WO2014133150A1 - Method for building three-dimensional model of organ, and program - Google Patents

Abstract

The present invention is a method for building a three-dimensional model of an organ, employing any of the following. If a subsequently selected pair of points to be linked both return to a starting point, a seventh procedure is terminated. Depending on the case, candidate points adjacent to one point to be linked and another point to be linked are selected as the next pair of points to be linked. The distance from the one point to be linked to a candidate point adjacent to the other point to be linked and the distance from the other point to be linked to a candidate point adjacent to the one point to be linked are calculated by three-dimensional space conversion, taking into consideration the distance between layers. The two points having the shorter distance therebetween among the two calculated distances are selected as the next pair of points to be linked.

Description

Method and program for organ 3D model construction Cross-reference of related applications

This international application claims priority based on Japanese Patent Application No. 2013-039593 filed with the Japan Patent Office on February 28, 2013, and Japanese Patent Application No. 2013-039593 The entire contents are incorporated into this international application.

The present invention relates to a method for constructing a three-dimensional model from a tomographic image of an organ such as a heart imaged by a tomography apparatus such as MRI (Magnetic Resonance Imaging) or CT (Computed Tomography).

In recent years, dynamic simulation of human organs using computer simulation has attracted attention. In addition, it is necessary to design a treatment tool used for the treatment of an organ disease according to the shape and symptoms of an individual patient, and computer simulation using an organ analysis model is effective.

For example, when designing a heart shape correction net for dilated cardiomyopathy currently under research and development, it is necessary to design the shape of each part of the net in accordance with the heart of the individual patient. Dynamic simulation is indispensable.

In order to carry out such a computer simulation of the heart, a 3D model of the heart to be analyzed is required. When a computer simulation is actually used in the design, the 3D model of the heart is constructed in a short time. It is important to.

Several techniques for constructing a three-dimensional model from a tomographic image of an organ imaged by a tomography apparatus have already been proposed (see, for example, Non-Patent Documents 1, 2, and 3). For example, in the technique described in Non-Patent Document 1, the shape of the heart is extracted semi-automatically from the MRI image. In the case of the technique described in Non-Patent Document 1, the shape of the heart lumen is extracted automatically. Regarding the shape of the outside of the heart, several markers are manually placed in each of the MRI images for a plurality of layers (slices), and the finite element model is deformed and fitted.

In the technique described in Non-Patent Document 2, MRI images are also used. Specifically, the parameters of the finite element model are fitted by manually placing markers on the MRI image. In this technique, only the left ventricle is targeted for extraction.

In the technique described in Non-Patent Document 3, CT images are used. Specifically, the heart shape is extracted from the CT image completely automatically. This technique is realized by utilizing the high image accuracy of CT.

By the way, when constructing a three-dimensional model from a plurality of tomographic images as described above, points distributed on each of a plurality of two-dimensional planes are connected by lines between adjacent two-dimensional planes, and are constituted by those lines. A method of generating a polygon and generating a three-dimensional model is used. When creating a triangular polygon by connecting a point and two other points with a line, one simple method is to select the two closest points based on the distance from the point and link (link) ) Can be considered.

However, when a three-dimensional model is constructed from a plurality of tomographic images as described above by such a simple method, for example, the direction of a boundary line (a line corresponding to the position of the outer surface or inner surface) that appears in an organ cross section suddenly changes. An unnatural link may be set in an edge portion or the like. Therefore, when such an unnatural link is set, there is a problem that the shape of the finally obtained three-dimensional model becomes unnatural.

In order to eliminate such unnaturalness, conventionally, it is necessary to manually adjust the shape of the final three-dimensional model. For this reason, it is difficult to automate this part, which is a cause of the time required for model creation.

It is desirable to provide a method for constructing a 3D model of an organ that can make the shape of the finally obtained 3D model more natural without relying on manual adjustment.

One aspect of the method for constructing a three-dimensional model of an organ of the present invention is a boundary line indicating an outer surface of an organ or an inner surface of an organ specified on a two-dimensional cross-sectional image of each layer obtained by imaging an organ over a plurality of layers with a tomography apparatus. Based on the first processing procedure for setting a plurality of points to be vertices of a triangular polygon on the boundary line, and on the two-dimensional cross-sectional image at each point set in the first processing procedure A second processing procedure for obtaining a tangential direction of the boundary line, and sequentially selecting a pair of adjacent layers from the plurality of layers while shifting one layer at a time, so that the boundary line of each layer is on the same plane For each point projected and set on both projected boundary lines, the distance from each point on the boundary line different from the boundary line including the reference point to the reference point, with each point as a reference point Calculate For each of the third processing procedure and the two points that are subject to calculation of the distance in the third processing procedure, an angle formed by the tangential directions corresponding to the two points is obtained, and the angle becomes large. A fourth coefficient for correcting the distance is obtained by obtaining a coefficient whose value after correction becomes larger than the value before correction and multiplying the coefficient by the distance between two points corresponding to the coefficient. And selecting the shortest distance from a plurality of corrected distances corresponding to one reference point based on the corrected distance corrected by the fourth processing procedure, and the reference A fifth processing procedure for setting a point at which the distance to a point is the shortest distance as a shortest point corresponding to the reference point, and a pair of layers adjacent to each other among the plurality of layers. Select the two layers in sequence by shifting them one by one. Each time, the reference point and the shortest point at which the distance to the shortest point corresponding to the reference point is the shortest when each point set on the boundary line in one layer is the reference point, A sixth processing procedure set as a starting point and a plurality of pairs of link target points where a link corresponding to one side of a triangular polygon is set from the two boundary lines where the starting point is set by the sixth processing procedure A pair of the starting points is selected as a pair of link target points, and thereafter, each of the points that are advanced from the selected link target point by one point around the predetermined direction to the next. Using the point as a candidate point, one of the pair of link target points previously selected and the candidate point on the boundary line different from the one link target point are used as the next pair of link targets. As a point And a seventh processing procedure that repeats the processing to be selected is executed by a computer to construct a three-dimensional model of the organ. In the seventh processing procedure, (A) is selected next. When the pair of link target points both return to the starting point, the seventh processing procedure is terminated, and (B) the pair of link targets previously selected in cases other than (A) When one link target point has already returned to the starting point among the points, the one link target point and the candidate point adjacent to the other link target point are used as the next pair of link target points. (C) In cases other than (A) and (B) above, the other link target up to the shortest point corresponding to one link target point among the pair of link target points previously selected The point has not been advanced and before When the one link target point has already been advanced to the shortest point corresponding to the other link target point, the one link target point and the candidate point next to the other link target point are It is selected as the next pair of link target points. (D) In cases other than (A), (B), and (C), one of the pair of link target points previously selected is one link target point And the distance between the candidate point next to the other link target point and the distance between the other link target point and the candidate point next to the one link target point, taking into account the distance between the layers Calculation is performed in three-dimensional space conversion, and two points forming the shorter distance among the two calculated distances are selected as the next pair of link target points.

In one aspect of the present invention configured as described above, in the first processing procedure, a plurality of points that are vertices of a triangular polygon are set on the boundary line indicating the outer surface of the organ or the inner surface of the organ. The boundary line used in the first processing procedure is obtained by imaging a plurality of layers of an organ in advance with a tomography apparatus and is identified on the two-dimensional cross-sectional image, but is identified by any technique. It doesn't matter.

For example, the boundary line itself may be manually specified on the two-dimensional cross-sectional image and the data provided, or a point on the boundary line may be manually specified on the two-dimensional cross-sectional image and based on the data A boundary line may be estimated. As such an estimation method, for example, a method of connecting the points specified on the boundary line by a cubic spline curve and adopting the curve as the boundary line can be considered. In this case, after generating the cubic spline curve, the data may be provided, or data indicating points on the boundary line is provided, and based on the data, the first processing procedure is performed. A cubic spline curve may be generated.

Based on the boundary line data obtained in this way, in the first processing procedure, a plurality of points that are vertices of triangular polygons are set on the boundary line. The number of points set here is not particularly limited, but the larger the number, the smoother the surface shape of the model finally obtained. Also, the distance between adjacent points can be set arbitrarily. For example, it may be set at an equal interval, or the point is set at a position where the center angle is equal to the center set near the center of the boundary line. Alternatively, it may be set at unequal intervals if necessary.

When a plurality of such points are set, a pair of points satisfying a predetermined condition is selected as a link target point by the second processing procedure to the seventh processing procedure. The link target points selected here are points (points at both ends of one side) forming one side of the triangular polygon in the finally obtained three-dimensional model. Note that such link target points only need to be stored as data indicating that, for example, whether to draw and display a three-dimensional model based on the stored data, or to use for purposes other than such display It is arbitrary.

In the second processing procedure to the seventh processing procedure, in particular, the distance obtained in the third processing procedure is corrected in the fourth processing procedure using the tangential direction obtained in the second processing procedure. There is a feature in the point. When the subsequent processing procedure is executed after such correction, the link target is not simply selected because the distance between the points is short, but there is no difference in the tangential direction as an important condition. After that, the link target is selected.

For this reason, in the portion having a similar tangent direction between the boundary lines of adjacent layers, a link is likely to be set between points in the portion, while in a portion where the tangential direction is greatly different, between the points in the portion. Unnatural links are not set. As a result, an unnatural triangular polygon is not generated on the finally obtained three-dimensional model, and a more natural three-dimensional model can be constructed.

Hereinafter, an example of a configuration that is preferably adopted in the present invention will be described. First, the fourth processing procedure corrects the point-to-point distance as the tangential direction is greatly different, thereby making it difficult to set a link between the points when determining the link target. .

Therefore, a specific correction method is not limited as long as such correction can be made. However, a preferable example can be given. That is, in the fourth processing procedure, when the angle Δθ formed by the tangential directions is obtained, based on the formula: c = 1 / (cos (Δθ)) 2, as the angle Δθ becomes larger, the correction becomes smaller. This is a procedure for correcting the distance by obtaining a coefficient c having a large corrected value with respect to the value of, and multiplying the coefficient c by the distance between two points corresponding to the coefficient c. It is preferable. According to the three-dimensional model construction method configured as described above, correction as expected can be performed in the fourth processing procedure.

Secondly, when both borders of adjacent layers are single annular borders, the link target may be selected by the above-mentioned method, but the organ is bifurcated. There may be places. In that case, two annular boundaries may be formed in one layer. In such a case, conventionally, manual adjustment (manual link target selection or polygon creation) has to be relied upon, which has been an obstacle to automating the creation of a three-dimensional model.

It is preferable to adopt the following configuration as a measure for removing such obstacles. That is, in the first treatment procedure, the outer surface of the organ or the inner surface of the organ is bifurcated, so that one layer has a single boundary line L and the next layer has two boundaries. When the lines U1 and U2 exist, the respective centroids G1 and G2 are calculated for the two boundary lines U1 and U2, and a straight line connecting the two centroids G1 and G2 and the two boundary lines U1, U2 and , Intersection points A and B are obtained, and a plurality of points set on the single boundary line L are evaluated as to which of the two boundary lines U1 and U2 is closer, and a boundary point that becomes a boundary at which the two points switch C and D are obtained, the midpoint M1 of the line segment AB connecting the intersections A and B and the midpoint M2 of the line segment CD connecting the boundary points C and D are obtained, and the length D1 of the line segment AB and the line segment CD are calculated. The length D2 is obtained, and the line segment M1-M2 connecting the midpoints M1, M2 is set to the internal ratio of D1: D2. A dividing point E is obtained, a single boundary line L is divided into two parts at boundary points C and D, and one of the divided parts close to the boundary line U1, a line segment CE and a line The boundary line L1 is constituted by the segment ED, and the boundary line L2 is constituted by the other part close to the boundary line U2, the line segment CE and the line segment ED, and on the boundary lines U1, U2, L1, and L2, A plurality of points as vertices of a triangular polygon are set, and in the second processing procedure to the seventh processing procedure, the boundary lines U1 and L1 and the boundary lines U2 and L2 are targeted. Select the link target point.

According to the three-dimensional model construction method configured as described above, since the single boundary line L is divided into the two boundary lines L1 and L2 in the bifurcated portion of the organ, the link target selection process is performed. A link target can be selected between each of the two boundary lines U1 and U2. Moreover, since the two boundary lines L1 and L2 share the line segment CE and the line segment ED, the points on the line segment CE and the line segment ED are located on the two boundary lines U1 and U2, respectively. Paired with the set point is set as a link target, so that a triangular polygon can be appropriately arranged even at a branching point.

Third, when multiple layers of tomographic images are taken, the image is not taken at the position on the opposite side of the layer that is the secondmost from the end with the layer at the farthest end sandwiched, but the most of the organ. There is an end (the extreme end of the outer surface or the extreme end of the lumen). Therefore, when it is desired to appropriately model the end of the organ in the three-dimensional model, it is preferable to employ the following configuration.

That is, one end point that is the apex of the triangular polygon is set at a position opposite to the second layer from the end across the layer at the end of the plurality of layers. , Including an edge processing procedure for selecting a pair of the extreme end point and each point on the boundary line of the outermost layer as a link target point, and the edge processing procedure is parallel to each of the plurality of layers. X coordinates xMin1, xMax1 at both ends of the distribution range in the x direction of the boundary line of the outermost layer, where x direction and y direction are two directions orthogonal to each other and z direction is a direction orthogonal to each of the plurality of layers. , Y coordinates yMin1, yMax1 at both ends of the distribution range in the y direction, and x coordinates xMin2, xMax2 at both ends of the distribution range in the x direction of the boundary line of the layer second from the end, and both ends of the distribution range in the y direction of The coordinates yMin2 and yMax2 are obtained, and two boundary line shifts dx1 = xMin1-xMin2, dx2 = xMax2-xMax1 at both end positions in the x direction, and two boundary line shifts dy1 = yMin1 at both end positions in the y direction. -YMin2, dy2 = yMax2-yMax1 is obtained, and the x-coordinate xMok of the point that internally divides between the x-coordinates xMin1, xMax1 by the ratio of dx1: dx2, and the y-coordinate xMin1, yMax1 between dy1: dy2 The y coordinate yMok of the point to be internally divided by the ratio is obtained, and based on the distance dz1 between the layer at the end and the layer second from the end, and the x coordinate xMin1, xMax1, xMin2, xMax2 , The distance dz2x from the outermost layer is (xMax1-xMin1): (xMax2- Min2) = dz2x: A distance dz2x satisfying a relationship of (dz1 + dz2x) is obtained, and a distance dz1 between the layer located at the end and the layer located second from the end, and the y coordinates yMin1, yMax1, yMin2, yMax2 Based on the above, a distance dz2y satisfying the relationship of (yMax1-yMin1) :( yMax2-yMin2) = dz2y: (dz1 + dz2y) is obtained from the distance dz2y from the outermost layer, and two distances dz2x, dz2y Among them, the smaller one is a distance dz2, and in a three-dimensional space, a point P that is equidistant from the x coordinates xMin1, xMax1 and equidistant from the y coordinates yMin1, yMax1, and a distance dz2 from the point P in the z direction. And the point Q of the x coordinate xMok and the y coordinate yMok A point R that internally divides the line segment PQ connecting the two lines into PR: RQ = 2: 1 is obtained, and the point R is set as the end point. According to the three-dimensional model construction method configured as described above, it is possible to appropriately form a three-dimensional model even at the extreme end of the organ.

The program for constructing a 3D model of an organ of the present invention according to one aspect is a program for causing a computer to execute the 3D model construction method as described above. Therefore, the operation and effect as described for the above-described three-dimensional model construction method are exhibited. Note that this three-dimensional model construction program also preferably has a processing procedure corresponding to the bifurcated portion of the organ and a processing procedure corresponding to the extreme end of the organ. Such a program can be provided by being recorded on various recording media that can be read by a computer, or can be provided in a state of being installed in a computer.

FIG. 1A is an explanatory diagram showing a configuration of the entire system that executes a 3D model construction process of an organ, and FIG. 1B is a flowchart of each process that constitutes the 3D model construction process. FIG. 2A is an explanatory diagram illustrating a boundary line drawn on a tomographic image of an organ, and FIGS. 2B and 2C are explanatory diagrams illustrating a procedure for selecting a link target from points set on the boundary line. FIG. 3A is an explanatory diagram showing a three-dimensional model configured by the three-dimensional model construction process of the present invention, and FIG. 3B is an explanatory diagram showing a three-dimensional model in which a link target is selected without correcting the distance between points. Explanatory drawing which shows the method of three-dimensionalization in the forked part of an organ. Explanatory drawing which shows the method of three-dimensionalization in the extreme end part of an organ.

DESCRIPTION OF SYMBOLS 1 ... Image processing workstation, 2 ... Tomography apparatus, 11 ... Control part, 12 ... Memory | storage part, 13 ... Display part, 14 ... Operation part.

Next, an embodiment of the present invention will be described with an example.
[System configuration]
In the embodiment described below, as shown in FIG. 1A, using an equipment including an image processing workstation 1 (corresponding to an example of a computer referred to in the present invention) and a tomography apparatus 2, the tertiary of the organ Build the original model. The image processing workstation 1 includes a control unit 11 having a known CPU, ROM, RAM, and the like, and a storage unit 12 in which various software such as an OS (Operating System) and an application program such as a 3D model construction program are stored. And a display unit 13 for displaying various types of information, and an operation unit 14 configured by a touch panel, other pointing devices, a keyboard, or the like.

The tomography apparatus 2 is a nuclear magnetic resonance diagnostic apparatus or a multi-row detector type CT diagnostic apparatus. As is well known, the nuclear magnetic resonance diagnostic apparatus is an apparatus for taking a tomographic image of a human body using nuclear magnetic resonance. As is well known, the multi-row detector CT diagnostic apparatus is an apparatus for taking a tomographic image of a human body using X-rays. Tomographic image data (MRI imaging data or CT contrast data) imaged by the tomography apparatus 2 is transmitted to the image processing workstation 1. The image processing workstation 1 performs boundary line extraction processing and three-dimensional polygon processing as described below based on the transmitted tomographic image data.

In the boundary line extraction process, as shown in FIG. 1B, first, an MRI (CT) tomographic image is taken (S1), followed by preprocessing of the image (S2), and further, the boundary line of the organ is extracted. Performed (S3). Among these, MRI (CT) tomographic imaging is performed by the tomographic apparatus 2. In S1, a tomographic image of an organ is captured over a plurality of layers at positions spaced in one direction. Thereby, tomographic image data for a plurality of layers is generated, and the plurality of tomographic image data is transmitted to the image processing workstation 1.

In the image processing workstation 1, image preprocessing is executed. In this image preprocessing, image processing for increasing the contrast (brightness / darkness difference) of the image, image processing for emphasizing the edge, and the like are performed, which makes it easier for the operator to recognize the boundary line of the outer surface or inner surface of the organ. . Subsequently, in the image processing workstation 1, an organ boundary line is extracted. In the case of the present embodiment, the image processing workstation 1 displays the tomographic image that has been preprocessed in S2 on the display unit 13 and receives an operation on the operation unit 14.

In this state, the operator operates the pointing device to specify some points on the boundary line to be extracted on the tomographic image displayed on the display unit 13. Here, when three or more points are designated, the image processing workstation 1 generates a cubic spline curve passing through each designated point, and the spline curve is displayed on the tomographic image displayed on the display unit 13. Overlapping display. FIG. 2A shows a display example in which a tomographic image of the heart, a plurality of points specifying boundary points on the tomographic image, and a cubic spline curve passing through the plurality of points are displayed on the display unit 13 in an overlapping manner.

The operator can adjust the shape of the spline curve by observing the displayed spline curve and specifying the point that seems to be necessary, so that the shape of the spline curve can be adjusted to the shape of the boundary line to be extracted. Can be brought closer. Note that the spline curve generation processing is performed on all of the tomographic images of a plurality of layers photographed by the tomography apparatus 2.

If the spline curve having the desired shape can be obtained in this way, the image processing workstation 1 executes a three-dimensional polygon processing based on the obtained spline curve data. In the three-dimensional polygon processing, at points other than the bifurcated part of the organ, the vertices of the triangular polygon are set on the boundary line, and the sides of the triangular polygon are set between the vertices (S11). Further, in the bifurcated portion of the organ, a boundary line is additionally set in the bifurcated portion, a vertex of the triangular polygon is set on the boundary line, and a side of the triangular polygon is set between the vertices (S12). At the extreme end of the organ, an extreme end point is additionally set next to the extreme end layer, and a triangular polygon side is set between vertices on the boundary line between the extreme end point and the extreme end layer (S13).

The processes of S11 to S13 may be performed in any order. In addition, the three-dimensional model of the organ obtained by the above processing can be used for various purposes. For example, the present invention can be used not only for displaying a three-dimensional shape as an image on a computer, but also for forming a three-dimensional object that actually reproduces the three-dimensional shape using a so-called 3D printer. It can also be used to analyze the three-dimensional shape of an organ and design a medical instrument for application to the organ.

[Details of S11]
Next, the processing procedure executed in S11 will be described in detail. In S11, according to the procedures # 1 to # 7 described below, points that become the vertices of the triangular polygon are set on the boundary lines at the adjacent positions, and the sides of the triangular polygon are selected between the vertices selected according to the predetermined procedure. Set the link that becomes. First, a plurality of points that are vertices of a triangular polygon are set on the boundary line (spline curve) obtained in S3 (procedure # 1). The points set here may or may not include the point specified by the user in S3, but in any case, the number necessary for generating the polygon on the above-mentioned spline curve. (It is an arbitrary number, but if it gives an example, about 100 points) are set.

Next, the tangential direction of the boundary line on the two-dimensional cross-sectional image at each point set in the procedure # 1 is obtained (procedure # 2). The tangential direction obtained in this procedure # 2 is stored in association with each point so that it can be used later. Subsequently, a pair of layers at adjacent positions is sequentially selected from a plurality of layers while shifting one layer at a time, and the boundary lines of each layer are projected on the same plane and set on both projected boundary lines. For each point, using each point as a reference point, the distance from each point on the boundary line different from the boundary line including the reference point to the reference point is calculated (procedure # 3).

Next, for each of the two points whose distances are to be calculated in step # 3, an angle formed by the tangential directions corresponding to each of the two points is obtained. A coefficient having a large value after correction is obtained, and the distance is corrected by multiplying the coefficient by the distance between two points corresponding to the coefficient (procedure # 4). In this embodiment, in step # 4, when the angle Δθ formed by the tangential directions is obtained, the value before correction is increased as the angle Δθ becomes larger based on the formula: c = 1 / (cos (Δθ)) 2. The coefficient c for which the value after correction becomes large is obtained. Then, the distance is corrected by multiplying the coefficient c by the distance between the two points corresponding to the coefficient c.

Then, based on the corrected distance corrected in step # 4, the shortest distance is selected from a plurality of corrected distances corresponding to one reference point, and the distance from the reference point becomes the shortest distance. The point is set to the shortest point corresponding to the reference point (procedure # 5). That is, in procedure # 5, the shortest point is set one by one in association with each point on the boundary line. When the point p1 is used as a reference, even when the shortest point with respect to the point p1 is the point p2, the shortest point with respect to the point p2 may be the point p3 when the point p2 is used as a reference. Therefore, the relationship between these reference points and the shortest points is stored for all points on the boundary line.

Next, select a pair of adjacent layers by shifting one layer at a time from multiple layers, and each point set on the boundary line in one layer each time the two layers are selected. The reference point and the shortest point with the shortest distance to the shortest point corresponding to the reference point are set as starting points (step # 6). That is, in procedure # 6, there is a relationship between the reference point and the shortest point, and the distance becomes the shortest and two points are selected and used as the starting point.

Then, a plurality of pairs of link target points on which links corresponding to one side of the triangular polygon are set are selected from the two boundary lines where the starting points are set in step # 6 (step # 7). . That is, first, as shown in FIG. 2B, k11 and k21 as the pair of starting points are selected as a pair of link target points. Thereafter, the respective points k12 and k22 that are advanced by one point around the predetermined direction (for example, around the direction indicated by the one-dot chain line arrow in FIG. 2B) from the selected link target point are used as candidate points. Either one of the selected pair of link target points k11 and k21 and a candidate point (k22 in the case of k11, k12 in the case of k21) on a boundary line different from the one link target point are The process of selecting as a pair of link target points is repeated.

Which of k12 and k22 is to be selected is determined by the method described later. For example, in the example shown in FIG. 2B, when the points k12 and k21 are selected as the next pair of link target points. As shown in FIG. 2C, at a position advanced from the selected link target points k12, k21 by one point around the predetermined direction (in the case of this embodiment, around the direction indicated by the one-dot chain line arrow in FIG. 2C). Each point k13, k22 is set as a new candidate point, and one of the pair of link target points k12, k21 selected previously and a candidate point (k12 of k12) on a different boundary line from the one link target point K22 in the case, and k13) in the case of k21 are selected as the next pair of link target points. If this process is repeated, the space between the two boundary lines is divided into a plurality of triangular areas by line segments connecting the link target points, so the boundary lines are filled with triangular polygons corresponding to the triangular areas. Thus, the three-dimensional modeling of the area between the boundary lines can be achieved.

By the way, in this procedure # 7, a pair of link target points is formulated according to the following conditions (A) to (D).
(A) If both of the pair of link target points to be selected next return to the starting point, the procedure # 7 is terminated. That is, when all the two boundary lines are divided into triangular regions, the processing is finished.
(B) In cases other than (A), when one link target point has already returned to the starting point among the pair of link target points previously selected, the one link target point and the other link target point Candidate points next to the points are selected as the next pair of link target points. That is, if the link target point makes a round on one boundary line and returns to the starting point, all candidate points remaining on the other boundary line are paired with the starting point on one boundary line as the link target point.
(C) In cases other than (A) and (B), the other link target point is advanced to the shortest point corresponding to one link target point among the pair of link target points previously selected. If one link target point has already been advanced to the shortest point corresponding to the other link target point, the one link target point and the candidate point next to the other link target point are The next pair of link target points is selected. That is, when selecting link target points, a pair of link target points is selected in consideration of the relationship with the shortest point corresponding to each point.
(D) In cases other than (A), (B), and (C), among the pair of link target points selected previously, a candidate point adjacent to one link target point and the other link target point And the distance between the other link target point and the candidate point next to the one link target point are calculated in terms of a three-dimensional space that takes into account the distance between the layers. The two points forming the shorter distance are selected as the next pair of link target points. That is, only in cases other than (A), (B), and (C), a pair of link target points is selected by a general method while paying attention to the distance between points in the three-dimensional space for the first time.

Thus, in the procedure for selecting the link target as described above (procedure # 7), the distance obtained in procedure # 3 is corrected in procedure # 4 using the tangential direction obtained in advance in procedure # 2. The link target is selected in consideration of the determination based on the corrected distance. Therefore, unlike the technology in which the link target is selected simply because the distance between the points in the three-dimensional space is short, the link target is selected after considering that there is no difference in the tangential direction as an important condition. The As a result, in the portion having a similar tangent direction between the boundary lines of adjacent layers, a link is likely to be set between the points in that portion, while in the portion having a greatly different tangent direction, the point between the points in that portion Unnatural links are no longer set in

For example, for example, in the regions A1 and A2 illustrated in FIG. 3A, the boundary lines at adjacent positions have similar shapes in the tangent direction. In such a case, points whose tangent slopes are relatively close are selected as link targets, and as a result, the triangular polygons generated there form a natural curved surface in appearance. When relatively close points are selected as link targets based only on the distance in the three-dimensional space, for example, on the boundary line in the region A3 as in the regions A3 and A4 illustrated in FIG. 3B, for example. All the points are paired with points in the limited area A4, and as a result, an unnatural curved surface that looks like a part of a cone in appearance may be formed locally. Therefore, selecting a link target point by the above-described method does not generate an unnatural triangular polygon on the finally obtained three-dimensional model, and constructs a more natural three-dimensional model. be able to.

[Details of S12]
When an organ has a bifurcated portion, two annular boundary lines may be formed in one layer. In such a case, a pair of link target points is selected by the following procedure at a stage corresponding to the above-described procedure # 1. First, as shown in FIG. 4A, if two layers adjacent to each other have a single boundary line L in one layer and two boundary lines U1 and U2 in the adjacent layer, the two boundary lines For U1 and U2, the respective centroids G1 and G2 are calculated. Then, intersections A and B between the straight line connecting the two centroids G1 and G2 and the two boundary lines U1 and U2 are obtained.

Also, with respect to a plurality of points set on a single boundary line L, it is evaluated which of the two boundary lines U1 and U2 is closer to each other, and boundary points C and D serving as boundaries at which the two points are switched are obtained. Then, as shown in FIG. 4B, the midpoint M1 of the line segment AB connecting the intersections A and B and the midpoint M2 of the line segment CD connecting the boundary points C and D are obtained. Subsequently, the length D1 of the line segment AB and the length D2 of the line segment CD are obtained, and a point E is obtained by dividing the line segment M1-M2 connecting the midpoints M1, M2 by the internal ratio of D1: D2.

Then, as shown in FIG. 4C, a single boundary line L is divided into two parts at boundary points C and D, and one of the divided parts close to the boundary line U1 and a line segment CE. The boundary line L1 is configured by the line segment ED, and the boundary line L2 is configured by the other part near the boundary line U2, the line segment CE, and the line segment ED. After dividing the single boundary line L into two boundary lines L1 and L2, a plurality of points which are the vertices of the triangular polygon are set on the boundary lines U1, U2, L1 and L2, and the procedure # 2 to procedure # 7, a link target point is selected between the boundary lines U1 and L1 and between the boundary lines U2 and L2.

If the link target point is set by such a method, since the single boundary line L is divided into the two boundary lines L1 and L2 in the bifurcated portion of the organ, the link target selection process is performed. A link target can be selected between each of the two boundary lines U1 and U2. Moreover, since the two boundary lines L1 and L2 share the line segment CE and the line segment ED, the points on the line segment CE and the line segment ED are located on the two boundary lines U1 and U2, respectively. Paired with the set point is set as a link target, so that a triangular polygon can be appropriately arranged even at a branching point.

[Details of S13]
As shown in FIG. 5A, when it is desired to place a triangular polygon at the extreme end of the organ, the following procedure is adopted. That is, the x direction and the y direction are two directions parallel to each of the layers and orthogonal to each other, and the direction perpendicular to each of the layers is the z direction. The coordinates xMin1, xMax1 and the y coordinates yMin1, yMax1 at both ends of the distribution range in the y direction are obtained (see FIG. 5B).

Also, x coordinates xMin2, xMax2 at both ends of the distribution range in the x direction of the boundary line of the second layer from the end, and y coordinates yMin2, yMax2 at both ends of the distribution range in the y direction are obtained. FIG. 5B illustrates the state seen from the direction in which the x and z coordinates can be seen, but the state seen from the direction in which the y and z coordinates are visible is obtained by replacing x in FIG. The same.)

Next, two boundary line deviations dx1 = xMin1-xMin2, dx2 = xMax2-xMax1 at both end positions in the x direction and two boundary line deviations dy1 = yMin1-yMin2, dy2 = yMax2− at both end positions in the y direction. Obtain yMax1. Subsequently, the x coordinate xMok of the point that internally divides the x coordinate xMin1, xMax1 by the ratio of dx1: dx2, and the y coordinate yMok of the point that internally divides the y coordinate yMin1, yMax1 by the ratio of dy1: dy2. Ask for.

Then, based on the distance dz1 between the outermost layer and the second layer from the end, and the x coordinates xMin1, xMax1, xMin2, xMax2, the distance dz2x from the outermost layer is (xMax1- The distance dz2x that satisfies the relationship xMin1) :( xMax2-xMin2) = dz2x: (dz1 + dz2x) is obtained. Further, based on the distance dz1 between the layer at the endmost and the layer at the second end from the end and the y coordinates yMin1, yMax1, yMin2, yMax2, the distance dz2y from the layer at the end is (yMax1- The distance dz2y satisfying the relationship yMin1) :( yMax2-yMin2) = dz2y: (dz1 + dz2y) is obtained.

The smaller one of these two distances dz2x and dz2y is defined as a distance dz2, and in a three-dimensional space, a point P that is equidistant from the x coordinate xMin1, xMax1, and equidistant from the y coordinate yMin1, yMax1, and from the point P A point R is obtained by dividing a line segment PQ that is separated by a distance dz2 in the z direction and connects the point Q that is the x coordinate xMok and the y coordinate yMok into PR: RQ = 2: 1. Is the extreme end point. Thus, since the end point R is determined, a pair of each point on the boundary line L and the end point R can be selected as a link target point, and a triangular polygon can be appropriately arranged even at the shortest point.

[Other Embodiments]
As mentioned above, although embodiment of this invention was described, this invention is not limited to said specific one Embodiment, In addition, it can implement with a various form.

For example, in the above-described embodiment, in step # 4, the coefficient c is obtained based on the mathematical formula: c = 1 / (cos (Δθ)) 2 in order to correct the point-to-point distance as the tangential direction is significantly different. In the above description, the coefficient c is multiplied by the distance between the two points corresponding to the coefficient c. However, the expression itself is not limited to the above expression as long as the coefficient c capable of equivalent correction can be obtained.

Claims (5)

1. Based on the boundary line indicating the outer surface of the organ or the inner surface of the organ specified on the two-dimensional cross-sectional image of each layer obtained by imaging the organ over a plurality of layers with the tomography apparatus, the vertex of the triangular polygon is set on the boundary line. A first processing procedure for setting a plurality of points,
   A second processing procedure for obtaining a tangential direction of the boundary line on the two-dimensional cross-sectional image at each point set in the first processing procedure;
   From among the plurality of layers, a pair of layers at adjacent positions are sequentially selected while being shifted one layer at a time, and the boundary lines of each layer are projected on the same plane, and each of the layers set on both projected boundary lines is selected. A third processing procedure for calculating a distance from each point on a boundary line different from the boundary line including the reference point to the reference point, with each point as a reference point;
   For each of the two points that are subject to calculation of the distance in the third processing procedure, an angle formed by the tangential directions corresponding to the two points is determined. The larger the angle, the more the value before correction. A fourth processing procedure for correcting the distance by obtaining a coefficient with a large value after correction and multiplying the coefficient by the distance between two points corresponding to the coefficient;
   Based on the corrected distance corrected by the fourth processing procedure, the shortest distance is selected from a plurality of corrected distances corresponding to one reference point, and the distance to the reference point is A fifth processing procedure for setting the shortest distance to the shortest point corresponding to the reference point;
   Each of the points set on the boundary line in one layer is selected from the plurality of layers by sequentially selecting a pair of adjacent layers while shifting one layer at a time. A sixth processing procedure for setting the reference point and the shortest point at which the distance to the shortest point corresponding to the reference point as the reference point is the shortest as a starting point, respectively;
   A procedure of selecting a plurality of pairs of link target points where a link corresponding to one side of a triangular polygon is selected from the two boundary lines where the starting point is set by the sixth processing procedure, The starting point is selected as a pair of link target points, and thereafter, each point at a position advanced by one point around the predetermined direction from the selected link target point as a candidate point is selected as a pair of points previously selected. A seventh processing procedure of repeating the process of selecting any one of the link target points and the candidate point on the boundary different from the one link target point as the next pair of link target points A method for constructing a three-dimensional model of an organ by causing a computer to execute processing including and
   In the seventh processing procedure,
   (A) When both of the pair of link target points to be selected next return to the starting point, the seventh processing procedure is terminated,
   (B) In a case other than (A) above, when one link target point has already returned to the starting point among the pair of link target points previously selected, the one link target point and the other The candidate point next to the link target point is selected as the next pair of link target points,
   (C) In cases other than (A) and (B), the other link target point advances to the shortest point corresponding to one link target point among the pair of link target points previously selected. If the one link target point has already been advanced to the shortest point corresponding to the other link target point, the one link target point is adjacent to the other link target point. The candidate points in are selected as the next pair of link target points,
   (D) In cases other than (A), (B), and (C), among the previously selected pair of link target points, the link target point and the other link target point are adjacent to each other. The distance between the candidate point and the distance between the other link target point and the candidate point adjacent to the one link target point are calculated in terms of a three-dimensional space considering the distance between layers, and the calculation is performed. A method for constructing a three-dimensional model of an organ, in which two points that are shorter of the two distances are selected as the next pair of link target points.
2. In the fourth processing procedure, when the angle Δθ formed by the tangential directions is obtained, based on the formula: c = 1 / (cos (Δθ)) 2, the value before correction increases as the angle Δθ increases. The coefficient c having a large value after correction is obtained, and the distance is corrected by multiplying the coefficient c by the distance between two points corresponding to the coefficient c. 2. A method for constructing a three-dimensional model of an organ according to 1.
3. In the first processing procedure,
   When the outer surface of the organ or the inner surface of the organ is bifurcated, there is a single boundary line L in one layer and two boundary lines U1 and U2 in the adjacent layer. ,
   For each of the two boundary lines U1 and U2, the respective centroids G1 and G2 are calculated, and intersections A and B between the two boundary lines U1 and U2 and a straight line connecting the two centroids G1 and G2 are obtained.
   For a plurality of points set on the single boundary line L, it is evaluated which of the two boundary lines U1 and U2 is closer to each other, and boundary points C and D serving as boundaries at which they are switched are obtained.
   Find the midpoint M1 of the line segment AB connecting the intersections A and B and the midpoint M2 of the line segment CD connecting the boundary points C and D;
   Find the length D1 of the line segment AB and the length D2 of the line segment CD,
   A point E is obtained by dividing the line segment M1-M2 connecting the midpoints M1, M2 by the internal ratio of D1: D2.
   A single boundary line L is divided into two parts at boundary points C and D, and one of the divided parts, which is close to the boundary line U1, and a boundary line L1 by a line segment CE and a line segment ED. , And the boundary line L2 is configured by the other part close to the boundary line U2 and the line segment CE and the line segment ED,
   On the boundary lines U1, U2, L1, and L2, a plurality of points that are the vertices of a triangular polygon are set,
   3. The link target point is selected between the boundary lines U1 and L1 and between the boundary lines U2 and L2 in the second processing procedure to the seventh processing procedure. 3. A method for constructing a three-dimensional model of an organ described in 1.
4. Further, among the plurality of layers, one end point that is the vertex of the triangular polygon is set at a position opposite to the layer that is second from the end across the layer at the end, An edge processing procedure for selecting a pair of an extreme end point and each point on the boundary line of the extreme end layer as a link target point; and
   In the end processing procedure,
   Two directions parallel to each of the plurality of layers and orthogonal to each other are defined as an x direction and a y direction, and a direction orthogonal to each of the plurality of layers is defined as a z direction.
   X coordinates xMin1, xMax1 at both ends of the distribution range in the x direction of the boundary line of the extreme end layer, and y coordinates yMin1, yMax1 at both ends of the distribution range in the y direction are obtained,
   X coordinate xMin2, xMax2 at both ends of the distribution range in the x direction of the boundary line of the second layer from the end, and y coordinates yMin2, yMax2 at both ends of the distribution range in the y direction are obtained,
   Two boundary line deviations dx1 = xMin1-xMin2, dx2 = xMax2-xMax1 at both end positions in the x direction, and two boundary line deviations dy1 = yMin1-yMin2, dy2 = yMax2-yMax1 at both end positions in the y direction. And
   An x coordinate xMok of a point that internally divides the x coordinate xMin1, xMax1 by a ratio of dx1: dx2, and a y coordinate yMok of a point that internally divides the y coordinate yMin1, yMax1 by a ratio of dy1: dy2. Seeking
   Based on the distance dz1 between the outermost layer and the second layer from the end, and the x coordinates xMin1, xMax1, xMin2, xMax2, the distance dz2x from the outermost layer is ( xMax1-xMin1) :( xMax2-xMin2) = dz2x: A distance dz2x satisfying the relationship of (dz1 + dz2x) is obtained,
   Based on the distance dz1 between the outermost layer and the second layer from the end and the y coordinates yMin1, yMax1, yMin2, yMax2, the distance dz2y from the outermost layer is ( yMax1-yMin1): (yMax2-yMin2) = dz2y: a distance dz2y that satisfies the relationship (dz1 + dz2y) is obtained,
   The smaller one of the two distances dz2x and dz2y is defined as a distance dz2.
   In a three-dimensional space, a point P that is equidistant from the x-coordinates xMin1, xMax1 and equidistant from the y-coordinates yMin1, yMax1, and a distance dz2 from the point P in the z-direction, and the x-coordinate xMok A point R that internally divides a line segment PQ connecting the y coordinate yMok with the point Q into PR: RQ = 2: 1 is obtained, and the point R is set as the extreme end point. The method for constructing a three-dimensional model of an organ according to any one of the above.
5. Based on the boundary line indicating the outer surface of the organ or the inner surface of the organ specified on the two-dimensional cross-sectional image of each layer obtained by imaging the organ over a plurality of layers with the tomography apparatus, the vertex of the triangular polygon is set on the boundary line. A first processing procedure for setting a plurality of points,
   A second processing procedure for obtaining a tangential direction of the boundary line on the two-dimensional cross-sectional image at each point set in the first processing procedure;
   From among the plurality of layers, a pair of layers at adjacent positions are sequentially selected while being shifted one layer at a time, and the boundary lines of each layer are projected on the same plane, and each of the layers set on both projected boundary lines is selected. A third processing procedure for calculating a distance from each point on a boundary line different from the boundary line including the reference point to the reference point, with each point as a reference point;
   For each of the two points that are subject to calculation of the distance in the third processing procedure, an angle formed by the tangential directions corresponding to the two points is determined. The larger the angle, the more the value before correction. A fourth processing procedure for correcting the distance by obtaining a coefficient with a large value after correction and multiplying the coefficient by the distance between two points corresponding to the coefficient;
   Based on the corrected distance corrected by the fourth processing procedure, the shortest distance is selected from a plurality of corrected distances corresponding to one reference point, and the distance to the reference point is A fifth processing procedure for setting the shortest distance to the shortest point corresponding to the reference point;
   Each of the points set on the boundary line in one layer is selected from the plurality of layers by sequentially selecting a pair of adjacent layers while shifting one layer at a time. A sixth processing procedure for setting the reference point and the shortest point at which the distance to the shortest point corresponding to the reference point as the reference point is the shortest as a starting point, respectively;
   A procedure of selecting a plurality of pairs of link target points where a link corresponding to one side of a triangular polygon is selected from the two boundary lines where the starting point is set by the sixth processing procedure, The starting point is selected as a pair of link target points, and thereafter, each point at a position advanced by one point around the predetermined direction from the selected link target point as a candidate point is selected as a pair of points previously selected. A seventh processing procedure of repeating the process of selecting any one of the link target points and the candidate point on the boundary different from the one link target point as the next pair of link target points A program that causes a computer to construct a three-dimensional model of an organ by causing a computer to execute a process including and
   In the seventh processing procedure,
   (A) When both of the pair of link target points to be selected next return to the starting point, the seventh processing procedure is terminated,
   (B) In a case other than (A) above, when one link target point has already returned to the starting point among the pair of link target points previously selected, the one link target point and the other The candidate point next to the link target point is selected as the next pair of link target points,
   (C) In cases other than (A) and (B), the other link target point advances to the shortest point corresponding to one link target point among the pair of link target points previously selected. If the one link target point has already been advanced to the shortest point corresponding to the other link target point, the one link target point is adjacent to the other link target point. The candidate points in are selected as the next pair of link target points,
   (D) In cases other than (A), (B), and (C), among the previously selected pair of link target points, the link target point and the other link target point are adjacent to each other. The distance between the candidate point and the distance between the other link target point and the candidate point adjacent to the one link target point are calculated in terms of a three-dimensional space considering the distance between layers, and the calculation is performed. A program for constructing a three-dimensional model of an organ that selects two points of the shorter distance as the next pair of link target points.

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