JPH09265526A - Center projecting method using eyeball conversion - Google Patents

Abstract

PROBLEM TO BE SOLVED: To obtain a projection image which is not reduced by eyeball conversion or enlarged to desired size without deterioration in picture quality by preliminarily finding the reduction rate of a projection object after the eyeball conversion as to a desired position pixel, giving the resulting enlargement rate as a constant in a calculation expression during eyeball conversion, and performing the eyeball conversion for all pixels. SOLUTION: An enlarged eyeball-converted reprojection image 100C is obtained from an eyeball-unconverted projection image 100A as an original projection image directly, without using a reduced projection image 100B. In this case, the reduction rate of the eyeball unconverted projection image 100A after the eyeball conversion is found as preliminary processing as to the pixel at a desired position of the projection image 100AZ. Then the enlargement rate calculated on the basis of this reduction rate is given as a constant in the calculation expression during eyeball conversion and this expression is used to perform the eyeball conversion including enlargement processing for all the pixels of the eyeball unconverted projection image 100A, thereby reprojecting the image on a projection surface formed of a plane.

Description

Detailed Description of the Invention

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a computer graphics, and more particularly to improvement of a central projection method using eyeball transformation which is effective for correction of image distortion caused by the central projection method.

[0002]

2. Description of the Related Art As shown in FIG. 5A, a center projection method projects a projection image 40A by projecting projection objects 40a and 40b onto a projection surface 4 by emitting light rays in a conical shape from a point (viewpoint) e. ，
It is a method of obtaining 40B. This method is applied to the projection of tomographic images and is used to construct three-dimensional images (for example,
Japanese Patent Application No. 6-3492).

By the way, conventionally, the projection plane in the above-described central projection method (general central projection method) is "Computer Graphix" (JD FOLEY &
A. Written by VAN DAM Translated by Atsumi Imamiya July 1, 1984
It was flat as you can see on pages 275-316 of the 5th Japan Computer Association).

For this reason, the following distortion was generated. FIG.
In (b), when the projection targets 40a and 40b are projected on the projection surface 4, they become projection images 40A and 40B, respectively. Assuming that the projection target 40a and the projection target 40b have the same length (dimension in the left-right direction in the drawing), the projection target 40b will be viewed obliquely, and therefore should appear shorter than the projection target 40a. However, as can be seen from FIG. 5 (b), this is not the case (longer conversely), and such distortion depending on the projection direction increases as the distance between the viewpoint e and the projection surface 4 decreases. There was a problem that

Therefore, the inventor of the present invention filed Japanese Patent Application No. 6-89770.
As shown in No. 6, the inventors have invented a projection method capable of eliminating the distortion of the projected image depending on the projection direction. This projection method is a central projection method in which light rays are emitted in a conical shape from the viewpoint and the projection target is projected onto the projection surface. By re-projecting on the projection plane composed of the plane, the distortion of the projected image depending on the projection direction is eliminated.

That is, FIG. 6A shows an eyeball, and a light ray 7 passes through a crystalline lens (lens) 6 to form an image on a spherical retina 5. In this way, in the natural world, the retina 5 is made spherical to eliminate the distortion depending on the projection direction. In this central projection method (hereinafter referred to as the central projection method using eyeball conversion), the projection surface is a hemispherical surface as shown in FIG. 6B (see projection spherical surface 3). Thereby, the distortion of the projected image depending on the projection direction is corrected so that the projection data (length or size) does not change due to the difference in the projection direction.

The details of the center projection method using eyeball conversion will be described below. FIG. 7 is a flowchart thereof. Figure 7
As shown in FIG. 2, the center projection method using eyeball transformation is a projection plane (primary projection plane: projection before distortion correction by eyeball transformation, which will be described in detail later) that is a plane formed by a general center projection method. Project onto a plane) (step 1). Then, after the projection or at the time of projection, the projection image of the projection target is obtained by re-projecting on the projection plane (secondary projection plane: projection plane after distortion correction by the below-mentioned eye transformation) by the below-mentioned eye transformation ( Step 2). Here, the eyeball conversion means a two hemispheres obtained by dividing a spherical surface having a center on the line of sight into two in a direction orthogonal to the line of sight at or after the projection of the projection target onto the projection plane. Of these, reprojection onto the projection plane is performed through projection onto the projection surface (projection spherical surface) having a hemispherical surface far from the viewpoint as the projection surface.

That is, according to the center projection method using the eyeball transformation, center projection is performed with the projection sphere as the projection surface. In this case, each point (address) along the hemisphere, which is the projection surface, is CRT. Corresponding to the display pixel (address) of. Then, in order to obtain the same effect as that projected on the projection spherical surface on a plane (CRT screen), eyeball conversion is performed and distortion correction is performed.

Next, the principle of the distortion correction by the eyeball conversion will be described with reference to FIGS. 8 and 9. First, referring to FIG. 8, FIG. 8 shows a case where the viewpoint e is h = 2R. In FIG. 8, 3 is the line of sight (Z
Two hemispheres I, I obtained by dividing a spherical surface having a center on the axis) in the direction orthogonal to the line of sight at the center position.
Of I, it is a projection surface (hereinafter referred to as a projection spherical surface) formed of a hemispherical surface (hemispherical surface I) farther from the viewpoint. Further, 4 is a projection plane formed of a plane (hereinafter referred to as a projection plane), which is also a projection plane before distortion correction by eyeball conversion, that is, a primary projection plane as a projection plane of a conventional method, and after distortion correction by eyeball conversion. It is also a secondary projection plane as a projection plane of.
The projection plane 4 corresponds to a screen which is a display surface of a CRT.

Further, X, Y and Z are each axis of the three-dimensional coordinate system,
O is the origin of the three-dimensional coordinate system, e is the viewpoint, h is the distance between the viewpoint e and the projection plane 4, R is the radius of the projection sphere 3, P is a point (X1, Y1) on the projection plane 4, and ψ is a straight line. An angle formed by OP and the X axis, Q is a point on the projection spherical surface 3 corresponding to a point P on the projection plane 4 (an intersection of the straight line Pe and the projection spherical surface 3), θ is an angle formed by the straight line Z1 Q and the Z axis, L is an arc OQ on the projection sphere 3, L'is L
Is a line segment on the straight line OP having the same length as, η is a CRT display address (taken in parallel with the X axis), and ξ is a CRT display address (taken in parallel with the Y axis).

According to this, the following equation is established. When h = 2 · R corresponding to the eyeball, tan (θ / 2) = sqrt (X
For the 1 ² + Y1 ² ) / 2R triangle X1 OP, tan (ψ) = Y1 / X1 is given.

Therefore, when X1 and Y1 are specified, the corresponding η1 and ξ1 are as follows: ψ = arctan (Y1 / X1) θ = 2 · arctan [sqrt (X1 ² + Y1 ² ) / 2R] L = R · θ (( 01), η1 = L · cos (ψ) ξ1 = L · sin (ψ).

These η1 and ξ1 are pixel addresses on the display memory. That is, the point (X1, Y1) on the projection plane 4 is displayed at the point (η1, ξ1) on the CRT screen, which means that the distortion correction by the eyeball conversion is performed.

Further, the image size is reduced by this eyeball conversion (from the point P to the point (η1, ξ1)). Therefore, the image size of the projection image on the projection plane 4 after distortion correction is
It becomes possible to project larger than the image size of the image projected after being corrected by the eyeball conversion.

Next, the case where the viewpoint e is other than h = 2R will be described with reference to FIG. 9A and 9B, the same reference numerals as those in FIG. 8 indicate the same or corresponding portions. Also,
U is the length of the straight line eQ, γ is the angle between the line segment eP and the Z axis,
w is the length of a straight line drawn from Q perpendicular to the Z axis.

According to this, the following equation holds. U = sqrt [(h−R) ² + R ² −2 · (h−R) · R · c
os (π−θ)], U · sinγ = R · sin θ.

Γ is given by tan γ = sqrt (X1 ² + Y1 ² ) / h. From this, when X1 and Y1 are specified, θ can be obtained.

Ψ is L when calculated from tan ψ = Y1 / X1
= R · θ, η1 = L · cosψ ξ1 = L · sinψ.

These η1 and ξ1 are pixel addresses on the display memory. That is, the point (X1, Y1) on the projection plane 4 is displayed at the point (η1, ξ1) on the CRT screen, which means that the distortion correction by the eyeball conversion is performed. The projection target may be data input by an input device such as a mouse, or may be data obtained by a calculation device such as a tomographic image (including a tomographic image obtained by decomposing a volume image by three-dimensional measurement). Good.

10 to 12 show a method (Japanese Patent Application No. 6-3492) for constructing a three-dimensional image from a plurality of tomographic images by a general center projection method. Even in such a case, As long as the central projection is performed, eyeball conversion is necessary to eliminate the distortion. An example of applying the central projection method using the eyeball conversion to the three-dimensional image forming method will be described below. In both cases of FIG. 11 and FIG. 12, it is necessary to first project a tomographic image on an X, Y projection plane (projection plane) 4 consisting of a plane, and then convert it to an η, ξ plane by eyeball conversion. Become.

First, in the method of constructing a three-dimensional image, coordinate conversion by central projection will be described. The conversion of the pixel coordinates of each tomographic image to the coordinates on the projection surface when projecting each tomographic image on the projection plane by the central projection is performed as follows.

In the example shown in FIG. 10, the coordinate system is set so that the projection plane, the tomographic image plane, and the xy plane are parallel to each other for simplification of description. In FIG. 10, x,
y and z are each axis of the three-dimensional coordinate system (x, y, z), and point e (x
1, y1, d1) is the position of the viewpoint e, P point (X, Y) is a point on the projection plane (corresponding to the display screen) 4, S point (x0, y0,
d0) is a point where the straight line 22 passing through the point e (x1, y1, d1) and the point P (X, Y) intersects with the tomographic image 23A.

D is the position of the projection plane 4 (on the z-axis),
It can be set arbitrarily.

D0 is the position of the tomographic image 23A (on the z-axis),
Determined at the time of measurement.

D1 is the z coordinate of the viewpoint e.

According to this, the following equation holds.

X = {(D-d1) / (d0-d1)} × (x0-x1) + x1 (1) Y = {(D-d1) / (d0-d1)} × (y0-y1) + Y1 (2) x0 = {(d0-D) / (d1-D)} * (x1-x) + X ... (3) y0 = {(d0-D) / (d1-D)} * (y1-- y) + Y (4) When the projected image is displayed on a display screen (not shown) corresponding to the projection surface 4 with 512 pixels in the vertical direction and 512 pixels in the horizontal direction, X and Y are from -256 to +256. Take a value. On the tomographic image 23A of d0 for each X and Y, x0 and y0 are determined by the above equations (3) and (4), and which point should be projected. Since there are a plurality of tomographic images 23 and a plurality of d0, a plurality of points x0 and y0 to be projected are determined for one set of X and Y.

In the same coordinate system, tomographic images 23B to 23E are prepared in addition to the tomographic image 23A, and a view seen from the y-axis direction is shown in FIG. In FIG. 11 (a),
The tomographic images 23A to 23E are tomographic images obtained at equal intervals in the same direction for the same object (in the illustrated example, they are at equal intervals,
It does not necessarily have to be at equal intervals), and the tomographic image 23
In B, the organ regions B1, B2, and B3 are highlighted. When the organ regions B1, B2, B3 are projected on the projection plane 4, B1
It becomes', B2 ', B3'. Similarly, when the organ regions C1 and C2 of the tomographic image 23C are projected on the projection plane 4, the regions become C1 'and C2'.

Here, the projection data (here, B1 ',
When writing B2 ', B3'; C1 ', C2') in the display memory (not shown), projection data existing farther from the viewpoint e is written first in order to produce a three-dimensional effect. ,
Later projection data is overwritten. Therefore, here, the projection data B is obtained from the projection data C1, C2.
Since 1, B2 and B3 exist farther than the viewpoint e, the projection data B1 ', B2' and B3 'are written first and the projection data C1' and C2 'are overwritten later. In FIG. 11A, projection data B1 ', B2', B3 '; C1
Although ′ and C2 ′ are shown separately from the projection plane 4, these are projection data B1 ′, B2 ′ and B to be written in the display memory.
3 ';C1', C2 'is simply for making the order easier to understand, and projection data B1', B2 ', B3' written first
Also, the projection data C1 'and C2' that are overwritten are actually written on the projection surface 4.

FIG. 11B is a more generalized view than FIG. 11A and shows an example in which the projection plane and the tomographic image plane are not parallel. In this case, the tomographic images 23A, 23B, 2
It is necessary to create the tomographic images 23a, 23b, 23c, ... Directed to the plane parallel to the projection plane 4 from 3C. Others are the same as in the case of FIG. Note that b1 ';c1', c2 ';d1' are organ regions b1; c1, c on the tomographic images 23b, 23c, 23d that have been interpolated.
2; d1 projection data.

FIG. 12 is a diagram for explaining the coordinate conversion by the central projection when the viewpoint, tomographic image and projection plane have a more complicated positional relationship, and is S point (x0, z on the tomographic image 23.
The projection result of (0, y0) is P point (x, y, z) on the projection plane.
Indicates that

In FIG. 12, the tomographic image 23 is projected when the tomographic image 23 is projected on the projection plane 4 by the central projection.
The conversion of the pixel coordinates of the above into the coordinates on the projection plane 4 is performed as follows. Where a is the intersection of the x-axis and the projection plane 4,
b is a point where the y axis intersects the projection plane 4, and c is a point where the z axis intersects the projection plane 4.

Further, α is an angle formed by a line obtained by projecting a perpendicular line drawn from the origin onto the projection plane 4 on the zx plane with the x axis, β is an angle formed by the perpendicular line with the xz plane, and point e (x1, y1, z1) is the position of the viewpoint e, point P (x, y, z) is a point on the projection plane (corresponding to the display screen) 4, point S (x0, z0, y0) is point e (x1, y1). , Z1) and the point at which the tomographic image 23 intersects with the straight line 22 passing through the point P (x, y, z), the following equation holds.

First, the projection plane 4 is represented by (x / a) + (y / b) + (z / c) = 1 (5). Further, a straight line 22 passing through the point e (x1, y1, z1) and the point P (x, y, z) is represented by (x0−x) / (x1−x) = (y0−y) / (y1−y) = (Z0−z) / (z1−z) (6)

The projection plane 4 is at point C1 (xc1, yc1, zc
When passing through 1), k1 = sinα k2 = cosα / sinβ k3 = cosα · cosβ / sinβ ai = 1 / a bi = 1 / b ci = 1 / c, and z = [X · k1−Y · k2-yc1 * K3-{(ci * k3 * zc1) / bi} + {(ai * k3 * X) / (bi * cos [alpha])}-{(ai * k3 * xc1) / bi}] / [1-{(ci · K3) / bi} + {(ai · k3 · sinα) / (bi · cosα)}] (7) x = (X−z · sinα) / cosα (8) y = [yc1 + {-ci -(Z-zc1) -ai * (x-xc1)}] / bi (9) Here, the point C1 (xc1, yc1, zc1) is, for example, from the viewpoint e (x1, y1, z1). As a point where the perpendicular line drawn to the projection plane 4 and the projection plane 4 intersect (the distance between this point and the viewpoint e is h), zc1 = z1 +-[h / sqrt {1+ (c ² / a ² ) + (c ² / b ² )}] (“−” of “z 1 + −” when z 0 <zc 1) (10) xc 1 = x 1 + Δc · (z 1 −zc 1) / A｝ (11) yc1 = y1 + {c ・ (z1−zc1) / b} (12)

When a projected image is displayed on a display screen (not shown) corresponding to the projection plane 4 with 512 pixels in the vertical direction and 512 pixels in the horizontal direction, X and Y take values from -256 to +256. The above (7) for each X and Y,
X and y are determined by the equations (8) and (9). x1 at point e,
Since y1 and z1 are given arbitrarily, the following (13), (14)
From the equation, the coordinates x0, x of the pixel S on the tomographic image of y0 = d0
z0 is determined.

X0 = {(d0-y) / (y1-y)} × (x1-x) + x (13) z0 = {(d0-y) / (y1-y)} × (z1-z) + Z (14) Since there are a plurality of tomographic images and a plurality of d0, a plurality of points x0 and y0 to be projected are determined for one set of X and Y.

Note that R in FIG. 12 indicates the distance from the viewpoint e to the point S, and this R is a parameter for obtaining the pixel value (luminance) at the point P. The pixel value at point P is proportional to the value obtained by subtracting the above R from the maximum value Rmax of the set pixel value (luminance). This point P is (η,
The pixel value is stored at the point (η, ξ) because it corresponds to the point ξ).

The above coordinate conversion is performed for all points on the projection plane 4 corresponding to the display screen. This is performed for all tomographic images 23. Furthermore, even if the three-dimensional image that is the resultant image is constructed,
It may be performed for each tomographic image.

[0040]

According to the center projection method using the eyeball transformation described above, the distortion of the projected image depending on the projection direction (the image distortion associated with the general center projection method) is corrected, and the difference in the projection direction. Therefore, the projection data will not be different from each other, and the observation and diagnosis of a three-dimensional image such as an inner wall surface image of a blood vessel by applying this method will be more effective. However, the obtained image (reprojection image) is inevitably reduced. Therefore, when it is desired to perform image observation and diagnosis with the original image size, that is, before the eyeball conversion or at a larger image size, it is conceivable to interpolate and enlarge the reduced image after the eyeball conversion. However, in the image obtained by simply interpolating and enlarging the reduced image after eyeball conversion in this way, the original data is all the reduced projected image data (not the original projection target data). There is a problem that the image quality deteriorates because the image is enlarged by using the interpolation method.

It is an object of the present invention to be able to correct image distortion associated with a general center projection method, and to obtain a projected image which is not reduced by eyeball conversion or enlarged to a desired size without image quality deterioration. It is an object of the present invention to provide a central projection method using eyeball transformation capable of performing the following.

[0042]

SUMMARY OF THE INVENTION The above object is to provide a spherical surface centered on the line of sight of a projection target after or at the time of projection by a central projection method on a projection plane consisting of a plane. Of two hemispheres obtained by dividing the hemisphere into two in the direction orthogonal to the line of sight, the projection consisting of the plane through the projection onto the projection plane (projection sphere) with the hemisphere on the side far from the viewpoint as the projection plane. In the central projection method using the eyeball transformation to re-project on the surface, the reduction rate after the eyeball transformation of the projection target is obtained by performing the eyeball transformation for the pixel at the desired position of the projection target, and based on this reduction rate. It is achieved by giving the calculated enlargement factor as a constant in the calculation formula at the time of eyeball conversion, and using this to perform the eyeball conversion for all the pixels of the projection target and re-projecting on the projection plane composed of the plane. .

When a projection image which is not reduced or is enlarged to a desired size is obtained from the projection image reduced by the eyeball transformation, all the original data is the reduced projection image data. Yes (rather than the original projection target data), the image will be enlarged by using the interpolation method, resulting in deterioration of image quality. On the other hand, the reduction rate after the eyeball conversion of the projection target is obtained by performing the eyeball conversion on the sampled desired position pixel of the projection target, and the enlargement ratio calculated thereby is set as a constant in the calculation formula at the time of the eyeball conversion. If a projection image that has no reduction or is enlarged to a desired size is obtained by the method of performing eyeball conversion on all pixels using this, even if an interpolation method is used, The original data is the original projection target data. That is, in the method of the present invention, it is possible to correct only the image distortion associated with the general center projection method without going through the reduced projection image after eyeball conversion, and there is no reduction due to eyeball conversion, or a projected image enlarged to a desired size. Can be obtained without image quality deterioration.

[0044]

BEST MODE FOR CARRYING OUT THE INVENTION Embodiments of the present invention will be described below with reference to the drawings. FIG. 1 is a flowchart showing an embodiment of a center projection method using eyeball conversion according to the present invention.

That is, according to the present invention, after or at the time of projection by the central projection method of the projection target onto a projection plane formed of a plane, the projection target is a spherical surface having its center on the line of sight orthogonal to the line of sight at the center position. Of the two hemispheres obtained by dividing into two in the direction, the projection on the projection plane (projection spherical surface) having the hemisphere on the side far from the viewpoint as the projection surface is re-projected to the projection surface composed of the plane. It is applied to a central projection method using eyeball transformation. In the center projection method using such eyeball conversion, first, the eyeball conversion (Japanese Patent Application No. 6-897) is performed for the pixel at the desired position of the projection target.
The eyeball conversion by No. 70: general eyeball conversion) is performed to obtain the reduction ratio e of the projection target after the eyeball conversion (step 110). Next, the enlargement rate e calculated based on this reduction rate is given as a constant in the equation for eyeball conversion (step 111). Then, the eyeball conversion (eyeball conversion in the present invention) is performed on all the pixels to be projected by using the calculation formula, and reprojection is performed on the projection plane composed of the plane (step 11).
As a result, the image distortion caused by the general center projection method is corrected, and a projected image which is not reduced by general eyeball conversion or enlarged to a desired size is obtained without image quality deterioration.

This will be described in detail with reference to FIG. 2. Now, with respect to the projection image 100A which has not been subjected to distortion correction by eyeball conversion (projection image without eyeball conversion) 100A, general eyeball conversion is performed to obtain a projection image 100B. Shall be obtained. In this case, the projection image 100A may be any projection image that is a target of general eyeball conversion, and it does not matter whether it is a single image or a plurality of images, but here, a plurality of tomographic images are stacked and stacked to form a three-dimensional image. It is a three-dimensional image of the inner wall surface of the blood vessel bifurcation reconstructed by obtaining an image and performing a process such as shading on a two-dimensional image viewed from an arbitrary direction. Multiple tomographic images are C
In addition to a plurality of tomographic images obtained by a T apparatus or the like, a plurality of tomographic images obtained by decomposing a volume image obtained by three-dimensional measurement by an MRI apparatus or the like may be used.

The projected image (eye-transformed reprojected image without magnification)
The image size of 100B is the projection image 100A without eye conversion.
As can be seen by comparing with the image size 100A ′ of No. Even if the reduced projection image 100B after the general eyeball conversion is simply interpolated and enlarged, the original image size 100
Projected image of A'or larger
The eye-transformed reprojection image) 100C is obtained, but the projection image 100C magnified by such route (a) is the data of the projection image 100B whose original data are all reduced (in the original projection image, The image quality is deteriorated because the image is deteriorated because it is enlarged by using the interpolation method instead of the data of a certain projected image 100A.

In the method of the present invention, the reduced projected image 100
The enlarged / eyeball-transformed reprojection image 100C is obtained directly from the projection image 100A without eyeball conversion, which is the original projection image, without going through B (route (a)), that is, via the route (b). At that time, as a preliminary process, an eyeball conversion (general eyeball conversion) is performed on a pixel at a desired position of the projection image 100A without eyeball conversion to obtain a reduction rate e after the eyeball conversion of the projection image 100A (see step 110 above). ).

Now, the pixel at the desired position of the projected image 100A,
Here, when the eyeball conversion is performed on the pixel EG1 located at the end in the + Y direction from the center of the projected image 100A, the pixel E
It is assumed that G1 has been reduced and moved to the position of the pixel EG1 '. At this time, if the reduction ratio r is r = r1 / r2 and r2 = image size 100A '(Y-axis direction) / 2, the projected image 10
In order to directly obtain the projection image 100C of the original image size 100A ′ (via the route (b)) from 0A, interpolation enlargement may be performed with the enlargement ratio e = constant / r. That is, when the constant is set to 1, interpolation enlargement may be performed with the enlargement ratio e = 1 / r.

Then, the enlargement ratio e thus obtained
Is given as a constant in the above-mentioned eyeball conversion (general eyeball conversion) calculation formula (see step 111 above). Specifically, the above-mentioned formula (01) is modified as L = e · R · θ (01 ').

Thereafter, using this equation (01 '), all the pixels of the projection image 100A without the eyeball transformation, which is the original projection image, are subjected to the eyeball transformation including the enlargement processing (eyeball transformation in the present invention), and from the plane. The projection plane is re-projected (see step 112 above).

Note that other formulas in the above eyeball conversion (general eyeball conversion) can be used as they are, except that the above formula (01) is modified to the formula (01 '). As described above, the image distortion caused by the general center projection method is corrected, and a projected image which is not reduced by general eyeball conversion or enlarged to a desired size can be obtained without image quality deterioration.

In the above embodiment, the pixel EG1 'is located at the end in the + Y direction from the center of the projected image 100A.
The case where the enlargement ratio is calculated to be 1 has been described, but the present invention is not limited to this. For example, pixel E
The enlargement ratio may be calculated so that G2 ′ is the edge in the + Y, + X direction from the center of the projected image 100A, that is, the pixel EG2 located in the upper right corner in the drawing.
An eyeball transformation (eyeball transformation in the present invention) projection image including the enlargement processing is shown in 100D in FIG. 100A 'in FIG.
Indicates the image size of the projection image 100A without eyeball conversion.
In addition, the pixels EG1 ′, EG2 ′, etc. are not the pixels EG1, EG2 actually located at the end of the projected image 100A, but the virtual pixels located at a position assumed to be outside thereof (projected image). The enlargement ratio may be calculated so as to be larger than 100A. In this case, further, only an arbitrary portion may be cut out from the entire eyeball conversion (eyeball conversion in the present invention) projection image including the obtained enlargement processing and displayed on the monitor. Further, the expansion ratio e = constant / constant in r is 1
It is not limited only to this, and can be set to an arbitrary value.

FIG. 4 is a block diagram showing a hardware configuration example to which the method of the present invention can be applied. In FIG.
50 is a CPU, 51 is a main memory, 52 is a magnetic disk,
53 is a display memory and 55 is a mouse controller, which are connected to a common bus 57. Magnetic disk 52
Stores a plurality of tomographic images, a program for execution calculation of the method of the present invention, various parameters, and the like.

The CPU 50 reads out these plural tomographic images and the programs and parameters for execution calculation of the method of the present invention, and uses the main memory 51 to perform eyeball conversion (general eyeball conversion for the desired pixel as the preliminary processing). And calculation of all the pixels of the projection image without the eyeball transformation which is the original projection image) and the like are sent to the display memory 53 and displayed on the CRT monitor 54. The mouse 56 connected to the mouse controller 55 uses the viewpoint position, the pixel EG1,
Specify EG2 etc. The image that has undergone eyeball conversion and distortion correction is stored in the magnetic disk 52 as necessary.

[0056]

As described above, according to the present invention, the eyeball conversion is preliminarily performed on the pixel at the desired position of the projection target to obtain the reduction ratio after the eyeball conversion of the projection target, and the enlargement ratio resulting from the conversion is calculated. It is given as a constant in the calculation formula at the time of conversion, and this is used to perform eyeball conversion for all pixels.In other words, projection without eyeball conversion, which is the original projection image, does not go through the reduced projection image after eyeball conversion. Since the re-projection image of the enlarged / eyeball conversion is obtained directly from the image, only the image distortion due to the general center projection method can be corrected, and there is no reduction due to the eyeball conversion or the projected image enlarged to a desired size. Is obtained without deterioration of image quality.

[Brief description of drawings]

FIG. 1 is a flowchart showing an embodiment of the method of the present invention.

FIG. 2 is an explanatory diagram of an embodiment of the method of the present invention.

FIG. 3 is an explanatory diagram of another embodiment of the method of the present invention.

FIG. 4 is a block diagram showing a hardware configuration example to which the method of the present invention is applicable.

FIG. 5 is an explanatory diagram of a center projection method and distortion.

FIG. 6 is an explanatory diagram of eyeball projection.

FIG. 7 is a flowchart showing an outline of a center projection method using general eyeball conversion.

FIG. 8 is a diagram illustrating the principle of distortion correction by general eyeball conversion.

FIG. 9 is a diagram explaining the principle of distortion correction by general eyeball conversion.

FIG. 10 is a diagram for explaining conversion of tomographic image pixel coordinates into coordinates on a projection plane in a method of forming a three-dimensional image.

FIG. 11 is a diagram for explaining conversion of pixel coordinates of a plurality of tomographic images into coordinates on the projection plane.

FIG. 12 is a diagram for explaining coordinate conversion by central projection when a viewpoint, a tomographic image, and a projection plane have a more complicated positional relationship.

[Explanation of symbols]

100A ... Projection image without eyeball conversion, 100A '... Projection image 1
00A image size, 100B ... Eyeball conversion reprojection image without enlargement, 100C, 100D ... Enlargement / eyeball conversion reprojection image,
50 ... CPU, 51 ... Main memory, 52 ... Magnetic disk,
53 ... Display memory, 54 ... CRT monitor, 55 ... Mouse controller, 56 ... Mouse, 57 ... Common bus, 3 ... Projection spherical surface, 4 ... Projection plane, X, Y, Z Each axis of three-dimensional coordinate system, O ... Tertiary Origin of original coordinate system, e ... viewpoint, h ... distance between viewpoint e and projection plane 4, R ... radius of projection sphere 3, P ... point (X1, Y1) on projection plane 4, ψ ... straight lines OP and X Angle formed by axis, Q ... Point on projection spherical surface 3 corresponding to point P on projection plane 4 (intersection point of straight line Pe and projection spherical surface 3), θ ... Straight line Z1 Q
And Z-axis, L ... Arc OQ, L '... on the projection sphere 3
Line segment on the straight line OP having the same length as L, η ... CRT display address (taken parallel to X axis), ξ ... CRT display address (taken parallel to Y axis), U ... Length of straight line eQ , Γ ...
The angle formed by the line segment eP and the Z axis, the length of a straight line perpendicular to the Z axis from w ... Q.

Claims (3)

[Claims] 1. After or at the time of projection by a central projection method of a projection target onto a plane projection plane, the projection target is a spherical surface having a center on the line of sight in a direction orthogonal to the line of sight at the center position. Of the two hemispheres obtained by division, the eyeball transformation for reprojecting onto the projection plane composed of the plane through projection on the projection plane (projection sphere) having the hemisphere on the side far from the viewpoint as the projection plane. In the central projection method used,
Obtain the reduction ratio after the eye conversion of the projection target by performing the eye conversion for the pixel of the desired position of the projection target, the expansion ratio calculated based on this reduction ratio as a constant in the calculation formula at the time of eye conversion. A central projection method using eyeball transformation, characterized in that the eyeball transformation is performed on all the pixels of the projection target by using this, and reprojection is performed on a projection plane composed of the plane. 2. The central projection method using eyeball transformation according to claim 1, wherein the projection target is a tomographic image. 3. The center projection method using eye conversion according to claim 2, wherein the tomographic image is a tomographic image obtained by decomposing a volume image by three-dimensional measurement.