JPH06274651A - Reconstituting method for density interpolation of three-dimensional image - Google Patents

Abstract

PURPOSE:To reconstitute a source three-dimensional object in short processing time with high accuracy. CONSTITUTION:In the case of calculating the density value of an arbitrary point P on a three-dimensional space, six points on a lattice plane image composed of six slice images surrounding the arbitrary point P are cared, first of all, the density value at the point P in respective directions (x), (y) and (z) is calculated from density values at the six points cared on the lattice plane image, further, intervals Dx, Dy and Dz of slice images in the respective directions (x), (y) and (z) are considered for those three density values, the density at the point P is finally calculated, the points with the equal density value calculated by applying this processing are linked, and the smooth three- dimensional object is reconstituted.

Description

Detailed Description of the Invention

[0001]

BACKGROUND OF THE INVENTION The present invention relates to x, which are orthogonal to each other.
A three-dimensional object placed in the y, z coordinate system is captured at a slice interval in each of the x, y, and z directions, and a plurality of slice images, which are an array of images, are received. The present invention relates to a reconstruction method by density interpolation of a three-dimensional image for reconstructing a three-dimensional object with density values, and particularly to a reconstruction method by density interpolation of a three-dimensional object using a lattice plane image.

[0002]

2. Description of the Related Art Generally, when a structure of an original three-dimensional object is reconstructed from a plurality of slice images, the larger the slice interval, the coarser the structure. Therefore, in order to form a smooth three-dimensional structure, density interpolation is performed between a plurality of slice images.

Conventionally, the following two methods are roughly considered as methods for interpolating density values from a plurality of slice images. First, as shown in FIG. 2, the focus is simply on the direction with the smallest inner slice interval in the three directions, and the density values in the two images in that direction are linearly interpolated to obtain an arbitrary target point P.
This is a method of obtaining the density value in. Secondly, as shown in FIG. 3, paying attention to eight grid points of the grid surface image surrounding the target point P, and taking into consideration the density value at the eight grid points and the distance from an arbitrary target point to each grid point. This is a method of performing the above interpolation to obtain the density value at the point P. Limiting the interpolation to eight surrounding grid points is disclosed as a conventional technique in, for example, Japanese Patent Application Laid-Open No. 2-58183.

[0004]

Among the conventional three-dimensional image interpolation methods, the former is interpolation in one direction, so that the accuracy of the density value at an arbitrary point of interest and the reconstructed three-dimensional object There was a problem that the accuracy was low. The latter is highly accurate because it considers three directions, but since the distance from the grid point to the point of interest is a three-dimensional distance, the more the number of points of interest, the longer the distance calculation time. There is a problem that it takes a lot of processing time to reconfigure.

An object of the present invention is to provide a reconstruction method by density interpolation of a three-dimensional image, which is capable of reconstructing a three-dimensional image by density interpolation with high accuracy and reduced processing time.

[0006]

A reconstruction method by density interpolation of a three-dimensional image according to the present invention is highly accurate and reduces the processing time when the density value of a point of interest is interpolated and the three-dimensional object is reconstructed. Therefore, pay attention to 6 points where perpendicular lines intersect from an arbitrary point of interest P drawn on the lattice plane image, and consider the density value at these 6 points and the distance (one-dimensional distance) from each point to the point of interest P. It is characterized by using the interpolation method described above.

That is, according to the present invention, a three-dimensional object placed in an x, y, z coordinate system orthogonal to each other is converted into an x, y, z
In a method of receiving a plurality of slice images, which is an array of images taken at respective slice intervals in each direction, and reconstructing the three-dimensional object from the plurality of slice images by density values, From the density values of the two slice images in the x direction, the two slice images in the y direction, and the two slice images in the z direction, which constitute the surrounding lattice plane image, the density values in a total of six slice images There is obtained a reconstruction method by density interpolation of a three-dimensional image, which is characterized in that the three-dimensional object is reconstructed by interpolating the density values of.

Further in accordance with the present invention, the point P in the x direction is
X1 and x2 at the points where the perpendiculars drawn from the two slice images in the x direction intersect, and the density values at the points x1 and x2 are f
x1 and fx2, and the distance from point P to points x1 and x2 is dx1
And dx2, and the points where the perpendiculars drawn from the point P in the y direction to the two slice images in the y direction intersect are y1 and y2,
The density values at the points y1 and y2 are fy1 and fy2, the distances from the point P to the points y1 and y2 are dy1 and dy2, and the points where the perpendiculars drawn from the point P to the two z-direction slice images intersect with respect to the z direction are defined. If the density values at z1 and z2, the points z1 and z2 are fz1 and fz2, and the distances from the point P to the points z1 and z2 are dz1 and dz2, the x direction, the y direction, and the z direction.
The density values fpx, fpy, and fpz at the point P relating to the direction are calculated from two images in each direction by fpi = (fi1 × di2 + fi2 × di1) / Di Di = di1 + di2 (where i = x, y, z, Di represents a space between two slice images in each direction.), And a reconstruction method by density interpolation of a three-dimensional image is obtained which is obtained by linear interpolation.

Further, according to the present invention, it is corrected that the degree to which the density value fpi in each direction influences the point P decreases as the distance Di between the two slice images in each direction increases. The density value fp at the point P is expressed by fp = (fpx / Dx + fpy / Dy + fpz / Dz) × {D
3. The method according to claim 2, wherein the value is determined based on x Dy Dz / (Dx Dy + Dy Dz + Dz Dx)}.
A reconstruction method by density interpolation of a three-dimensional image is obtained.

Further, according to the present invention, by paying attention to a plurality of arbitrary points in the three-dimensional space, the density value fp at each target point P is obtained, and points having the same density are connected to each other, thereby smoothing. Three
A reconstruction method by density interpolation of a three-dimensional image characterized by reconstructing a three-dimensional object is obtained.

[0011]

DESCRIPTION OF THE PREFERRED EMBODIMENTS The present invention will be described below with reference to the drawings.

FIG. 1 is a diagram for explaining a reconstruction method by density interpolation of a three-dimensional image according to an embodiment of the present invention. FIG. 1 shows the positional relationship between an arbitrary point of interest P to be obtained by interpolation and the lattice plane image. The points where the perpendiculars drawn from the point P intersect in the x direction are x1 and x2, the density values at those points are fx1 and fx2, and the distances from the point P to x1 and x2 are dx1 and dx2, respectively. The same applies to the y and z directions.

First, a point P concerning the x-direction, the y-direction and the z-direction.
The density values fpx, fpy, and fpz at are calculated from two images in each direction by linear interpolation as in the following equation.

Fpi = (fi1 × di2 + fi2 × di1) / Di Di = di1 + di2 where i = x, y, z The density value in each direction has a greater influence on the point P as the distance Di between slice images increases. Get smaller. Therefore, considering the image interval in each direction, the density value fp at the point P is expressed by the following equation.

Fp = (fpx / Dx + fpy / Dy + fpz / Dz) × {D
x Dy Dz / (Dx Dy + Dy Dz + Dz Dx)} By applying the above formula, the density values for a large number of arbitrary points in the three-dimensional space are obtained, and by connecting points of equal density, smooth points are connected. 3D objects can be reconstructed.

[0016]

As described above, the present invention focuses on the six points of the lattice plane image of the given slice image.
The effect is that the original three-dimensional object can be reconstructed with high accuracy and a short processing time.

[Brief description of drawings]

FIG. 1 is a diagram for explaining a reconstruction method by density interpolation of a three-dimensional image according to an embodiment of the present invention, which shows an attention point P in a three-dimensional space and a grid screen image in the interpolation method used in the present invention. It is a figure showing the positional relationship of.

FIG. 2 is a diagram showing a positional relationship between a target point P in a three-dimensional space and a slice image in a conventional one-direction interpolation method.

FIG. 3 is a diagram showing a positional relationship between a target point P in a three-dimensional space and eight lattice points in a conventional interpolation method using eight lattice points.

[Explanation of symbols]

P point of interest Dx, Dy, Dz x, y, z spacing of slice images in each direction

Claims (4)

[Claims] 1. A plurality of slices, which are an array of images obtained by photographing a three-dimensional object placed in mutually orthogonal x, y, and z coordinate systems at respective slice intervals in each of the x, y, and z directions. In the method of receiving an image and reconstructing the three-dimensional object from the plurality of slice images by using density values, two slice images in the x direction and two y images forming a lattice plane image surrounding the target point P are formed. Characterized in that the three-dimensional object is reconstructed by interpolating the density value at the point of interest from the density values in a total of six slice images of the slice images in the direction and two slice images in the z direction. A reconstruction method of a three-dimensional image by density interpolation. 2. The points where the perpendiculars drawn from the point P in the x direction to the two slice images in the x direction intersect are x1 and x2,
The density values at the points x1 and x2 are fx1 and fx2, the distances from the point P to the points x1 and x2 are dx1 and dx2, and the points where the perpendiculars drawn from the point P to the two y-direction slice images intersect in the y-direction Let y1 and y2 be the density values at points y1 and y2 be fy1 and fy2, and the distances from point P to points y1 and y2 be dy1 and dy2. Perpendicular lines drawn from the point P to two slice images in the z direction with respect to the z direction. Let z1 and z2 be the intersecting points, fz1 and fz2 be the density values at points z1 and z2, and dz1 and dz2 be the distances from point P to points z1 and z2. The density values fpx, fpy, and fpz are calculated from two images in each direction: fpi = (fi1 × di2 + fi2 × di1) / Di Di = di1 + di2 (where i = x, y, z, and Di is 2 in each direction). Based on the interval between slice images.) The method for reconstructing a three-dimensional image by density interpolation according to claim 1, wherein the reconstruction is performed by linear interpolation. 3. An interval Di between two slice images in each direction
In order to correct that the density value fpi in each direction has a smaller influence on the point P as becomes larger, the density value fp at the point P is calculated as fp = (fpx / Dx + fpy / Dy + fpz / Dz) × {D
3. The method according to claim 2, wherein the value is determined based on x Dy Dz / (Dx Dy + Dy Dz + Dz Dx)}.
Reconstruction method of three-dimensional image by density interpolation. 4. A smooth three-dimensional object is reconstructed by paying attention to a plurality of arbitrary points in a three-dimensional space, obtaining a density value fp at each target point P, and connecting points having equal density. The reconstruction method by density interpolation of a three-dimensional image according to claim 3, wherein the reconstruction method is configured.