JP6070377B2 - Boundary identification device, boundary identification method, program, and recording medium - Google Patents

Description

  The present invention relates to a boundary specifying device and a boundary specifying method for specifying a boundary of a region included in a position space of an image. The present invention also relates to a program for operating a computer as such a boundary identification device, and a computer-readable recording medium in which such a program is recorded. The specification of the area included in the position space of the image is sometimes called image area division.

  To extract various information (shape, volume, topology, etc.) from 3D images taken with CT (Computed Tomography), MRI (Magnetic Resonance Imaging), confocal laser microscope, etc. It is necessary to extract a region corresponding to an object from an image. For this reason, various identification methods for identifying the boundary between these regions have been developed. For example, Implicit surface reconstruction described in Non-Patent Documents 1 and 2 is an example.

  In the implicit surface reconstruction method, f (p) = 0, f (p + εn) = e, and a boundary passing through a point p designated by the user and having a vector n designated by the user as a normal vector, , F (p−εn) = − e is specified as a zero level set of the scalar field f.

G. Turk, et.al, "Modeling with implicit surfaces that interpolate", ACM TOG 21, 4 (2002), 855-873. F. Heckel, et.al, "Interactive 3D medial image segmentation with energy-minimizing implicit function", VCBM 35, 2 (2011), 275-287

  However, the conventional implicit function curved surface reconstruction method has a problem that it is difficult to derive a zero level set that accurately represents the boundary of a target region (a region corresponding to an observation target).

  For example, the boundary of the target area exists along the edge of the image (the portion where the gradient strength of the image is large), but the boundary specified by the conventional implicit function curved surface reconstruction method starts from the point p specified by the user. It does not follow the edge of the image at a distance. This is because in the conventional implicit function surface reconstruction method, the scalar field f is generated without referring to the pixel value.

  The present invention has been made in view of the above problems, and an object of the present invention is to provide a boundary specifying device and boundary that can derive a zero level set that accurately represents the boundary of a region as compared with the conventional implicit surface reconstruction method. It is to realize a specific method.

In order to solve the above-described problem, the boundary specifying device according to the present invention uses an r-dimensional pixel value I (x) corresponding to each point x in the s-dimensional (s is an integer of 2 or more) space R ^s. With respect to the constructed image I, the boundary δD of the region D included in the s-dimensional space R ^s is defined as N points p _i designated as points on the boundary δD, and the boundary δD at each point p _i . In a boundary identification device that identifies based on N s-dimensional vectors n _i designated as normal vectors, an image manifold M = {(x, wcI (x)) ∈R ^{s + r} | x ΕR ^s } (where wc is an arbitrary real number greater than 0) and a constraint point p ′ _i = (p _i , wcI (p) on the image manifold M corresponding to each point p _{i i))} and the constraint point derivation unit that derives a ∈R ^{s + r,} corresponding to the s-dimensional vector _{n i} The constraint vector n ′ _i = J (p _i ) n _i / | J (p _i ) n _i | (J (p _i ) is the mapping r at the point p _i : x → r (x) = A constraint vector deriving unit for deriving (a Jacobian matrix of x, wcI (x))) and a scalar field f on the coupling space R ^{s + r} , and for each constraint point p ′ _i , the first constraint condition f (p ' _i ) = 0 and the second constraint condition ∇f (p ′ _i ) = wbn ′ _i + (1−wb) (n _i , 0) (wb is an arbitrary real number between 0 and 1) A scalar field generator for generating a smooth scalar field f, and a zero level set derivation unit for deriving a zero level set Z = {x∈R ^s | f (r (x)) = 0} of the scalar field f. It is characterized by having.

In order to solve the above-described problem, the boundary specifying method according to the present invention uses an r-dimensional pixel value I (x corresponding to each point x in the s-dimensional (s is an integer of 2 or more) space R ^s. ), The boundary δD of the region D included in the s-dimensional space R ^s is defined as N points p _i designated as points on the boundary δD, and the boundary at each point p _i In the boundary specifying method specified based on N s-dimensional vectors n _i designated as normal vectors of δD, the image manifold M = {(x, wcI (x)) εR ^{s + r} corresponding to the image I An image manifold generation step for generating | x∈R ^s } (wc is an arbitrary real number greater than 0), and a constraint point p ′ _i = (p _i , wcI) on the image manifold M corresponding to each point p _{i (p} i)) and the constraint point derivation step of deriving a ∈R ^{s + r,} each s-dimensional Vector _{n i} to the corresponding s + r-dimensional vector a is the constraint vector _{n 'i = J (p i} ) n i / | J (p i) n i | (J (p i) mapping at the point _{p i} is r: x → a constraint vector deriving step for deriving r (x) = (Jacobi matrix of x, wcI (x))) and a scalar field f on the coupling space R ^{s + r} , for each constraint point p ′ _i , the first The constraint condition f (p ′ _i ) = 0 and the second constraint condition ∇f (p ′ _i ) = wbn ′ _i + (1−wb) (n _i , 0) (wb is 0 or more and 1 or less) A scalar field generation step for generating a smooth scalar field f satisfying the real number), and a zero level set for deriving a zero level set Z = {x∈R ^s | f (r (x)) = 0} of the scalar field f A derivation step.

The zero level set Z derived as described above passes through the designated N points {p ₁ , p ₂ ,..., P _N }, and a vector n _i in which the normal vector at each point p _i is designated. Is an s-1 dimensional manifold that matches Moreover, the zero level set Z derived as described above has a clear edge along the edge in the region where the edge of the image I (the portion where the gradient intensity | ∇I (x) | of the image I is large) exists. Smoothing is performed in a region where the gradient intensity | ∇I (x) | of the image I is generally small. Therefore, according to said structure, the smooth zero level set Z which expresses the boundary of an object area | region (area | region D) more correctly than before can be derived | led-out.

  In the boundary identification device according to the present invention, it is preferable that the scalar field generation unit generates a scalar field f defined by equation (2) described later.

  According to said structure, the scalar field f can be easily produced | generated by solving simultaneous equations (5) mentioned later.

  In the boundary identification device according to the present invention, it is preferable that the image manifold generation unit generates the image manifold M using the value of the parameter wc designated by the user.

  According to the above configuration, the user can freely control the degree to which the derived zero level set is influenced by the image.

  In the boundary identification device according to the present invention, it is preferable that the scalar field generation unit generates the scalar field f using the value of the parameter wb specified by the user.

  According to the above configuration, the user can freely control whether to give priority to deriving a zero level set that does not include extra connected components or to give priority to following the edge of the image. Is possible.

  In the boundary identification device according to the present invention, the image data is a CT (Computed Tomography) image or an MRI (Magnetic Resonance Imaging) image obtained by imaging a living body, and the region D is the CT image or the MRI. It is preferable that the region corresponds to the part of the living body in the image.

  According to said structure, even if it is a case where the area | region D respond | corresponds to the site | parts which have a complicated shape like an anal sphincter, the boundary (delta) D can be pinpointed correctly.

  Note that a program for causing a computer to operate as the boundary specifying device and a computer-readable recording medium in which such a program is recorded are also included in the scope of the present invention.

According to the present invention, it is possible to derive a zero level set Z that expresses the boundary of the region D included in the position space R ^s of the image I more accurately than before.

It is a block diagram which shows the structure of the boundary identification apparatus which concerns on one Embodiment of this invention. It is a figure for demonstrating operation | movement of the boundary identification apparatus shown in FIG. (A) is a top view which shows the provided image I. FIG. (B) is a perspective view showing an image manifold M generated by the boundary identification device. (C) is a perspective view showing the value on the image manifold M of the scalar field f generated by the boundary specifying device. (D) is a perspective view showing the zero-level curved surface Z ′ together with the image manifold M. FIG. (E) It is a top view which shows boundary (delta) D identified by the boundary identification apparatus with the image I. FIG. (A) to (d) are a schematic sectional view (upper stage) showing the zero-level curved surface Z ′ together with the image manifold M, a plan view (middle stage) showing the zero-level curve Z together with the image I, and zero. The perspective view which showed level curved surface Z 'with the image manifold M is included. (A) shows the parameter wb value set to 0.0, (b) shows the parameter wb value set to 0.1, and (c) shows the parameter wb value set to 0.5. In the set item (d), the value of the parameter wb is set to 1.0. FIG. 2 is a block diagram of a computer that functions as the curve specifying device shown in FIG. 1. It is a figure which shows the output image output from the boundary identification apparatus shown in FIG.

  A boundary identification device according to an embodiment of the present invention will be described below with reference to the drawings.

Note that the boundary identification device according to the present embodiment displays an image I composed of pixel values I (x) corresponding to each point x in the discrete s-dimensional (s is a predetermined integer of 2 or more) space R ^s. It is a device for processing. Here, the pixel value I (x) is an element of a discrete r-dimensional (r is a predetermined integer of 1 or more) space R ^r (for example, when the image I is a monochrome image, r = 1). When the image I is an RGB color image, r = 3).

In the following description, the image I is identified with the mapping I: x → I (x) from the discrete s-dimensional space R ^s to the discrete r-dimensional space R ^r . Further, in the following description, the start region R ^s of the map I is referred to as a “positional space” of the image I, and the end region R ^r of the map I is referred to as a “value space” (range domain) of the image I. Call.

[Configuration of boundary identification device]
A configuration of the boundary identification device 1 according to the present embodiment will be described with reference to FIG. FIG. 1 is a block diagram showing the configuration of the boundary identification device 1.

The boundary specifying device 1 includes N points {p ₁ , p ₂ ,..., P _N } designated by the user and N s-dimensional vectors {n ₁ , n ₂ ,. _N } and the boundary δD of the region D included in the position space R ^s of the image I based on _N }. As the image I, a two-dimensional or three-dimensional MRI (Magnetic Resonance Imaging) image obtained by imaging a living body (for example, a human body) is assumed, and a region D (particularly an organ, tumor, A lump part such as a tissue or a skeleton).

  The boundary δD specified by the boundary specifying device 1 is an s−1-dimensional manifold (curved when s = 2, curved surface when s = 3) that satisfies the following conditions (A) and (B).

(A) The boundary δD passes through _N points {p ₁ , p ₂ ,..., P _N } specified by the user.

(B) The normal vector of the boundary δD at each point p _i matches the vector n _i specified by the user.

  The boundary δD specified by the boundary specifying device 1 further has the following properties (C) and (D).

  (C) In the region where the edge of the image I (the portion where the gradient intensity | ∇I (x) | of the image I is large) exists, the boundary δD is along the edge.

  (D) In a region where there is no clear edge (a region where the gradient intensity | ∇I (x) | of the image I is generally small and blurred), the boundary δD is smooth.

In order to specify such a boundary δD, the boundary specifying device 1 uses an image manifold M corresponding to the image I. Here, the image manifold M corresponding to the image I, mapping r from the spatial domain ^{R s} to the direct product space ^{R s} × ^{R r:} x → range of r (x) = (x, wcI (x)) { It refers to an s-dimensional manifold defined as r (x) εR ^s × R ^r | xεR ^s }. In the following description, the final region of the mapping r, that is, the direct product space R ^s × R ^r is referred to as a “joint space” (bilateral domain or joint spatial range domain).

  As shown in FIG. 1, the boundary specifying device 1 can be configured by an image manifold generating unit 11, a constraint point deriving unit 12, a constraint vector deriving unit 13, a scalar field generating unit 14, and a zero level set deriving unit 15. it can. The function of each block provided in the boundary specifying device 1 will be described as follows.

  The image manifold generation unit 11 is configured to generate an image manifold M corresponding to the image I from the given image I and the scalar value wc specified by the user. For example, when the image I is given as an s-dimensional array having an r-dimensional array I (x) as an element, the image manifold generation unit 11 stores an array representing the image manifold M, that is, an s + r-dimensional array r ( An s-dimensional array having x) = (x, wc · I (x)) as an element is generated.

The constraint point deriving unit 12 derives a point p ′ _i = r (p _i ) on the image manifold M corresponding to the point p _i ∈R ^s specified by the user for each integer i of 1 ≦ i ≦ N. It is the structure for doing. For example, when the image manifold M is given as an s-dimensional array having the s + r-dimensional array r (x) as an element, the constraint point deriving unit 12 acquires the element r (p _i ) of the s-dimensional array. To obtain a point p ′ _i on the image manifold M. Hereinafter, the point p ′ _i on the image manifold M derived by the constraint point deriving unit 12 will be referred to as “constraint point p ′ _i ”.

Here, the processing of the constraint point deriving unit 12 assuming that the point p _i specified by the user is a point arranged at a pixel position (an element of the position space R ^s which is a discrete s-dimensional space) is illustrated. However, it is not limited to this. For example, when the point p _i designated by the user is a point arranged at a position other than the pixel position, the constraint point deriving unit 12 performs mapping I ′ (x) obtained by linear interpolation of the mapping I (x). The point p ′ _i = r (p _i ) on the image manifold M may be derived using (a function on the continuous s-dimensional space R ^s ).

The constraint vector deriving unit 13 s + r-dimensional vector n ′ _i = J (p _i ) n _i / | J (p) corresponding to the s-dimensional vector n _i specified by the user for each integer i of 1 ≦ i ≦ N. _i ) A configuration for deriving n _i |. Here, J _{(p i)} is the Jacobian matrix of the mapping r at the point _{p i.} Since the mapping r is a mapping from the s-dimensional space R ^s to the s + r-dimensional space R ^{s + r} , the Jacobian matrix J (p _i ) of the mapping r at the point p _i is a matrix of s + r rows and s columns. The s + r-dimensional vector n ′ _i is included in the tangent space Tp ′ _i M of the image manifold M at the point p ′ _i and the projection onto the position space R ^s is parallel to the s-dimensional vector n _i. It becomes a vector. The s + r-dimensional vector n ′ _i derived by the constraint vector deriving unit 13 is hereinafter referred to as “constraint vector n ′ _i ”.

Here, the Jacobian matrix J (p _i ) is defined by the following equation (1). In the following equation (1), E represents a unit matrix of s rows and s columns, I _j (x) represents the j-th element (1 ≦ j ≦ r) of the r-dimensional vector I (x), and x _k represents the k-th element (1 ≦ k ≦ s) of the s-dimensional vector x.

The constraint vector n ′ _i is derived, for example, by (1) calculating the Jacobian matrix J (p _i ) of the mapping r at the point p _i from the image manifold M, and (2) the Jacobian matrix J (p _i ) calculating a matrix product _{J (p i) n} i of the s-dimensional vector _{n i,} (3) matrix product _{J (p} i) norm of _{n i} | calculating a | _{J (p i) n} i , (4) dividing each element of the matrix product J (p _i ) n _i by the norm | J (p _i ) n _i |. Here, the element ∂I _j (p _i ) / ∂x _k of the Jacobian matrix J (p _i ) is obtained by applying a known Sobel filter to the function I _j (x) on the position space R ^s. Can be derived. Since the other steps can be realized by a known algorithm, the description thereof is omitted here.

The scalar field generation unit 14 is configured to generate a scalar field f on the coupling space R ^{s + r} that satisfies the following constraints (A ′) and (B ′). Incidentally, in the constraint condition _{(B ') (n i,} 0) is below the first component to the s-th component match the corresponding component of the s-dimensional vector n _i, from the s + 1 component to the s + r component It means an s + r-dimensional vector that becomes zero. Also, wb in the following constraint condition (B ′) is a scalar value of 0 or more and 1 or less specified by the user.

(A ′) For each integer i where 1 ≦ i ≦ N, f (p ′ _i ) = 0.

(B ′) For each integer i where 1 ≦ i ≦ N, ∇f (p ′ _i ) = wbn ′ _i + (1−wb) (n _i , 0).

In the present embodiment, it is assumed that the scalar field f is B-HRBF (Bilateral Hermite Radial Basis Function) defined by the following equation (2). In the following equation (2), φ is a kernel defined by φ (t) = t ^ 3, and P is a polynomial defined by P (x ′) = a · x ′ + b. Α _i εR and β _i εR ^{s + r} are undetermined coefficients satisfying the following equations (3) and (4).

Scalar field generating unit 14 generates a scalar field f of the binding space ^{R s + r} satisfies the constraints (A ') and _{(B') α i ∈R,} β i ∈R s + r, a∈R s + r , And bεR.

Additional constraints (A ') and (B') that satisfies ^{_{α i ∈R, β i ∈R s}} + r, a∈R s + r, and b∈R may be obtained by solving the following simultaneous equations (5) Can do.

Here, the block K _ij is a matrix defined by the following equation (6), and the block S _j is a matrix defined by the following equation (7). The vectors s, w _i , and c _i are vectors defined by the following equation (8).

Scalar field generating unit 14, by solving the simultaneous equations (5), satisfy the above constraint condition (A ') and _{(B') α i ∈R,} β i ∈R s + r, a∈R s + r, and b ΕR is calculated. Since simultaneous equations (5) can be solved by a known algorithm, the description thereof is omitted here.

The zero level set deriving unit 15 is a configuration for deriving a zero level set Z = {xεR ^s | f (r (x)) = 0} of the scalar field f on the image manifold M. The derivation of the zero level set Z is, for example, (1) calculating the value of f (r (x)) for all the points x in the position space R ^s , and (2) f (r (x)) = 0. And the process of constructing a set of x.

However, when the zero level set Z is derived by such a method, the following problems occur. That is, the zero level set Z derived by such a method includes any of these points in addition to the connected component passing through the given N points {p ₁ , p ₂ ,..., P _N }. It may contain connected components that do not pass. In order to derive the zero level set Z by such a method, a calculation time that increases in proportion to the s-th power of the resolution of the image I is required. In order to avoid such a problem, the zero level set Z may be derived using a known surface tracking algorithm (sometimes called a surface tracking marching cubes algorithm). A surface level algorithm may be used to derive a zero level set Z composed only of connected components including given N points {p ₁ , p ₂ ,..., p _N }. For the surface tracking algorithm, see, for example, “F. Shekhar, et.al, Octree-Based Decimation of Marching Cubes Surfaces, In Proc. Of IEEE Vis. (1996), 335-342”.

  The boundary specifying device 1 outputs the zero level set Z derived by the zero level set deriving unit 15 to the outside as the boundary δD. For example, an image in which the boundary δD is added on the image I is output to the display.

Here, a configuration in which the user directly specifies _N points {p ₁ , p ₂ ,..., P _N } and N s-dimensional vectors {n ₁ , n ₂ ,. Although described, the present invention is not limited to this. N points {p ₁ , p ₂ ,..., P _N } and N s-dimensional vectors {n ₁ , n ₂ ,..., _{N N} } are indirectly specified by the user, for example, position space R outline of the region D in ^s (the case of s = 2), or, it may be adopted to designate the contour lines of the region D in the two-dimensional cross-section of the spatial domain R ^s (for s ≧ 3) to the user . In this case, the boundary identification device 1 selects N points on the designated contour line (contour line designated by the user), and selects the selected N points {p ₁ , p ₂ ,..., P _N }. And The boundary identification device 1 calculates a vector orthogonal to the specified contour at each point p _i, the calculated vector and n _i. By adopting such a configuration, the operation required by the user becomes easier. For the method of allowing the user to specify the contour line of the region D, refer to the published publication (Japanese Patent Application Laid-Open No. 2012-010893) of the patent application (Japanese Patent Application No. 2010-149497) filed earlier by the applicant of the present application.

[Operation example of boundary identification device]
An example of the operation of the boundary identification device 1 will be described with reference to FIG. The operation example described below is an operation example when s = 2 and r = 1.

FIG. 2A is a plan view showing a given image I. FIG. In such an image I, the user designates a point p _i on the boundary δD of the region of interest D. The user, in such an image I, to specify the normal vector n _i boundary δD at the point p _i.

  The boundary identification device 1 generates an image manifold M from the given image I. FIG. 2B is a perspective view showing the image manifold M generated by the boundary specifying device 1.

Next, the boundary identification device 1 derives a constraint point p ′ _i corresponding to the point p _i specified by the user. Further, the boundary identification device 1 derives a constraint vector n ′ _i corresponding to the vector n _i specified by the user. FIG. 2B shows the constraint point p ′ _i and the constraint vector n ′ _i derived by the boundary identification device 1.

  Next, the boundary identification device 1 generates a scalar field f that satisfies the above-described constraints (A ′) and (B ′). FIG. 2C is a perspective view showing values on the image manifold M of the scalar field f generated by the boundary specifying device 1.

Next, the boundary identification device 1 derives a zero level curve Z = {xεR ^s | f (r (x)) = 0} of the scalar field f. The zero level curve Z derived by the boundary specifying device 1 is an intersection line Z′∩ between the zero level curved surface Z ′ = {x′∈R ^s × R ^r | f (x ′) = 0} and the image manifold M. Matches M. FIG. 2D is a perspective view showing the zero-level curved surface Z ′ together with the image manifold M. It can be seen from FIG. 2D that the zero level curve Z follows the edge in the region where the edge of the image I exists, and that the zero level curve Z becomes smooth in the region where the edge of the image I does not exist.

FIG. 2E is a plan view showing the zero level curve Z of the scalar field f, that is, the boundary δD specified by the boundary specifying device 1 together with the image I. The boundary δD specified by the boundary specifying device 1 passes through _N points {p ₁ , p ₂ ,..., P _N } specified by the user, and the normal vector of the boundary δD at each point p _i is that match the specified vector n _i by the user, seen from Fig. 2 (e).

As shown in FIG. 2 (e), the zero level curve Z includes, in addition to the connected components passing through the given N points {p ₁ , p ₂ ,..., P _N }, Connected components that do not pass through either are included. However, if the surface tracking algorithm is used to derive the zero level curve Z, it is possible to avoid the latter connected component being specified as the boundary δD.

[Parameter wb included in constraint (B ′)]
In the boundary identification device 1, the constraint condition (B ′) imposed on the scalar field f is not ∇f (p ′ _i ) = n ′ _i but ∇f (p ′ _i ) = wbn ′ _i + (1−wb ) (N _i , 0). Hereinafter, the significance of the parameter wb in the constraint condition (B ′) will be described with reference to FIG.

3A to 3D are schematic cross-sectional views showing the zero-level curved surface Z ′ = {x′∈R ^s × R ^r | f (x ′) = 0} together with the image manifold M, respectively. (Upper stage), a plan view (middle stage) showing a zero level curve Z = {xεR ^s | f (r (x)) = 0} together with an image I, and a zero level curved surface Z ′ = {x′εR ⁵ is a perspective view showing ^s × R ^r | f (x ′) = 0} together with an image manifold M. FIG. 3A shows the parameter wb set to 0.0, FIG. 3B shows the parameter wb set to 0.1, and FIG. 3C shows the parameter wb. FIG. 3D shows the parameter wb set to 1.0, with the value set to 0.5.

When wb = 1, ∇f (p ′ _i ) is substantially orthogonal to the position space R ^s as shown in FIG. As a result, the zero-level curved surface Z ′ becomes a curved surface (an arm-shaped curved surface opened in the positive direction of the I axis) substantially parallel to the position space R ^s . For this reason, the zero-level curved surface Z ′ easily intersects with the inclined portion of the image manifold M (the portion where the gradient intensity | ∇I (x) | That is, the zero level curve Z can easily follow the edge of the image I. However, the zero-level curved surface Z ′ substantially parallel to the position space R ^s easily intersects with not only the peak of the image manifold M corresponding to the region D but also the other peaks of the image manifold M in the vicinity thereof. For this reason, the zero level curve Z is likely to include an extra connected component (a connected component other than the connected components surrounding the region D).

On the other hand, when wb = 0, as shown in FIG. 3A, に な る f (p ′ _i ) is parallel to the position space R ^s . As a result, the zero-level curved surface Z ′ becomes a curved surface (cylindrical curved surface surrounding the peak of the image manifold M corresponding to the region D) substantially orthogonal to the position space R ^s . In this case, the shape of the zero level curve Z is hardly affected by the image manifold M (the shape of the zero level curved surface Z ′ viewed from the positive direction of the I axis is substantially the shape of the zero level curve Z). . Therefore, the zero level curve Z does not completely follow the edge of the image I, but draws a smooth curve. However, the zero-level curved surface Z ′ substantially orthogonal to the position space R ^s is unlikely to intersect with other peaks of the image manifold M in the vicinity of the peak corresponding to the region D. For this reason, the zero level curve Z is difficult to include an extra connected component (a connected component other than the connected components surrounding the region D).

  Thus, as the value of the parameter wb approaches 0, the zero level curve Z is less likely to include an extra connected component, but the edge followability of the zero level curve Z is reduced. On the other hand, as the value of the parameter wb approaches 1, the edge followability of the zero level curve Z is improved, but the zero level curve Z is likely to include an extra connected component. Therefore, the boundary specifying device 1 employs a configuration in which the value of the parameter wb is designated by the user.

  When the zero level curve Z includes an extra connected component, the user can reset the value of the parameter wb to a smaller value. When the zero level curve Z does not follow the edge, the user can reset the value of the parameter wb to a larger value. By repeating such a setting operation several times while recalculating the zero level curve Z, it is possible to obtain a zero level curve Z that does not include an extra connected component and follows the edge. In the example shown in FIG. 3, by setting the value of the parameter wb to 0.1, a zero level curve Z that does not include an extra connected component and follows the edge can be obtained (FIG. 3B). )reference).

[Configuration example of boundary identification device]
The boundary identification device 1 can be configured using a computer (electronic computer). FIG. 4 is a block diagram illustrating a configuration of a computer 100 that can be used as the boundary identification device 1.

  As illustrated in FIG. 4, the computer 100 includes an arithmetic device 120, a main storage device 130, an auxiliary storage device 140, and an input / output interface 150 that are connected to each other via a bus 110. An example of a device that can be used as the arithmetic device 120 is a CPU (Central Processing Unit). Further, as a device that can be used as the main storage device 130, for example, a semiconductor RAM (random access memory) can be cited. An example of a device that can be used as the auxiliary storage device 140 is a hard disk drive.

As shown in FIG. 4, the input device 200 and the output device 300 are connected to the input / output interface 150. A pointing device for performing an operation to specify the points p _i and vector n _i is an example of an input device 200 connected to the input-output interface 150. Further, the display of the boundary δD together with the image I is an example of the output device 300 connected to the input / output interface 150.

  The auxiliary storage device 140 stores various programs for operating the computer 100 as the boundary specifying device 1. Specifically, an image manifold generation program, a constraint point derivation program, a constraint vector derivation program, a scalar field generation program, and a zero level set derivation program are stored.

  The arithmetic device 120 expands the respective programs stored in the auxiliary storage device 140 on the main storage device 130 and executes instructions included in the respective programs expanded on the main storage device 130, thereby executing the computer 100. Are operated as the image manifold generating unit 11, the constraint point deriving unit 12, the constraint vector deriving unit 13, the scalar field generating unit 14, and the zero level set deriving unit 15 shown in FIG.

The main storage device 130 includes an image I (an array representing), an image manifold M (an array representing), an undetermined multiplier defining a scalar field f (α _i εR, β _i εR ^{s + r} , aεR). ^The storage unit 20 (see FIG. 1) for storing the values of ^{s + r} and bεR), the B-HRBF matrix (an array that represents) appearing on the left side of the simultaneous equations (5), and the zero level set Z (an array that represents) ).

  Here, the configuration in which the computer 100 functions as the boundary specifying device 1 using the program recorded in the auxiliary storage device 140 that is an internal recording medium has been described, but the present invention is not limited to this. . That is, a configuration in which the computer 100 functions as the boundary specifying device 1 using a program recorded on an external recording medium may be employed. The external recording medium may be any computer-readable recording medium, such as a tape system such as a magnetic tape or a cassette tape, a magnetic disk such as a floppy (registered trademark) disk / hard disk, or a CD-ROM / MO / MD / Disk systems including optical disks such as DVD / CD-R, card systems such as IC cards (including memory cards) / optical cards, or semiconductor memory systems such as mask ROM / EPROM / EEPROM (registered trademark) / flash ROM Can be realized.

  Further, the computer 100 may be configured to be connectable to a communication network, and each program code described above may be supplied to the computer 100 via the communication network. The communication network is not particularly limited. For example, the Internet, intranet, extranet, LAN, ISDN, VAN, CATV communication network, virtual private network, telephone line network, mobile communication network, satellite communication. A net or the like is available. Further, the transmission medium constituting the communication network is not particularly limited. For example, even in the case of wired such as IEEE 1394, USB, power line carrier, cable TV line, telephone line, ADSL line, etc., infrared rays such as IrDA and remote control, Bluetooth ( (Registered trademark), 802.11 wireless, HDR, mobile phone network, satellite line, terrestrial digital network, and the like can also be used.

[Example of boundary identification device output]
Finally, an output example of the boundary identification device 1 will be described with reference to FIG. FIG. 5 is a diagram illustrating an output image output from the boundary identification device 1.

  In the output image shown in FIG. 5, the boundary of the region D1 corresponding to the anal sphincter and the boundary of the region D2 corresponding to the tumor specified by the boundary specifying device 1 are shown. In addition, in order to obtain the output image shown in FIG. 5, the image input to the boundary identification device 1 is an MRI image obtained by imaging a human body.

  In order to specify the boundary of the region D1 corresponding to the anal sphincter, the contour line γ1 designated by the user is 14 lines. Further, in order to specify the boundary of the region D2 corresponding to the tumor, there are four contour lines γ2 designated by the user. Thus, if the boundary specifying device 1 is used, the shape of a part having a complicated shape can be reproduced very accurately by only specifying a small number of contour lines.

[Additional Notes]
The present invention is not limited to the above-described embodiments, and various modifications can be made within the scope shown in the claims. That is, embodiments obtained by combining technical means appropriately modified within the scope of the claims are also included in the technical scope of the present invention.

  For example, in this specification, although the embodiment which assumed application to a medical MRI image was disclosed, the application range of this invention is not limited to a medical MRI image. That is, the present invention can be applied to medical images and can also be applied to industrial images. The present invention can also be applied to MRI images, CT images, confocal laser microscope images, and internal structure microscope images. be able to.

  For example, in a CT image or MRI image obtained by imaging a living body (for example, a human body), a process of specifying a boundary of a region corresponding to a part of the living body (for example, a massive part such as an organ or a tumor) This process is suitable for application of the present invention. In addition, in a confocal laser microscope image or internal structure microscope image obtained by imaging a cell, a process of specifying a boundary of a region corresponding to the cell site (for example, a cell organelle such as a nucleus or mitochondria) is also performed. This is a process suitable for application of the present invention. Furthermore, in a CT image obtained by imaging a structure (such as an industrial part), the boundary of a region corresponding to a part embedded in the structure or a bubble formed in the structure The process of specifying is also included in the scope of the present invention.

  It can be suitably used for area division of medical or industrial images.

DESCRIPTION OF SYMBOLS 1 Boundary identification apparatus 11 Image manifold generation part 12 Constraint point derivation part 13 Constraint vector derivation part 14 Scalar field generation part 15 Zero level set derivation part 100 Computer 140 Auxiliary storage device (recording medium)

Claims (8)

An area included in the s-dimensional space R ^s with respect to the image I composed of the r-dimensional pixel values I (x) corresponding to the respective points x in the s-dimensional (s is a predetermined integer of 2 or more) space R ^s boundaries [delta] D of D, a n points p _i designated as a point on the boundary [delta] D, the n number of s-dimensional vector n _i designated as the normal vector of the boundary [delta] D at each point p _i In the boundary identification device that identifies based on:
An image manifold generation unit for generating an image manifold M = {(x, wcI (x)) εR ^{s + r} | xεR ^s } corresponding to the image I (wc is an arbitrary real number greater than 0);
A constraint point deriving unit for deriving a constraint point p ′ _i = (p _i , wcI (p _i )) ∈R ^{s + r} on the image manifold M corresponding to each point p _i ;
Constraint vector n ′ _i = J (p _i ) n _i / | J (p _i ) n _i (J (p _i ) is a mapping r at point p _i, which is an s + r-dimensional vector corresponding to each s-dimensional vector n _i : a constraint vector deriving unit for deriving x → r (x) = (Jacobi matrix of x, wcI (x));
A scalar field f on the coupling space R ^{s + r} , and for each constraint point p ′ _i , the first constraint condition f (p ′ _i ) = 0 and the second constraint condition ∇f (p ′ _i ) = a scalar field generation unit that generates a smooth scalar field f satisfying wbn ′ _i + (1−wb) (n _i , 0) (wb is an arbitrary real number between 0 and 1);
A zero level set derivation unit for deriving a zero level set Z = {x∈R ^s | f (r (x)) = 0} of the scalar field f.
A boundary identification device characterized by that. The scalar field generation unit generates a scalar field f defined by the following equation:
The boundary identification device according to claim 1.
The image manifold generation unit generates the image manifold M using the value of the parameter wc designated by the user.
The boundary identification device according to claim 1 or 2, characterized in that. The scalar field generation unit generates a scalar field f using the value of the parameter wb specified by the user.
The boundary specifying device according to any one of claims 1 to 3, wherein The image I is a CT (Computed Tomography) image or MRI (Magnetic Resonance Imaging) image obtained by imaging a living body,
The region D is a region corresponding to the part of the living body in the CT image or MRI image.
The boundary identification device according to any one of claims 1 to 4, wherein An area included in the s-dimensional space R ^s with respect to the image I composed of the r-dimensional pixel values I (x) corresponding to the respective points x in the s-dimensional (s is a predetermined integer of 2 or more) space R ^s boundaries [delta] D of D, a n points p _i designated as a point on the boundary [delta] D, the n number of s-dimensional vector n _i designated as the normal vector of the boundary [delta] D at each point p _i In the boundary identification method to identify based on:
An image manifold generation step for generating an image manifold M = {(x, wcI (x)) εR ^{s + r} | xεR ^s } corresponding to the image I (wc is an arbitrary real number greater than 0);
A constraint point deriving step for deriving a constraint point p ′ _i = (p _i , wcI (p _i )) ∈R ^{s + r} on the image manifold M corresponding to each point p _i ;
Constraint vector n ′ _i = J (p _i ) n _i / | J (p _i ) n _i | (J (p _i ) is a mapping r at point p _i, which is an s + r-dimensional vector corresponding to each s-dimensional vector n _i. A constraint vector deriving step for deriving x: r (x) = (Jacobi matrix of x, wcI (x))),
A scalar field f on the coupling space R ^{s + r} , and for each constraint point p ′ _i , the first constraint condition f (p ′ _i ) = 0 and the second constraint condition ∇f (p ′ _i ) = a scalar field generation step for generating a smooth scalar field f satisfying wbn ′ _i + (1−wb) (n _i , 0) (wb is an arbitrary real number not less than 0 and not more than 1);
Deriving a zero level set Z = {xεR ^s | f (r (x)) = 0} of the scalar field f.
A boundary identification method characterized by that.   A program for operating a computer as the boundary specifying device according to any one of claims 1 to 5, wherein the computer functions as each part of the boundary specifying device.   A computer-readable recording medium on which the program according to claim 7 is recorded.