut method, but can be applied to any algorithm based on optimization theory.

4. It can be applied to different statistical shape models and eigenspace division methods.

5. World's highest accuracy for pancreas segmentation in 3D abdominal CT images.

FIG. 19 shows an outline of the processing of the related art. FIG. 19 shows processing in a case where the technique of the above-mentioned US Pat. No. 8,249,349 is applied to pancreas segmentation using a statistical shape model. As shown in FIG. 19, the conventional method requires a process of generating a shape template set T (⊂S) and a clustering process for the set T. In the present embodiment, as described above, a large number of shape templates are used. This eliminates the need for the pre-processing required by the conventional method using. Incidentally, the conventional method image which has been treated with (aforementioned U.S. Pat. No. 8,249,349) a two-dimensional, while the maximum number of shapes is ^107, the algorithm used in this embodiment is a three-dimensional shape (10 ⁹ or more) can be considered.

  In the embodiment, a level set distribution model (LSDM; sometimes referred to as a signed distance model) is used as a statistical shape model. In the following, first, the eigenvectors and eigenvalues of the statistical shape model (LSDM) are calculated in the statistical shape model generation device 10, and then the shape parameters of the statistical shape model are estimated in the image processing device 100, and the estimation is performed. 4 shows an optimal segmentation algorithm based on a statistical shape model using shape parameters.

[First Embodiment]
<Configuration of Statistical Shape Model Generator 10 According to First Embodiment>
The statistical shape model generation device 10 according to the first embodiment can be represented by the functional blocks shown in FIG. These functional blocks can be realized by the hardware configuration of the computer shown in FIG. The configuration of the computer will be described with reference to FIG.

  A statistical shape model generation device 10 according to the first embodiment shown in FIG. 2 is a CPU (Central Processing Unit; Central Processing Unit) that performs processing according to the present embodiment of the statistical shape model generation device 10 based on a program. ) 21, a RAM (Random Access Memory) 22 used as a work area or the like when the CPU 21 executes various programs, and a ROM (Read Only Memory) 23 which is a recording medium in which various control programs, various parameters, and the like are stored in advance. And a hard disk 24 (described as “HDD” in the figure) used for storing various information, an input device 25 including a keyboard and a mouse, a display device 26 including a display, and a LAN (Local Area Network). And the like, and exchanges various kinds of information between the communication device 27 that performs communication using the communication device 27 and the image information providing device 30 that is connected to the outside. (In the figure, "external IF" and described) output interface unit 28 includes a, it is configured are connected to each other by a system bus BUS29.

  The CPU 21 accesses the RAM 22, the ROM 23, and the hard disk 24, acquires various information via the input device 25, displays various information on the display device 26, performs communication processing of various information using the communication device 27, and an input / output interface unit. Input of information from an external device including the image information providing device 30 connected to the MFP 28 can be performed.

  The CPU 21 reads the program for controlling the processing according to the present embodiment stored in the hard disk 24 into the RAM 22 and executes the program, thereby causing the statistical shape model generating apparatus 10 according to the present embodiment shown in FIG. Are executed.

  With such a computer configuration, the statistical shape model generation device 10 according to the present embodiment shown in FIG. 1 is configured. FIG. 1 shows a configuration serving as a functional block, while FIG. 2 shows a connection state of devices and the like. As described above, since the functional blocks and the devices and the like constitute the statistical shape model generating apparatus 10 in an organic and mutually related manner, FIG. 1 will be described in detail together with FIG. 2.

  The statistical shape model generation device 10 includes a learning reception unit 12, a learning unit 14, a statistical shape model, and a function configured using software including a computer hardware and a control program illustrated in FIG. A database 16 is provided.

  The learning accepting unit 12 accepts, as learning data, a plurality of images representing a subject which is a specific object, in which a subject area is obtained in advance. Since the specific object to be the subject in the present embodiment is the pancreas, the learning reception unit 12 receives a plurality of images in which the region of the pancreas is obtained in advance.

  The learning unit 14 calculates an eigenvector and an eigenvalue based on a plurality of images in which the pancreas region received by the learning reception unit 12 is obtained in advance. For example, the learning unit 14 calculates an eigenvector and an eigenvalue by principal component analysis based on a plurality of images in which the region of the pancreas is obtained in advance. By calculating the eigenvector, an eigenspace based on the eigenvector is generated. The learning unit 14 stores the calculated eigenvectors and eigenvalues in the statistical shape model database 16.

  Here, an example of the shape of the liver is shown in FIG. 3 (note that the example shown in FIG. 3 is a liver, but the nature of the problem is the same as that of the pancreas). As shown in FIG. 3, the shape of the liver varies. Therefore, in the embodiment, a variation in shape is represented by a small number of shape parameters using a statistical shape model representing the shape of a specific object. FIG. 4 shows an eigenvector of the shape of the liver corresponding to the first principal component obtained by the principal component analysis. As shown in FIG. 4, it can be seen that the shape of the represented liver changes according to the value of the shape parameter α corresponding to the eigenvector. Here, σ is a parameter representing statistical variation.

  FIG. 5 shows an example of a statistical shape model. As shown in FIG. 5, there are various statistical shape models, but in the present embodiment, LSDM (for example, a reference (Cremers, D., Rousson, M., See Deriche, R., “A review of statistical approaches to level set segmentation: integrating color, texture, motion and shape.”, International journal of computer vision 72 (2), 2007, p.195-215.) Is used.

  The LSDM is a representative statistical shape model, creates a signed distance image for a graphic label of learning data, and performs linear statistical analysis (for example, PCA or ICA) on the signed distance image. This is a method of expressing an arbitrary shape by the following equation (1).

Here, the above equation (1) is an equation relating to the pixel p (∈P). Note that P represents a pixel set, φ ^p (α) represents a level set function corresponding to an arbitrary shape relating to the pixel p, μ ^p represents an average level set function relating to the pixel p, and λ _i represents the i-th represents the _{^{eigenvalues, {u 1 p, ...,}} u d p} represents the component for the pixel p at the d _{eigenvectors, α = [α 1, ...} , α d] T , the eigenspace on of ^{_{R α = {r∈R d ||| r}} || ∞ ≦ w} of area (usually in the range of ± 3 [sigma]) representing the shape parameters defined in. W indicates a positive constant. The shape in the digital image is obtained by mapping the parameter α with a function g shown in the following equation (2). In the embodiment, a case where the dimension of the eigenspace is d = 2 will be described as an example.

  Here, L = {0, 1} is a label set, 0 indicates a background, and 1 indicates a figure. y represents one shape in the image. In the case of LSDM, a function g that maps the parameter α to a shape is a Heaviside function H (•) as shown in the following equation (3).

FIG. 6 shows the relationship between the LSDM eigenspace (space with eigenvectors) and the shape set S in the digital image when d = 2. The function g is a mapping from the eigenspace onto the shape set S of the digital image. The shape set S 集合 L ^{| P |} is an image of g. As shown in FIG. 6, a set of shape labels forms a polygon in the eigenspace. Each shape y∈S has an original image in the eigenspace.

  The statistical shape model database 16 stores the eigenvectors and eigenvalues calculated by the learning unit 14.

<Configuration of Image Processing Apparatus 100>
Image processing apparatus 100 according to the present embodiment can be represented by the functional blocks shown in FIG. Further, these functional blocks can be realized by the hardware configuration of the computer shown in FIG.

  As shown in FIG. 7, the image processing apparatus 100 includes, as functions shown in FIG. 7, a receiving unit 102, an arithmetic unit 104, and an output unit. A part 120.

  The receiving unit 102 receives a three-dimensional three-dimensional abdominal CT image as an input image. The receiving unit 102 receives the early phase image, the portal phase image, and the late phase image as a three-dimensional three-dimensional abdominal CT image.

  The calculation unit 104 extracts a pancreas region from the three-dimensional abdominal CT image received by the reception unit 102. The calculation unit 104 includes a statistical shape model database 106 and an image processing unit 108.

  The statistical shape model database 106 stores the same eigenvectors and eigenvalues as the statistical shape model database 16.

  The image processing unit 108 includes an inter-image registration unit 110, a spatial standardization unit 112, and a segmentation unit 114.

  The inter-image registration unit 110 performs registration between the early phase image, the portal vein phase image, and the late phase image received by the reception unit 102 (for example, Shimizu, A., Kimoto, T., Kobatake, H., Nawano, S., Shinozaki, K., “Automated pancreas segmentation from three-dimensional contrast-enhanced computed tomography.”, International journal of computer assisted radiology and surgery 5 (1), 2010, p.85- 98.), and generate an alignment image.

  The spatial standardization unit 112 performs spatial standardization based on the alignment image generated by the inter-image alignment unit 110, for example, using a predetermined nonlinear function so as to match the alignment image with a standard image. (For example, Shimizu, A., Kimoto, T., Kobatake, H., Nawano, S., Shinozaki, K., “Automated pancreas segmentation from three-dimensional contrast-enhanced computed tomography.”, International journal of computer assisted radiology and surgery 5 (1), 2010, p.85-98.), and generate a spatially standardized image.

  In the eigenspace based on the pre-computed eigenvectors stored in the statistical shape model database 106, the segmentation unit 114 optimizes the objective function based on the input image received by the reception unit 102. The shape parameter indicating the shape of the subject represented by the spatially standardized image generated by the spatial standardization unit 112 is estimated, and the area of the subject represented by the spatially standardized image is obtained. Specifically, the segmentation unit 114 extracts a region of the subject while estimating the shape parameters.

  As shown in FIG. 6, a point on the eigenspace based on the eigenvector indicates a shape parameter of the statistical shape model. Further, the objective function is determined in advance so as to represent a value corresponding to the likelihood of the shape of the specific object represented by the shape parameter indicated by the point on the eigenspace and the difference in pixel value between adjacent pixels in the input image. Have been.

In general, the size (= the number of shapes on a digital image) of the shape set L ^{| P |} is enormous and cannot be handled by the conventional algorithm. The algorithm in the present embodiment is different from the conventional one in that the optimization of the objective function is performed in the eigenspace, whereby an enormous number of shapes can be efficiently handled.

The segmentation unit 114 optimizes the objective function of the following equation (4) according to a search algorithm for repeatedly dividing a convex polygon on the eigenspace and searching for a convex polygon including a point indicating an optimal shape parameter. Next, a shape parameter representing the shape of the subject represented by the input image is estimated. The convex polygon on the eigenspace to be searched represents the shape of a specific object represented by a point indicating the optimal shape parameter.
Further, the segmentation unit 114 searches the vertices of the convex polygon in the search algorithm, calculates the lower bound of the objective function for the set of shapes included in the convex polygon, and finds a point indicating the optimal shape parameter. Search for a convex polygon on the included eigenspace.
Note that, in the present embodiment, the segmentation unit 114 searches for a convex polygon on the eigenspace in order to describe a case where the eigenspace is two-dimensional, as an example. The segmentation unit 114 searches for a convex polyhedron in the eigenspace. In addition, a straight line that divides the eigenspace at the time of search becomes a hyperplane when the eigenspace is three-dimensional or more.

  An important idea in the present embodiment is to use the fact that a shape set on a digital image corresponds to a convex polygon on an eigenspace as shown in FIG. In the embodiment of the present invention, by utilizing this fact, it is possible to efficiently handle many shapes at once.

  Based on the fact that a plurality of shape sets on the digital image correspond to convex polygons on the eigenspace, the segmentation unit 114 corresponds to a convex shape on the eigenspace corresponding to a shape that minimizes a preset objective function. Search for a polygon. Then, the segmentation unit 114 finds a shape that minimizes the objective function from the shape set S based on the searched convex polygon on the eigenspace, and uses the found shape as prior knowledge to define the shape as the area of the subject. Extract as In this embodiment, the graph cut (the above-mentioned Boykov, Y., Veksler, O., Zabih, R., “Fast approximate energy minimization via graph cuts.”, Pattern Analysis and Machine Intelligence, IEEE Transactions on 23 (11), 2001, p. 1222-1239.). An example in which an energy function often used as an objective function set in advance will be described. The objective function used in the present embodiment is shown in the following equation (4).

Here, N is a set of pairs of adjacent pixels. x _p represents the label of the pixel p, a value of 0 if the background, taking a value of 1 if figure. Also, I _p denotes a pixel value of the pixel p, y _p represents the value of the estimated shape of the pixel p, the estimated shape takes a value of 0 if the background, taking a value of 1 if the figure .

_{Further, F p (I p, y} p) in the above formula (4) _{and, B p (I p, y} p) and the following equation (5) is defined by (6). Here, the following equation (5) represents the cost of assigning the pixel p as a figure, and the following equation (6) represents the cost of assigning the pixel p as a background.

_Ip represents the pixel value of pixel p, and _Iq represents the pixel value of pixel q. Λ ₁ and λ ₂ are predetermined positive constants. In addition, P _pq (I _p , I _q ) in the above equation (4) is defined by the following equation (7), and evaluates a difference in pixel value between the adjacent pixels p and q.

  In the present embodiment, a branch and bound search algorithm, which is one of general optimization algorithms, is used as an objective function optimization method represented by the above equation (4). This embodiment proposes a method for efficiently calculating the lower bound of an objective function for a shape set. An important idea for efficiently calculating the lower bound of the objective function for a set of shapes is that examining only the vertices of a convex polygon gives the lower bound of the objective function for all the sets of shapes included in the convex polygon. is there.

  If the above equation (4) is expressed using a function g (α) instead of the shape y, it can be expressed by the following equation (8).

[Branching process]
In the branching process of the branch and bound search algorithm, when a parent node H ₀ (∈R _α ) is given, the parent node H ₀ is decomposed into child nodes H ₁ and H ₂ , and the objective function shown in the above equation (8) Is represented by the following equation (9).

Here, for the dividing process in the branching process, various dividing methods are possible. In the present embodiment, as shown in the following equations (10) and (11), the parent node H ₀ becomes the child nodes H ₁ and H _{2 according to} the sign of φ ^k (α) shown in the above equation (1). Divided into Note that the pixel k represents a pixel selected by sampling from the set Q.

Here, the set Q is a set of pixels k such that a straight line φ ^k (α) = 0 that cuts the node H ₀ in the eigenspace as shown in the following equation (12). When the eigenspace is three-dimensional or more, the set Q is a set of pixels k such that a hyperplane φ ^k (α) = 0 that cuts the node H ₀ in the eigenspace.

V ₀ represents a vertex set of the convex polygon represented by the node H ₀ . V ₀ can be obtained by analytically solving simultaneous equations of φ ^e (α) corresponding to the edge of H ₀ .

[Bounding process]
In the branching process of the branch and bound search algorithm, the lower bound L (H _i ) (i = {1, 2}) is given by the following equations (13) to (14).

Equation (13) above is Jensen's inequality for the minimization problem. The change between “max” and “min” in equation (14) is based on the minus sign in equation (5). Further, the maximum value and the minimum value of phi (alpha) in Arufa∈H _i, based on the basic theory of linear programming, is obtained from the vertex set V _i of H _i, the following equation (15) and (16) Can be represented by

  In addition, the segmentation unit 114 repeatedly divides the convex polygon on the eigenspace so that the areas of the two convex polygons after division correspond to each other (so that the areas are substantially equal), so that the optimal polygon is repeated. Search for a convex polygon on the eigenspace containing points indicating shape parameters.

Table 1 shows the pseudo code of the segmentation algorithm by the segmentation unit 114. First, when the target image I is given, the segmentation unit 114, the entire eigenspace ^{_{R α = {r∈R d ||| r}} || ∞ ≦ w} to start processing as a parent node _{H 0.} That is, the segmentation unit 114 starts processing the R _alpha as root, divides the parent node H ₀ by the pixel k selected by using the function the Select (Q) from the digital image. Child nodes _{H 1} and _{H 2} after the division are placed in Queue. However, it is assumed that the nodes put in Queue are arranged such that the lower bound values are in ascending order. Next, the segmentation unit 114, a Queue, and the parent node H ₀ Select the lowest lower bound of the node is repeated until the processing Q is an empty set. From the result at the end of the repetition, an optimal shape parameter is obtained and an optimal shape is obtained. Then, the segmentation unit 114 obtains an optimal segmentation result using the optimal shape.

Note that H ₀ represents a convex polygon in the eigenspace. The initial value of _{H 0} corresponds to R _alpha. H ₁ and H ₂ represent two convex polygons formed by dividing H ₀ . Q is a set of pixels on the dividable digital image H _0. Queue represents a queue containing convex polygon nodes (used in the Branch and bound search algorithm). Select (Q) represents a function for selecting a pixel k for division.

Further, a new proposal on Select (Q) for efficiently operating the algorithm is also an important feature in the present embodiment. Here, Select (Q) is a function for selecting a pixel for dividing a convex polygon from an image. In order to perform a search efficiently, convex (Q) corresponding to child nodes H ₁ and H ₂ after division is selected. In the present embodiment, a division method in which the areas of polygons are almost equal was proposed, and the efficiency was verified with an actual image.

  In the present embodiment, the function shown in the following equation (17) is used as Select (Q).

  here,

  It is.

FIG. 8 shows a conceptual diagram of the operation of the function of the above equation (17). As shown in FIG. 8, the action of the above formula (17), Intuitively, selects pixels p that divides the H ₀ into two regions having the same area as that of (H _{1, H 2).}

  The segmentation unit 114 uses the shape represented by the optimum shape parameter of the searched specific object as a priori knowledge, and converts the region of the subject having the shape of the specific object into the spatial standardization unit 112 so as to optimize the objective function. From the spatially standardized image generated by.

  The output unit 120 outputs the region of the subject extracted by the segmentation unit 114 as a result.

<Operation of Statistical Shape Model Generation Apparatus 10>
Next, the operation of the statistical shape model generation device 10 will be described.

  The processing of the statistical shape model generation device 10 shown in FIG. 9 is performed by the CPU 21 shown in FIG. 2 based on a program stored in the HDD 24 or the like. When a plurality of images in which pancreatic regions are obtained in advance are input to the statistical shape model generation device 10, a learning processing routine shown in FIG. 9 is executed.

  First, in step S100, the learning accepting unit 12 accepts a plurality of images in which pancreatic regions have been obtained in advance.

  Next, in step S102, the learning unit 14 calculates an eigenvector and an eigenvalue by principal component analysis based on a plurality of images in which the pancreas region received in step S100 is obtained in advance.

  In step S104, the learning unit 14 stores the eigenvectors and eigenvalues calculated in step S102 in the statistical shape model database 16, and ends the learning processing routine.

<Operation of Image Processing Apparatus 100>
Next, the operation of the image processing apparatus 100 will be described.

  The processing of the image processing apparatus 100 shown in FIG. 10 is performed by the CPU 21 shown in FIG. 2 based on a program stored in the HDD 24 or the like. First, when the eigenvectors and eigenvalues stored in the statistical shape model database 16 of the statistical shape model generation device 10 are input to the image processing device 100, they are stored in the statistical shape model database 106. Then, when a three-dimensional three-dimensional abdominal CT image is input to the image processing apparatus 100 as an input image, the image processing routine shown in FIG. 10 is executed.

  In step S200, the receiving unit 102 receives a three-dimensional three-dimensional abdominal CT image as an input image.

  In step S202, the inter-image positioning unit 110 performs positioning between the early phase image, the portal vein phase image, and the late phase image received as the three-phase three-dimensional abdominal CT image in step S200. Then, an alignment image is generated.

  In step S204, the spatial standardization unit 112 generates a spatial standardized image based on the alignment image generated in step S202, for example, using a nonlinear function.

  In step S206, the segmentation unit 114 optimizes the objective function based on the input image received in step S200 in the eigenspace based on the pre-calculated eigenvector stored in the statistical shape model database 106. As described above, the shape parameter representing the shape of the subject represented by the spatial standardized image generated in step S204 is estimated, and the shape of the subject represented by the spatial standardized image is obtained. Step S206 is realized by the segmentation processing routine shown in FIG.

<Segmentation processing routine>
In step S300, the segmentation unit 114 sets the entire eigenspace R _alpha as a parent node _{H 0.}

In step S302, the segmentation unit 114, as shown in the equation (12), the set of splittable pixel k parent node _{H 0,} is set as the set Q.

  In step S304, the segmentation unit 114 initializes Queue.

In step S306, the segmentation unit 114 combines the combination of the parent node H ₀ set in step S300 with the lower bound L (H ₀ ; I) corresponding to the parent node H ₀ calculated according to the above equation (14). , Stored in the Queue initialized in step S304.

  In step S308, the segmentation unit 114 selects a pixel k from the set Q set in step S302 or the set Q updated in step S316 described below according to the above equation (17).

In step S310, the segmentation unit 114, the above formula parent node _{H 0} is set in the step S300, the or parent node _{H 0} updated in step S314 to be described later, by using a pixel k selected in step S308 (10) and divided according to (11), sets the child nodes _{H 1} and _{H 2.}

In step S312, the segmentation unit 114, the lower bound L corresponding to the child node _{H 1} calculated in accordance with the set child nodes _{H 1} and the formula in the above step S310 (14); a combination of _(H 1 I) , Queue. Also, the lower bound L corresponding to the child node _{H 2} calculated in accordance with the set child nodes _{H 2} and the equation in step S310 (14); a combination of _(H 2 I), and stored in Queue.

In step S314, the segmentation unit 114, among the stored node in Queue, select the lowest lower bound of the node, the parent node _{H 0,} updates the selected node.

In step S316, the segmentation unit 114, based on the parent node _{H 0} updated in the step S314, the as shown in the equation (12), the set Q, the set of splittable pixel k of the parent node _{H 0} Update to In the case where there is no pixel k dividable parent node H ₀ is the set Q is updated to an empty set.

  In step S318, the segmentation unit 114 determines whether the set Q is an empty set. If the set Q is an empty set, the process returns to step S308. On the other hand, if the set Q is not an empty set, the process proceeds to step S320.

In step S320, the segmentation unit 114 is finally updated by selecting the shape parameter alpha ^* in the parent node H ₀ above step S314, the substituted a selected shape parameter alpha ^* the function g, the specific Determine the shape y ^* of the object.

In step S322, based on the specific object shape y ^* and the objective function determined in step S320, the segmentation unit 114 subjects the object region x having the specific object shape to optimize the objective function. ^* Is extracted from the spatially standardized image generated in step S204.

In step S324, the segmentation unit 114 outputs the region x ^{* of} the subject extracted in step S322 as a result.

Next, returning to the image processing routine, in step S208, the output unit 120 outputs as a result the region x ^{* of} the subject extracted in step S206, and ends the image processing routine.

  As described above, in the image processing apparatus 100 of the present embodiment, as a function of the computer processing based on the program, (A) the eigenvector calculated in advance based on a plurality of images in which the region of the subject is obtained in advance is used as the basis. (B) In the eigenspace indicating the shape parameter of the statistical shape model representing the shape of the specific object, the point on the eigenspace indicates the specific parameter represented by the shape parameter indicated by the point on the eigenspace. Shape parameters representing the shape of the subject represented by the input image so as to optimize a predetermined objective function representing a value corresponding to the likelihood of the shape of the object and the difference between pixel values between adjacent pixels in the input image Is estimated. The region of the subject is extracted from the input image using the shape of the specific object represented by the estimated shape parameter as prior knowledge. As a result, it is possible to suppress an increase in the amount of calculation and accurately extract the region of the subject.

  Further, the image processing apparatus 100 according to the present embodiment can extract a region of a subject at high speed.

  One of the important differences between the proposed algorithm and the conventional algorithm is that no preprocessing is required. Conventionally, a pre-process for preparing a shape in advance and performing clustering is required, and a considerable amount of time and memory are required for the pre-process. However, the pre-process is not required at all in the proposed algorithm in the present embodiment. As a result, cost reduction was realized.

  Further, in the embodiment of the present invention, an experiment for segmenting the pancreas from 140 three-dimensional abdominal CT images was performed to verify processing accuracy and processing time, and the following results were obtained.

1. The world's highest accuracy was obtained for pancreas segmentation from 3D abdominal CT images.
2. It is theoretically guaranteed that the value after minimization of the objective function by the proposed algorithm is always smaller than that of the conventional method, but this was confirmed in actual images.
3. Compared to the maximum number of conventional techniques shapes covered in (the U.S. Pat. No. 8,249,349) is 10 ^7, the proposed method it has become possible to handle the number of more than 10 ^9. Further, the image is conventionally limited to a two-dimensional image, but a three-dimensional image having a number of pixels nearly two digits larger can be handled.

[Second embodiment]
Next, a second embodiment will be described. Note that the configurations of the statistical shape model generation device and the image processing device according to the second embodiment are the same as those of the first embodiment, and thus the same reference numerals are given and the description is omitted.

  The second embodiment is different from the first embodiment in that a shape parameter representing the shape of a subject is estimated using an approximate solution.

FIG. 12 is a diagram for explaining an approximate solution method according to the second embodiment. As shown in FIG. 12, unlike the strict solution method used in the first embodiment, the shape parameter is estimated by an approximate solution in the second embodiment. In the second embodiment, as shown in FIG. 12, the sampling points are set in a grid on the eigenspace and the division of the convex polygon using a straight line determined from the sampling points is repeated. The setting of the sampling point is performed according to a predetermined sampling parameter k. For example, if the sampling parameters k = 4, 2 ⁴ sampling points for each dimension of the eigenspace is set.

  First, the segmentation unit 114 of the image processing apparatus according to the second embodiment sets sampling points in a lattice on the eigenspace.

Then, the segmentation unit 114 sets a straight line from the sampling points set on the eigenspace so that the areas of the two convex polygons after division correspond to each other, and divides the convex polygon by the set straight line. Then, the search for the convex polygon including the point indicating the optimal shape parameter is repeated to estimate the shape parameter representing the shape of the subject represented by the input image.
Linear Specifically, in pseudo-code segmentation algorithm shown in Table 1, instead of the process of dividing the parent node H ₀ by the pixel k selected by using the function the Select (Q), which is determined from the sampling point using, performs processing for dividing a parent node H _0.

  In the second embodiment, by using the approximate solution method, the number of dimensions of the eigenspace can be increased, and the shape parameter can be accurately estimated.

FIG. 13 shows the results of 140 cases of pancreas recognition performed by the image processing apparatus according to the second embodiment. In FIG. 13, a broken-line circle represents the result of pancreatic recognition by the image processing device according to the first embodiment, and a solid-line circle represents the result of pancreatic recognition by the image processing device according to the second embodiment. .
As shown in FIG. 13, it can be seen that by using the approximate solution method, a higher segmentation accuracy than the exact solution is achieved by increasing the number of dimensions of the eigenspace.

  FIG. 14 shows an approximate solution of the second embodiment, a solution in a case where the method described in the above-mentioned US Pat. No. 8,249,349 is applied to pancreas segmentation, and an exact solution of the first embodiment. The result of comparing the calculation time of the solution is shown. FIG. 14 shows a change in calculation time when the dimension d of the eigenspace is increased. In the strict solution method, the upper limit of the calculation time was set to 100 hours. For the approximate solution, the value of the sampling parameter was set to k = 4. As the CPU, 3.1 GHz Intel (R) Xeon (R) was used, and 1 CPU was used for preprocessing and 2 CPU was used for optimization.

  As shown in FIG. 14, when the approximate solution is used, the case where the exact solution of the first embodiment is used and the method described in US Pat. No. 8,249,349 are applied to the pancreas segmentation. It can be seen that the calculation cost when the number of dimensions of the eigenspace is increased can be greatly reduced as compared with the case where

  Note that other configurations and operations of the image processing apparatus according to the second embodiment are the same as those of the first embodiment, and a description thereof will not be repeated.

  As described above, according to the image processing apparatus according to the second embodiment, sampling points are set in a grid on convex polygons in the eigenspace, and are set as convex polygons in the eigenspace. By repeatedly performing the search by dividing the convex polygon using the straight line, the shape parameter representing the shape of the subject represented by the input image is estimated. The region of the subject is extracted from the input image using the shape of the specific object represented by the estimated shape parameter as prior knowledge. As a result, it is possible to suppress an increase in the amount of calculation and accurately extract the region of the subject.

  Further, a more advanced statistical shape model with an increased number of dimensions can be used by the approximate solution method.

[Third Embodiment]
Next, a third embodiment will be described. Since the configurations of the statistical shape model generation device and the image processing device according to the third embodiment are the same as those of the first embodiment, the same reference numerals are given and the description is omitted.

  The third embodiment differs from the second embodiment in that a shape parameter representing the shape of a subject is estimated using an approximate solution in which sampling points are randomly set.

  FIG. 15 is a diagram for explaining an approximate solution method according to the third embodiment. As shown in FIG. 15, in the third embodiment, the sampling points are randomly set on the eigenspace, and the process of dividing the convex polygon using a straight line determined from the sampling points is repeated.

  The segmentation unit 114 of the image processing device according to the third embodiment first sets sampling points randomly on the eigenspace.

  Then, the segmentation unit 114 sets a straight line from the sampling points set on the eigenspace so that the areas of the two convex polygons after division correspond to each other, and divides the convex polygon by the set straight line. Then, the search for the convex polygon including the point indicating the optimal shape parameter is repeated to estimate the shape parameter representing the shape of the subject represented by the input image.

Linear Specifically, in pseudo-code segmentation algorithm shown in Table 1, instead of the process of dividing the parent node H ₀ by the pixel k selected by using the function the Select (Q), which is determined from the sampling point It performs a process of dividing the parent node H ₀ using.

  Note that other configurations and operations of the image processing apparatus according to the third embodiment are the same as those of the first or second embodiment, and thus description thereof is omitted.

  As described above, according to the image processing apparatus according to the third embodiment, the sampling points are randomly set on the convex polygon in the eigenspace, and are set to the convex polygon in the eigenspace. The shape parameter representing the shape of the subject represented by the input image is estimated by repeating the search by dividing the convex polygon using the straight line. The region of the subject is extracted from the input image using the shape of the specific object represented by the estimated shape parameter as prior knowledge. As a result, it is possible to suppress an increase in the amount of calculation and accurately extract the region of the subject.

[Fourth Embodiment]
Next, a fourth embodiment will be described. Since the configurations of the statistical shape model generation device and the image processing device according to the fourth embodiment are the same as those of the first embodiment, the same reference numerals are given and the description is omitted.

  The fourth embodiment differs from the first to third embodiments in that the objective function is extended.

In the first embodiment, using the above formula (4) as the objective _{function, F p (I p, y} p) in the above formula (4) and _{B p (I p, y p} ) is the formula ( The cases defined in 5) and (6) have been described.

  In the fourth embodiment, the objective function represented by the above equation (4) monotonically changes as the likelihood of the shape of a specific object with respect to the value of the shape label in a pixel corresponding to the shape of the specific object represented by the shape parameter. Define to include a monotonic function and extend the objective function.

Specifically, in the fourth _{embodiment, F p (I p, y} p) in the above formula (4) and _{B p (I p, y p} ) and the following formula (18), (19 ) And extend the objective function.

FIG. 16 is a diagram showing a sufficient condition for the lower bound of the objective function to satisfy monotonicity. The sufficient condition is that h ^F _p (y) and h ^B _p (y) (∀p∈P) are monotonic functions that decrease and increase monotonically with respect to y _q (∀q∈P), respectively. As shown in FIG. 16, the label pair {y, y '} ^{L | P |}

, The relationship shown in the following equation (20) holds.

FIG. 17 shows an example of h ^F _p (y) and h ^B _p (y) satisfying the relationship of the above equation (20). In the example shown in FIG. 17, h ^F _p (y) and h ^B _p (y) are defined by the distance function shown in the following equation (21).

The monotone functions h ^F _p (y) and h ^B _p (y) are defined by the signed distance function shown in the above equation (21), and the penalty near the contour of the shape is reduced. Segmentation errors can be reduced.

  As described above, according to the image processing apparatus according to the fourth embodiment, as the likelihood of the shape of a specific object in the objective function, the value of the shape label in the pixel with respect to the shape of the specific object represented by the shape parameter Is defined to include a monotone function that changes monotonically with respect to. As a result, the region of the subject can be accurately extracted.

In the fourth embodiment, a monotone function h ^F _p (y) and h ^B _p (y) that minimizes energy at the correct contour of the shape of a specific object is introduced into the objective function. Thus, a better objective function can be used.

[Fifth Embodiment]
Next, a fifth embodiment will be described. Note that the configurations of the statistical shape model generation device and the image processing device according to the fifth embodiment are the same as those of the first embodiment, and thus the same reference numerals are given and the description is omitted.

  The fifth embodiment is different from the first to fourth embodiments in that a function g for mapping the parameter α on the eigenspace to a shape is extended.

  In the first embodiment, the case where the function g of the mapping in the above equation (2) is defined by the Heaviside function H (·) in the above equation (3) has been described.

  In the fifth embodiment, a function g for mapping a shape parameter to the shape of a specific object is defined to include a predetermined function f, and the function g for mapping is extended.

Also, extended result as equation (23) below the functions g _p mapping, also made available shape representations other than the level set function (e.g., Kilian M. Pohl et al., "Logarithm Odds Maps for Shape Representation ”, Proc. Of Medical Image Computing and Computer-Assisted Intervention, Vol.4191, pp.955-963, 2006.

  Here, f represents a predetermined monotone function, and t represents a predetermined threshold.

  For example, a case where LogOdds is used as an example of a possible shape expression represented by a statistical shape model will be described. When the class representing the shape is 2, and LogOdds is used as a statistical shape model, it is expressed by the following equation.

  FIG. 18 shows an example in which LogOdds is used as a statistical shape model. As shown in FIG. 18, the shape representation is extended by using LogOdds.

  As described above, according to the statistical shape model generation device according to the fifth embodiment, a more advanced statistical data is obtained by expanding the function g to be mapped (introducing the predetermined function f and the threshold value t). The dynamic shape model becomes available.

  Note that the present invention is not limited to the above-described example, and various modifications and applications can be made without departing from the gist of the present invention.

  Since this embodiment is fundamental, its application range is considered to be wide. Specifically, the present invention can be widely used for image recognition processing for a graphic whose shape or the like fluctuates statistically. For example, it can be used not only for other organs and other medical images (for example, MR and PET), but also for recognition of a face from a face image and processing for recognizing a specific figure from a general landscape image. is there. In the present embodiment, the pancreas is targeted, but the spleen may be targeted as another organ, for example.

Further, in the first embodiment, the case where LSDM is used as a statistical shape model has been described as an example, but the present invention is not limited to this. It can be used in the case of other statistical shape models instead of LSDM. As long as the statistical shape model can be expressed by a linear function (strictly, the function φ for a pixel is a linear function) as in the above equation (1), the present embodiment can be applied to other statistical shape models. Can be applied. Depending on the objective function and the optimization method, the present embodiment can be applied to a statistical shape model other than the statistical shape model represented by the linear function such as the equation (1) shown in the embodiment. Can be applied.
Further, as shown in the fifth embodiment, various statistical shape models can be used by expanding the mapping function g.

  Further, in the first embodiment, the case where the dimension of the eigenspace is 2 (d = 2) has been described as an example, but the present invention is not limited to this. For example, a higher-dimensional eigenspace may be targeted. For example, as shown in the second and third embodiments, the dimension of the eigenspace can be increased by using the approximate solution.

In the above embodiment, when the dimension of the eigenspace is increased to 3 or more, the convex polygon corresponds to the convex polycell, and the area of the convex polygon corresponds to the volume of the convex polycell.
Therefore, when the dimension of the eigenspace is increased to 3 or more, the segmentation unit 114 repeatedly divides the convex polyvesicle on the eigenspace and searches for a convex polyvesicle including a point indicating an optimal shape parameter according to a search algorithm. The shape parameter representing the shape of the subject represented by the input image is estimated so as to optimize the objective function represented by the above equation (4).
In addition, the segmentation unit 114 searches for a convex multivessel on an eigenspace including a point indicating an optimal shape parameter by calculating a lower bound of an objective function for a shape set included in the convex polyvessel in a search algorithm. , And estimate the shape parameters.
In addition, the segmentation unit 114 divides the convex polyvesicle on the eigenspace so that the volumes of the two convex polyvesicles after the division correspond to each other, and generates the convex polyvesicle on the eigenspace including points indicating the optimal shape parameters. The search for multivesicles is repeated to estimate shape parameters.

Further, in the embodiment, the case where the eigenspace is divided by the pixels k included in the set Q selected according to the above equation (17) has been described as an example. However, the present invention is not limited to this, and the present invention is not limited to this. The present invention is also applicable to convex polygons created by the division method. For example, as shown in the second embodiment, the present invention can be applied to a convex polygon in which an eigenspace is regularly divided, such as a lattice.
In this case, Tightness (one of the three conditions for guaranteeing optimality) may not be satisfied depending on the degree of division.

  Here, Tightness will be briefly described.

  The above equation (14) is shown as the following equation (24).

In this case, when the following equation for all the leaf nodes _{H i} (25) is satisfied, tightness is established.

  When the fineness of the division is coarse, Expression (25) does not hold, and Tightness may not hold, and only an approximate solution may be obtained. However, when the dimension d of the eigenspace is increased, There is an advantage that the calculation cost can be further reduced. It should be noted that by slightly sacrificing the optimality, the user can select the balance between the calculation cost and the calculation accuracy, which is an important point regarding the extension of the proposed method of the present embodiment. is there. At this time, the point that the optimality is not guaranteed is the same as in the above-mentioned US Pat. No. 8,249,349, but it should be noted that no pre-processing is required as compared with the above-mentioned US Pat. No. 8,249,349. I want to.

  In addition, the objective function and algorithm for minimization used the objective function shown in the above embodiment, and the branch and bound method and the graph cut method. The present invention is not limited to this and can be applied.

  After the approximate solution according to the second or third embodiment is executed, the exact solution according to the first embodiment may be executed.

  In the computer configuration shown in FIG. 2, a program for realizing the function of each processing unit according to the embodiment is recorded on a computer-readable recording medium, and the program recorded on the recording medium is stored in a computer system. The processing by each component may be executed by reading and executing the program, or the program may be read by using a communication function (not shown).

  Note that the computer-readable recording medium refers to a portable medium such as a flexible disk, a magneto-optical disk, a ROM, and a CD-ROM, and a storage device such as a hard disk built in a computer system.

  Further, the above program may be transmitted from a computer system storing the program in a storage device or the like to another computer system via a transmission medium or by a transmission wave in the transmission medium. Here, the "transmission medium" for transmitting a program refers to a medium having a function of transmitting information, such as a network (communication network) such as the Internet or a communication line (communication line) such as a telephone line.

  Further, the program may be for realizing a part of the functions described above. Furthermore, what can implement | achieve the function mentioned above in combination with the program already recorded on the computer system, and what is called a difference file (difference program) may be sufficient.

  In the present embodiment, each processing unit of the statistical shape model generation device 10 shown in FIG. 1 and the image processing device 100 shown in FIG. 7 is configured by a computer capable of executing each function by a program. However, a hardware configuration including a logic element circuit may be adopted.

  Further, the computer configuration of the statistical shape model generation device 10 and the image processing device 100 shown in FIG. 2 may be changed as appropriate.

  As described above, the embodiment has been described in detail with reference to the drawings. However, the specific configuration is not limited to the embodiment and includes a design and the like within a range not departing from the gist.

  Further, the program of the embodiment may be provided by being stored in a storage medium.

  A computer-readable medium according to an embodiment is a program for extracting a region of a subject from an input image representing a subject, which is a specific object. And (B) an eigenspace in which the region of the subject is an eigenspace based on eigenvectors calculated in advance based on the plurality of images obtained in advance. In the eigenspace where the upper point indicates the shape parameter of the statistical shape model representing the statistical variation of the shape of the specific object, the shape parameter indicated by the point on the eigenspace represents based on the input image. To optimize a predetermined objective function representing a value corresponding to the likelihood of the shape of the specific object and a difference between pixel values of adjacent pixels in the input image. Estimating the shape parameter representing the shape of the subject represented by the input image, and extracting the area of the subject from the input image, using the shape of the specific object represented by the estimated shape parameter as prior knowledge. It is a computer-readable medium storing a program for causing it to function as a segmentation unit.

  The disclosure of Japanese Application 2014-169911 is incorporated herein by reference in its entirety.

  All documents, patent applications, and technical standards mentioned herein are to the same extent as if each individual document, patent application, and technical standard were specifically and individually stated to be incorporated by reference. Incorporated herein by reference.

Claims (19)

An image processing apparatus for extracting an area of the subject from an input image representing a subject which is a specific object,
Receiving means for receiving the input image;
(A) a plurality of learning images representing the subject, wherein the subject area is an eigenspace based on eigenvectors calculated in advance based on the plurality of images obtained in advance, and (B) In the eigenspace in which a point on the eigenspace indicates a shape parameter of a statistical shape model representing a statistical variation of the shape of the specific object,
Based on the input image, a value corresponding to a likelihood of the shape of the specific object represented by the shape parameter indicated by the point on the eigenspace and a difference in pixel value between adjacent pixels in the input image. Estimating the shape parameters representing the shape of the subject represented by the input image so as to optimize a predetermined objective function,
As a priori knowledge of the shape of the specific object represented by the estimated shape parameters, a region of the subject, a segmentation unit that extracts from the input image,
An image processing apparatus including: The segmentation means includes:
Based on the input image, so as to optimize the objective function, while estimating the shape parameters representing the shape of the subject represented by the input image,
The image processing apparatus according to claim 1, wherein a region of the subject is extracted from the input image, using the shape of the specific object represented by the estimated shape parameter as prior knowledge. The segmentation means comprises:
The convex polymorphism on the eigenspace including points indicating the optimal shape parameters is obtained by repeatedly dividing the convex multicellular body on the eigenspace representing the shape set including the shape of the specific object represented by the point indicating the optimal shape parameter. According to a search algorithm for searching for a cell, to optimize the objective function, estimate the shape parameter representing the shape of the subject represented by the input image,
3. The image processing apparatus according to claim 1, wherein the region of the subject is extracted from the input image, using the shape of the specific object represented by the estimated shape parameter as prior knowledge. 4.   The segmentation means searches for a convex multivessel on the eigenspace including a point indicating an optimal shape parameter by calculating a lower bound of the objective function for a shape set included in the convex polyvesicle in the search algorithm. Then, the shape parameters representing the shape of the subject represented by the input image are estimated, and the shape of the specific object represented by the estimated shape parameters is used as prior knowledge, and the area of the subject is input to the input image. The image processing device according to claim 3, wherein the image processing device extracts the image data from the image.   The segmentation means divides the convex polyvesicles on the eigenspace so that the volumes of the two convex polyvesicles after division correspond to each other, and includes a convex shape on the eigenspace including a point indicating an optimal shape parameter. By repeatedly searching for the multivesicular body, the shape parameters representing the shape of the subject represented by the input image are estimated, and the shape of the specific object represented by the estimated shape parameters is used as prior knowledge, and The image processing apparatus according to claim 4, wherein the region is extracted from the input image. The segmentation means sets a sampling point on the eigenspace, and divides the convex polyhedron using a hyperplane determined from the sampling points set on the eigenspace to indicate an optimal shape parameter. Iterating the search for convex multivesicular bodies on the eigenspace including, estimating the shape parameters representing the shape of the subject represented by the input image,
The image processing device according to claim 4, wherein the region of the subject is extracted from the input image, using the shape of the specific object represented by the estimated shape parameter as prior knowledge.   The image processing apparatus according to claim 4, wherein the segmentation unit arbitrarily sets a sampling point on the eigenspace.   The said objective function contains the monotone function which changes monotonically with respect to the value of the shape label in the pixel with respect to the shape of the said specific object which the said shape parameter represents as the likelihood of the shape of the said specific object. The image processing apparatus according to claim 1. The search algorithm, the image processing apparatus according to any one of claims 3 to 7 is a Branch and bound method and a graph cut method. An image processing method in an image processing device that includes an accepting unit and a segmentation unit, and extracts an area of the subject from an input image representing a subject that is a specific object,
The receiving means receiving the input image;
The segmentation means includes: (A) a plurality of learning images representing the subject, wherein a region of the subject is an eigenspace based on eigenvectors calculated in advance based on the plurality of images obtained in advance. And (B) in the eigenspace indicating a shape parameter of a statistical shape model representing a statistical variation of the shape of the specific object, based on the input image, Optimize a predetermined objective function representing a value corresponding to the likelihood of the shape of the specific object represented by the shape parameter indicated by the upper point and a difference in pixel value between adjacent pixels in the input image. As described above, the shape parameter representing the shape of the object represented by the input image is estimated, and the shape of the specific object represented by the estimated shape parameter is determined in advance as prior knowledge. The area of the object, extracting from the input image,
An image processing method including: The step of extracting the area of the subject from the input image,
In the eigenspace,
Based on the input image, so as to optimize the objective function, while estimating the shape parameters representing the shape of the subject represented by the input image,
The image processing method according to claim 10, wherein a region of the subject is extracted from the input image, using the shape of the specific object represented by the estimated shape parameter as prior knowledge. The step of extracting the area of the subject from the input image,
The convex polymorphism on the eigenspace including points indicating the optimal shape parameters is obtained by repeatedly dividing the convex multicellular body on the eigenspace representing the shape set including the shape of the specific object represented by the point indicating the optimal shape parameter. According to a search algorithm for searching for a cell, the shape parameter representing the shape of the subject represented by the input image is estimated so as to optimize the objective function, and the specific object represented by the estimated shape parameter is The image processing method according to claim 11, wherein a region of the subject is extracted from the input image using a shape as prior knowledge.   The step of extracting the region of the subject from the input image by the segmentation means includes calculating, in the search algorithm, a lower bound of the objective function with respect to a set of shapes included in the convex polyvesicle, thereby obtaining an optimal shape parameter. Estimating the shape parameters representing the shape of the subject represented by the input image by searching for convex polyvesicles on the eigenspace that includes points indicating the shape of the specific object represented by the estimated shape parameters The image processing method according to claim 12, wherein the region of the subject is extracted from the input image, using as the prior knowledge.   The step of extracting the region of the subject from the input image by the segmentation means divides the convex polyvesicles in the eigenspace so that the volumes of the two convex polyvesicles after division correspond to each other, and Iteratively searching for convex polyvesicles on the eigenspace including points indicating the optimal shape parameters, estimates the shape parameters representing the shape of the subject represented by the input image, and estimates the shape parameters 14. The image processing method according to claim 13, wherein the region of the subject is extracted from the input image, using the shape of the specific object represented by the expression as prior knowledge. The step of extracting the region of the subject from the input image by the segmentation means includes setting a sampling point on the eigenspace, and using a hyperplane determined from the sampling point set on the eigenspace. The shape parameters representing the shape of the subject represented by the input image are estimated by repeating the search for the convex polyvesicles on the eigenspace including the points indicating the optimal shape parameters by dividing the convex polyvesicles. ,
The image processing method according to claim 13, wherein the region of the subject is extracted from the input image, using the shape of the specific object represented by the estimated shape parameter as prior knowledge.   15. The image processing method according to claim 13, wherein the step of the segmentation unit extracting the region of the subject from the input image arbitrarily sets a sampling point on the eigenspace.   The said objective function contains the monotone function which changes monotonically with respect to the value of the shape label in the pixel with respect to the shape of the said specific object which the said shape parameter represents as the likelihood of the shape of the specific object. The image processing method according to claim 1. The image processing method according to any one of claims 12 to 16 , wherein the search algorithm is a branch and bound method or a graph cut method.   A program for causing a computer to function as each unit of the image processing apparatus according to claim 1.