Method of constructing three-dimensional image such as...

Details Method of constructing three-dimensional image such as... Method of constructing three-dimensional image such as...

1995-06-05

2003-03-18

Chauhan, Ulka J. (Department: 2671)

Computer graphics processing and selective visual display system

Computer graphics processing

Three-dimension

Reexamination Certificate

active

06535212

ABSTRACT:

BACKGROUND OF THE INVENTION
The present invention relates to a three-dimensional image constructing method in which a plurality of tomographic images, for example, obtained by an X-ray computerized tomography (CT) apparatus or obtained by decomposing a volume image measured three-dimensionally by an MRI apparatus are stacked up to thereby obtain a stacked three-dimensional image (three-dimensional original image) and then two-dimensional images obtained by observing the stacked three-dimensional image from arbitrary directions are shaded to construct a three-dimensional image (which means an image constituted by two-dimensionally arranged pixels but made to look like a three-dimensional image by shading).
The three-dimensional image constructing method of this type is known heretofore. As a conventional method, a parallel projection method is used for transformation of coordinates of pixels into a coordinate system of a projection plane equivalent to a display screen.
The parallel projection method used conventionally for transformation of coordinates of pixels is effective for constructing a three-dimensional image obtained by observing a subject such as for example an internal organ, or the like, from the outside of the subject. The method is however unsuitable for constructing a three-dimensional image obtained by observing the subject from the inside (that is, by placing a view point in the inside of the subject). Accordingly, the conventional parallel projection method cannot satisfy the demand that three-dimensional images should be obtained as if the inside of the subject was observed through an endoscope.
Therefore, a three-dimensional image constructing method disclosed in Japanese application No. 6-3492, which is one of the Japanese priority applications of U.S. application Ser. No. 08/374,088 which has been incorporated herein by reference, has been developed. This is a method in which transformation of coordinates of pixels on each tomographic image into coordinates on a projection plane is performed by using a central projection method to thereby project each tomographic image onto the projection plane; and pixel values are given to the coordinates of pixels on the projection plane in accordance with a shading algorithm to perform shading to thereby construct a three-dimensional image. Referring to
FIG. 1
, this three-dimensional image constructing method will be described below.
FIG. 1
is a view for explaining the coordinate transformation based on central projection method and shows that projection of a point S(x
0
, z
0
, y
0
) on a tomographic image
30
onto a projection plane
20
results in a point P(x, y, z) on the projection plane
20
. Assume now that a plurality of tomographic images
30
(#
1
, #
2
, . . . , #n) exist in practice.
In
FIG. 1
, at the time of projection of a tomographic image
30
onto the projection plane
20
according to the central projection method, the coordinates of pixels of the tomographic image
30
are transformed into coordinates on the projection plane
20
as follows.
Here, a represents a point of intersection of the x axis and the projection plane
20
, b represents a point of intersection of the y axis and the projection plane
20
, and c represents a point of intersection of the z axis and the projection plane
20
.
Further, a represents an angle between the x axis and a line obtained through projection, onto the z-x plane, of a perpendicular from the origin to the projection plane
20
; &bgr; represents an angle between the above-mentioned perpendicular and the x-z plane; a point e(x
1
, y
1
, z
1
) represents the position of a view point e: a point P(x, y, z) represents a point on the projection plane (equivalent to the display screen)
20
; and a point S(x
0
, z
0
, y
0
) represents a point of intersection of the tomographic image
30
and a line
22
passing through the point e(x
1
, y
1
, z
1
) and the point P(x, y, z).
Under the aforementioned definition, the following equations hold.
First, the projection plane
20
is given by the equation:
(
x/a
)+(
y/b
)+(
z/c
)=1  (1)
Further, the line
22
passing through the point e(x
1
, y
1
, z
1
) and the point P(x, y, z) is given by the equation:
(
x0
-
x
)
/
(
x1
-
x
)
=
(
y0
-
y
)
/
(
y1
-
y
)
=
(
z0
-
z
)
/
(
z1
-
z
)
(
2
)
When the projection plane
20
is drawn through a point C
1
(xc
1
, yc
1
, zc
1
), the values z, x and y are given by the following equations:
z=[X·k
1
−
Y·k
2
−
yc
1
·
k
3
−{(
ci·k
3
·
zc
1
)/
bi}+{
(
ai·k
3
·
X
)/(
bi·
cos &agr;)}−{(
ai·k
3
·
xc
1
)/
bi}]/[
1−{(
ci·k
3
)/
bi}+{
(
ai·k
3
·sin &agr;)/(
bi
·cos &agr;)}]  (3)
x=
(
X−z·
sin &agr;)/cos &agr;  (4)
y=[yc
1
+{−
ci·
(
z−zc
1
)−
ai·
(
x−xc
1
)}]/
bi
  (5)
in which k
1
=sin &agr;, k
2
=cos &agr;/sin &bgr;, k
3
=cos &agr;·cos &bgr;/sin &bgr;, ai=1/a, bi=1/b, and ci=1/c.
Here, as the aforementioned point C
1
(xc
1
, yc
1
, zc
1
), for example, a point of intersection of a perpendicular drawn from the view point e(x
1
, y
1
, z
1
) to the projection plate
20
and the projection plane
20
may be used under the conditions as follows:
zc
1
=
z
1
±[
h/
sqrt{1+(
c
2
/a
2
)+(
c
2
/b
2
)}](“−” in “
z
1
±” is valid in the case of
z
0
<
zc
1
)  (6)
xc
1
=
x
1
+{
c·
(
z
1
−
zc
1
)/
a}
  (7)
 
yc
1
=
y
1
+{
c
·(
z
1
−
zc
1
)/
b}
  (8)
in which h represents the length of the perpendicular from the view point e(x
1
, y
1
, z
1
) to the projection plane
20
.
When the projected image is expressed with 512 pixels by 512 pixels on the display screen (not shown) equivalent to the projection plane
20
, each of X and Y takes values of −256 to +256. Values of x and y are determined correspondingly to the respective values of X and Y in accordance with the aforementioned equations (3), (4) and (5). Because x
1
, y
1
and z
1
of the point e are given freely, coordinates x
0
and z
0
of the pixel point S on the tomographic image y
0
=d
0
are determined in accordance with the following equations (9) and (10).
x
0
={(
d
0
−
y
)/(
y
1
−
y
)}×(
x
1
−
x
)+
x
  (9)
z
0
={(
d
0
−
y
)/(
y
1
−
y
)}×(
z
1
−
z
)+
z
  (10)
Because d
0
takes a plurality of values correspondingly to the plurality of tomographic images, a plurality of points (x
0
, z
0
) to be projected are determined correspondingly to one combination of X and Y on the projection plane.
In
FIG. 1
, L represents the distance from the view point e to the point S, and L is a parameter for obtaining the pixel value (luminance) of the point P. The pixel value of the point P is proportional to a value obtained by subtracting the above L from the maximum pixel value L max which is set in advance. As the value of L max−L increases, the density on the screen is made bright.
The aforementioned coordinate transformation is performed with respect to all the points on the projection plane
20
equivalent to the display screen. Further, the aforementioned coordinate transformation is performed with respect to all the tomographic images
30
.
Further, shading is performed so that a scenographic feeling is given to construct a three-dimensional image when the tomographic images are displayed on a two-dimensional display screen. A predetermined shading algorithm, for example, a depth method, is used for shading, so that pixel values are given to coordinates of respective pixels on the projection plane
20
in accordance with the shading algorithm.
According to the method of
FIG. 1
, a three-dimensional image can be obtained as if the inside of a subject is observed through an endoscope, becaus

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