JP3706098B2 - 3D image construction method - Google Patents

Description

ここで、上記Ｃ１点（ｘｃ_１，ｙｃ_１，ｚｃ_１）には、例えば、視点ｅ（ｘ_１，ｙ_１，ｚ_１）から投影平面４に下ろした垂線と投影平面４の交わる点（この点と視点ｅ間の距離はｈ）として、
ｚｃ_１＝ｚ_１＋−〔ｈ／ｓｑｒｔ｛１＋（ｃ^２／ａ^２）＋（ｃ^２／ｂ^２）｝〕（「ｚ_１＋−」の「−」はｚ_０＜ｚｃ_１のとき） …（１０）
ｘｃ_１＝ｘ_１＋｛ｃ・（ｚ_１−ｚｃ_１）／ａ｝ …（１１）
ｙｃ_１＝ｙ_１＋｛ｃ・（ｚ_１−ｚｃ_１）／ｂ｝ …（１２）
を使ってもよい。
【００４２】
投影された画像を投影平面４に相当する表示画面（図示せず）上に、縦５１２画素×横５１２画素で表示するとき、Ｘ，Ｙは−２５６から＋２５６までの値を取る。それぞれのＸ，Ｙに対して上掲（７），（８），（９）式によりｘ，ｙが決まる。ｅ点のｘ１，ｙ１，ｚ１は任意に与えるので、下掲（１３），（１４）式により、ｙ０，ｄ０の断層像上で画素Ｓ点の座標ｘ０，ｚ０が決まる。
【００４３】
ｘ_０＝｛（ｄ_０−ｙ）／（ｙ_１−ｙ）｝×（ｘ_１−ｘ）＋ｘ …（１３）
ｚ_０＝｛（ｄ_０−ｙ）／（ｙ_１−ｙ）｝×（ｚ_１−ｚ）＋ｚ …（１４）
断層像は複数あって、ｄ０も複数個あるので、１組のＸ，Ｙに対して複数の投影すべき点ｘ_０，ｙ_０が決まる。
【００４４】
なお、図６中のＲは視点ｅからＳ点までの距離を示すもので、このＲはＰ点の画素値（輝度）を求める際のパラメータとなる。Ｐ点の画素値は、設定された画素値（輝度）の最大値Ｒｍａｘから上記Ｒを引算した値に比例する。このＰ点は表示メモリ上では（η，ξ）点に対応するので（η，ξ）点に前記画素値を格納する。
【００４５】
以上のような座標変換を、表示画面に相当する投影平面４上の全ての点について行う。また、全ての断層像２３について行う。更に、構成された結果像である三次元画像に対して行っても、あるいは構成前の１枚、１枚の断層像に対して行ってもよい。
【００４６】
図７は本発明方法が適用可能なハードウェア構成例を示すブロック図である。
この図７において、５０はＣＰＵ、５１は主メモリ、５２は磁気ディスク、５３は表示メモリ、５５はマウスコントローラで、これらは共通バス５７に接続されている。磁気ディスク５２には、複数の断層像及び本発明方法の実行演算のためのプログラムなどが格納されている。
【００４７】
ＣＰＵ５０は、これら複数の断層像及び本発明方法の実行演算のためのプログラムを読み出し、主メモリ５１を用いて眼球変換等の演算を行い、その結果を表示メモリ５３に送り、ＣＲＴモニタ５４に表示させる。マウスコントローラ５５に接続されたマウス５６は、眼球変換等の演算の際の、視点位置等を指定する。
眼球変換され歪補正された画像は、必要に応じて磁気ディスク５２に格納される。
【００４８】
【発明の効果】
以上説明したように本発明によれは、投影方向に依存する投影像の歪が補正され、投影方向の違いによって投影データ（長さないし大きさ）が異なってしまうことが防止できるという効果がある．
【図面の簡単な説明】
【図１】本発明方法の概略を示すフローチャートである。
【図２】眼球変換による歪補正の原理説明図である。
【図３】同じく眼球変換による歪補正の原理説明図である。
【図４】三次元画像の構成方法における断層像画素座標の投影面上の座標への変換を説明するための図である。
【図５】同じく複数の断層像についての画素座標の投影面上の座標への変換を脱明するための図である。
【図６】視点、断層像及び投影面がより複雑な位置関係をもった場合の中心投影による座標変換を説明するための図である。
【図７】本発明方法が適用可能なハードウェア構成例を示すブロック図である。
【図８】眼球投影の説明図である。
【図９】中心投影方法と歪の説明図である。
【符号の説明】
３ 投影球面
４ 投影平面
Ｘ，Ｙ，Ｚ 三次元座標系の各舳
Ｏ 三次元座標系の原点
ｅ 視点
ｈ 視点ｅと投影平面４との距離
Ｒ 投影球面３の半径
Ｐ 投影平面４上の点（Ｘ１，Ｙ１）
ψ 直線ＯＰとＸ軸とのなす角
Ｑ 投影平面４上のＰ点に対応する投影球面３上の点（直線Ｐｅと投影球面３の交点）
θ 直線Ｚ１ ＱとＺ軸のなす角
Ｌ 投影球面３上の円弧ＯＱ
Ｌ′ Ｌと同じ長さをもった直線ＯＰ上の線分
η ＣＲＴ表示アドレス（Ｘ軸に平行にとる）
ξ ＣＲＴ表示アドレス（Ｙ軸に平行にとる）
Ｕ 直線ｅＱの長さ
γ 線分ｅＰとＺ軸とのなす角
ｗ ＱからＺ舳に垂直に下ろした直線の長さ[0001]
[Industrial application fields]
The present invention relates to computer graphics, and more particularly to a three-dimensional image construction method for improving central projection.
[0002]
[Prior art]
The center projection method is a method of projecting a projection target onto the projection plane 4 by emitting light rays in a conical shape from one point (viewpoint) e as shown in FIG. This method is applied to the projection of a tomographic image and is used for the construction of a three-dimensional image (for example, JP-A-6-3492).
[0003]
By the way, conventionally, the projection plane in the above-described central projection method (general central projection method) is “Computer Graphics” (JD FOLEY & A. VAN. DAM), which is a typical document relating to computer graphics. It was a flat surface as can be seen from pages 275-316 of the translation of Tomomi Imamiya, July 15, 1984, published by the Japan Computer Association.
[0004]
[Problems to be solved by the invention]
As described above, in the prior art, the projection surface in the central projection method is a plane. For this reason, in FIG. 9B in which the following distortion has occurred, when the projection objects 40a and 40b are projected onto the projection plane 4, projection images 40A and 40B are obtained, respectively. If the lengths (the horizontal dimension in the drawing) of the projection target 40a and the projection target 40b are the same, the projection target 40b is viewed from an oblique direction, and thus should appear shorter than the projection target 40a.
[0005]
However, as can be seen from FIG. 9B, this does not happen (in contrast, it becomes longer), and the distortion depending on the projection direction increases as the distance between the viewpoint e and the projection plane 4 decreases. There was a problem of becoming.
[0006]
An object of the present invention is to provide a three-dimensional image construction method that can eliminate distortion of a projected image that depends on the projection direction.
[0007]
[Means for Solving the Problems]
The present invention uses a three-dimensional image constructing apparatus including a setting unit and first and second projecting units to project a projection line in a conical shape from a viewpoint to a projection target that is a three-dimensional data group. In the three-dimensional image construction method by the central projection method of projecting the projection target on the plane projection plane to obtain the central projection data and constructing the three-dimensional image from the central projection data, the setting means A first step of setting a viewpoint and the projection plane; a first step of setting a virtual sphere model between the viewpoint and the projection plane and contacting the viewpoint and the projection plane at one point; and the first projection Means for projecting the projection target viewed from the viewpoint onto the spherical surface of the set spherical model and obtaining spherical projection data; and the obtained spherical projection data by the second projection means. Throw on the projection surface A third step of obtaining projection data in which positional distortion dependent on the projection direction generated when the central projection data is projected is corrected, and a three-dimensional image by the central projection method, A configuration method is disclosed.
[0008]
The present invention further includes a step of enlarging an image size of the projection target when projecting the spherical projection data obtained by projecting onto the spherical model in the third step onto the projection plane. A three-dimensional image construction method using a central projection method according to claim 1 is disclosed.
[0009]
Furthermore, the present invention uses a three-dimensional image construction apparatus comprising setting means, first and second projection point acquisition means, and distance calculation means, and uses a viewpoint as a vertex to project a projection line in a conical shape from the viewpoint. In the three-dimensional image construction method based on the central projection method in which a projection data is obtained by projecting the projection target onto a flat projection surface and a three-dimensional image is constructed from the projection data. A first step of setting a viewpoint and a projection plane, and a sphere model between the viewpoint and the projection plane and in contact with the projection plane at one point; and a projection line is given by the first projection point acquisition unit. A second step of projecting the projection target point on the spherical surface of the spherical model and the projection plane where the projection lines intersect to obtain a projection point Q on the spherical surface and a projection point P on the projection plane; By the distance calculation means, the projection point Q and A third step of obtaining a distance L along the spherical surface with the projection plane contact of the model, and the second projection point acquisition means based on the distance L and the angle φ of the projection point P on the projection plane. And a fourth step of obtaining a projection point G on the projection plane in which the positional distortion depending on the projection direction obtained in correspondence with the projection point Q is corrected. An image construction method is disclosed.
[0010]
【Example】
Embodiments of the present invention will be described below with reference to the drawings.
FIG. 1 is a flowchart showing an embodiment of the center projection method according to the present invention.
As shown in FIG. 1, in the central projection method according to the present invention, a projection target is first a projection plane composed of a plane by a general central projection method (primary projection plane: a projection plane before distortion correction by eyeball transformation described later, ie, Projection onto a conventional projection plane (step 1).
[0011]
Then, after or at the time of projection, reprojection is performed on the projection plane (secondary projection plane: a projection plane after distortion correction by eyeball conversion described later) by eyeball conversion described later to obtain a projection image of the projection target ( Step 2).
[0012]
Here, the eyeball transformation refers to two hemispherical surfaces obtained by dividing a spherical surface having a center on the line of sight into two in the direction perpendicular to the line of sight at the center position after or upon projection onto the projection plane. Of these, re-projection onto the projection plane through projection onto the projection plane (projection sphere) having a hemisphere far from the viewpoint as the projection plane.
[0013]
That is, in the present invention, the projection spherical surface is used as a central projection, and in this case, each point (address) along the hemispherical surface that is the projection surface corresponds to a display pixel (address) of the CRT. Then, in order to obtain the same effect as that projected onto the projection spherical surface on a plane (CRT screen), eyeball transformation is performed and distortion correction is performed.
[0014]
Hereinafter, the principle of distortion correction by eyeball transformation of the method of the present invention will be described with reference to FIGS.
First, referring to FIG. 2, FIG. 2 shows a case where the viewpoint e is h = 2R. In FIG. 2, reference numeral 3 denotes a hemisphere on the side farther from the viewpoint out of two hemispheres I and II obtained by dividing a spherical surface centered on the line of sight (Z axis) in the direction perpendicular to the line of sight at the center position. A projection surface (hereinafter referred to as a projection sphere) composed of a surface (hemispherical surface I). Reference numeral 4 denotes a flat projection plane (hereinafter referred to as a projection plane), which is a projection plane before distortion correction by eyeball transformation, that is, a primary projection plane as a projection plane of the conventional method, and after distortion correction by eyeball transformation. It is also a secondary projection plane as a projection plane. The projection plane 4 corresponds to a screen that is a display surface of the CRT.
[0015]
Also,
X, Y, Z are the axes of the three-dimensional coordinate system,
O is the origin of the 3D 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 on the projection plane 4 (X ₁ , Y ₁ ),
ψ is the angle between the straight line OP and the X axis,
Q is a point on the projection sphere 3 corresponding to the point P on the projection plane 4 (intersection of the straight line Pe and the projection sphere 3),
θ is the angle between the straight line Z ₁ Q and the Z axis,
L is an arc OQ on the projection spherical surface 3,
L ′ is a line segment on the straight line OP having the same length as L,
η is a CRT display address (taken parallel to the X axis),
ξ is the CRT display address (taken parallel to the Y axis),
It is.
[0016]
According to this, the following equation holds.
When h = 2 · R corresponding to the eyeball,
For the triangle eOP, tan (θ / 2) = sqrt (X ₁ ² + Y ₁ ² ) / 2R
For triangle X ₁ OP, tan (φ) = Y ₁ / X ₁
Is given.
[0017]
Therefore, if X ₁ and Y ₁ are specified, the corresponding η ₁ and ξ ₁ are
ψ = arctan (Y ₁ / X ₁ )
θ = 2 · arctan [sqrt (X ₁ ² + Y ₁ ² ) / 2R]
L = R · θ
Use
η ₁ = L · cos (ψ)
ξ ₁ = L · sin (ψ)
It becomes.
[0018]
These η ₁ and ξ ₁ are pixel addresses on the display memory. That is, the point (X ₁ , Y ₁ ) of the projection plane 4 is displayed at the point (η ₁ , ξ ₁ ) on the CRT screen, and thus distortion correction by eyeball transformation has been performed. become.
[0019]
Further, the image size is reduced by this eyeball transformation (from point P to point (η ₁ , ξ ₁ )). Therefore, the image size of the projected image on the projection plane 4 after distortion correction can be projected larger than the image size of the image that has been corrected and projected by eyeball conversion.
[0020]
Next, the case where the viewpoint e is other than h = 2R will be described with reference to FIG. 3A and 3B, the same reference numerals as those in FIG. 2 denote the same or corresponding parts.
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 the straight line from Q to the Z axis,
It is.
[0021]
According to this, the following equation holds.
U = sqrt [(h−R) ² + R ² −2 · (h−R) · R · cos (π−θ)]
Then,
U · sinγ = R · sinθ
It becomes.
[0022]
Γ is
tan γ = sqrt (X ₁ ² + Y ₁ ² ) / h
Given in.
From this, when X ₁ and Y ₁ are designated, θ is obtained.
[0023]
Since φ is determined from tan φ = Y ₁ / X ₁ , L = R · θ,
η ₁ = L · cos φ
ξ ₁ = L · sinφ
It becomes.
[0024]
These η ₁ and ξ ₁ are pixel addresses on the display memory. That is, the point (X ₁ , Y ₁ ) of the projection plane 4 is displayed at the point (η ₁ , ξ ₁ ) on the CRT screen, and thus distortion correction by eyeball transformation has been performed. become.
[0025]
The projection target may be data input by an input device such as a mouse, or data obtained as a result of calculation by an arithmetic device such as a tomogram (including a tomogram obtained by decomposing a volume image obtained by three-dimensional measurement). Good.
[0026]
4 to 6 show a method (Japanese Patent Application No. 6-3492) for constructing a three-dimensional image from a plurality of tomographic images by a general central projection method. In such a case, central projection is performed. As described above, in order to eliminate distortion, eyeball transformation is necessary. Hereinafter, an example in which the method of the present invention is applied to a method for constructing a three-dimensional image will be described. In either case of FIGS. 5 and 6, a tomographic image is first projected on a plane X, Y projection plane (projection plane) 4 and then converted into η and ξ planes by eyeball transformation. Become.
[0027]
First, in the above three-dimensional image construction method, coordinate conversion by center projection will be described. Conversion of the pixel coordinates of each tomographic image into coordinates on the projection surface in projecting each tomographic image onto the projection surface by central projection is performed as follows.
[0028]
In the example shown in FIG. 4, in order to simplify the explanation, the coordinate system is taken so that the projection plane, the tomographic image plane, and the xy plane are parallel to each other.
In FIG. 4,
x, y, z are axes of the three-dimensional coordinate system (x, y, z),
The point e (x ₁ , y ₁ , d ₁ ) is the position of the viewpoint e,
P point (X, Y) is a point on the projection plane (corresponding to the display screen) 21;
The point S (x ₀ , y ₀ , d ₀ ) is the point where the line 22 passing through the point e (x ₁ , y ₁ , d ₁ ) and the point P (X, Y) intersects with the tomographic image 23A,
It is.
[0029]
Also,
D is the position of the projection plane 21 on the projection plane 21 (on the z axis) and can be arbitrarily set.
[0030]
d ₀ is the position of the tomographic image 23A (on the z axis) and is determined at the time of measurement.
[0031]
d ₁ is the z coordinate of the viewpoint e,
It is.
[0032]
According to this, the following equation holds.
X = {(D−d ₁ ) / (d ₀ −d ₁ )} × (x ₀ −x ₁ ) + x _l (1)
Y = {(D−d ₁ ) / (d ₀ −d ₁ )} × (y ₀ −y ₁ ) + y ₁ (2)
_{x 0 = {(d 0 -D} ) / (d 1 -D)} × (x 1 -x) + X ... (3)
_{y 0 = {(d 0 -D} ) / (d 1 -D)} × (y 1 -y) + Y ... (4)
[0033]
When the projected image is displayed on a display screen (not shown) corresponding to the projection plane 21 in a vertical 512 pixel × horizontal 512 pixel, X and Y take values from −256 to +256. For the respective X and Y, on the d ₀ tomographic image 23A, x ₀ and y ₀ 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 d ₀ , a plurality of points x ₀ and y ₀ to be projected are determined for a set of X and Y.
[0034]
In the same coordinate system, tomographic images 23B to 23E are prepared in addition to the tomographic image 23A, and a diagram viewed from the y-axis direction is shown in FIG. In FIG. 5A, tomographic images 23A to 23E are tomographic images obtained at equal intervals in the same direction with respect to the same object (in the illustrated example, they are equal intervals, but are not necessarily equal intervals). In the tomographic image 23B, the organ regions B ₁ , B ₂ and B ₃ are emphasized. When the organ regions B ₁ , B ₂ , B ₃ are projected onto the projection plane 21, they become B ₁ ′, B ₂ ′, B ₃ ′. Similarly, when organ regions C ₁ and C ₂ of the tomographic image 23C are projected onto the projection plane 21, they become C ₁ 'and C ₂ '.
[0035]
Here, when writing projection data (here, B ₁ ′, B ₂ ′, B ₃ ′; C ₁ ′, C ₂ ′) in a display memory (not shown), a three-dimensional effect is produced. , Projection data existing farther from the viewpoint e is written first, and projection data closer thereto is overwritten later. Accordingly, here, since the projection data B ₁ , B ₂ , and B ₃ are located farther from the viewpoint e than the projection data C ₁ and C ₂ , the projection data B ₁ ′, B ₂ ′, and B ₃ ′ are given first. The projection data C ₁ ′ and C ₂ ′ are overwritten later. In FIG. 7A, projection data B ₁ ′, B ₂ ′, B ₃ ′: C ₁ ′, C ₂ ′ are shown separately from the projection plane 21, but this is projection data to be written into the display memory. B ₁ ′, B ₂ ′, B ₃ ′; only because the order of C ₁ ′, C ₂ ′ is easy to understand, and the projection data B ₁ ′, B ₂ ′, B ₃ ′ written first is overwritten on it. Actually, the projection data C ₁ ′ and C ₂ ′ are also written on the projection plane 21.
[0036]
FIG. 5B is a more generalized example than FIG. 5A, and shows an example where the projection plane and the tomographic image plane are not parallel. In this case, it is necessary to create tomographic images 23a, 23b, 23c... Directed to a plane parallel to the projection plane 21 by interpolation calculation from the tomographic images 23A, 23B, 23C. Others are the same as in the case of FIG. Note that b ₁ ′; c ₁ ′, c ₂ ′; d ₁ ′ are projection data of the organ regions b ₁ ; c ₁ , c ₂ ; d ₁ on the tomographic images 23 b, 23 c, and 23 d that have been interpolated. .
[0037]
FIG. 6 is a diagram for explaining coordinate transformation by central projection when the viewpoint, tomographic image, and projection plane have a more complicated positional relationship. S point (x ₀ , z ₀ , y on the tomographic image 23 is illustrated. ₀ ) indicates that the projection result is P point (x, y, z) on the projection plane.
[0038]
In FIG. 6, the conversion of the pixel coordinates of the tomographic image 23 to the coordinates on the projection plane 4 in the projection of the tomographic image 23 onto the projection plane 4 by center projection is performed as follows.
here,
a is the point where the x-axis and the projection plane 4 intersect,
b is the point where the y-axis and the projection plane 4 intersect,
c is the point where the z-axis and the projection plane 4 intersect,
It is.
[0039]
Also,
α is an angle formed by a line projected from the origin to the projection plane 4 on the zx plane and the x axis.
β is the angle between the perpendicular and the xz plane,
The point e (x ₁ , y ₁ , z ₁ ) is the position of the viewpoint e,
P point (x, y, z) is a point on the projection plane (corresponding to the display screen) 4,
The S point (x ₀ , z ₀ , y ₀ ) is the point where the straight line 22 passing through the e point (x ₁ , y ₁ , z ₁ ) and the P point (x, y, z) and the tomographic image 23 intersect,
Then, the following equation holds.
[0040]
First, the projection plane 4 is (x / a) + (y / b) + (z / c) = 1 (5)
It is represented by
The straight line 22 passing through the point e (x ₁ , y ₁ , z ₁ ) and the point P (x, y, z) is (x ₀ −x) / (x ₁ −x) = (y ₀ −y) / (Y ₁ -y) = (z ₀ -z) / (z ₁ -z) (6)
Given in.
[0041]
When the projection plane 4 passes through the C1 point (xc ₁ , yc ₁ , zc ₁ ),
k ₁ = sin α
k ₂ = cos α / sin β
k ₃ = cos α · cos β / sin β
a _i = 1 / a
b _i = 1 / b
c _i = 1 / c
As

Here, the C1 point (xc ₁ , yc ₁ , zc ₁ ) is, for example, a point (this point) where the perpendicular line dropped from the viewpoint e (x ₁ , y ₁ , z ₁ ) to the projection plane 4 and the projection plane 4 intersect. The distance between point and viewpoint e is h)
zc ₁ = z ₁ + − [h / sqrt {1+ (c ² / a ² ) + (c ² / b ² )}] (“−” in “z ₁ + −” is z ₀ <zc ₁ ) (10)
xc ₁ = x ₁ + {c · (z ₁ −zc ₁ ) / a} (11)
yc ₁ = y ₁ + {c · (z ₁ −zc ₁ ) / b} (12)
May be used.
[0042]
When a projected image is displayed on a display screen (not shown) corresponding to the projection plane 4 with 512 pixels vertically × 512 pixels horizontally, X and Y take values from −256 to +256. For each X and Y, x and y are determined by the above equations (7), (8) and (9). Since x1, y1, and z1 of the e point are arbitrarily given, the coordinates x0 and z0 of the pixel S point are determined on the tomographic images of y0 and d0 by the following equations (13) and (14).
[0043]
_{x 0 = {(d 0 -y} ) / (y 1 -y)} × (x 1 -x) + x ... (13)
z ₀ = {(d ₀ −y) / (y ₁ −y)} × (z ₁ −z) + z (14)
Since there are a plurality of tomographic images and a plurality of d0, a plurality of points x ₀ and y ₀ to be projected are determined for a set of X and Y.
[0044]
Note that R in FIG. 6 indicates the distance from the viewpoint e to the S point, and this R is a parameter for obtaining the pixel value (luminance) of the P point. The pixel value at point P is proportional to a value obtained by subtracting R from the maximum value Rmax of the set pixel value (luminance). Since the P point corresponds to the (η, ξ) point on the display memory, the pixel value is stored at the (η, ξ) point.
[0045]
The coordinate conversion as described above is performed for all points on the projection plane 4 corresponding to the display screen. This is performed for all tomographic images 23. Furthermore, it may be performed on a three-dimensional image that is a constructed result image, or may be performed on one tomographic image before construction.
[0046]
FIG. 7 is a block diagram showing a hardware configuration example to which the method of the present invention can be applied.
In FIG. 7, 50 is a CPU, 51 is a main memory, 52 is a magnetic disk, 53 is a display memory, 55 is a mouse controller, and these are connected to a common bus 57. The magnetic disk 52 stores a plurality of tomographic images, a program for executing calculation of the method of the present invention, and the like.
[0047]
The CPU 50 reads out the plurality of tomographic images and a program for execution calculation of the method of the present invention, performs calculation such as eyeball conversion using the main memory 51, sends the result to the display memory 53, and displays it on the CRT monitor 54. Let A mouse 56 connected to the mouse controller 55 designates a viewpoint position and the like for calculations such as eyeball conversion.
The image subjected to eyeball transformation and distortion correction is stored in the magnetic disk 52 as necessary.
[0048]
【The invention's effect】
As described above, according to the present invention, the distortion of the projection image depending on the projection direction is corrected, and it is possible to prevent the projection data (not length or size) from being different depending on the projection direction. .
[Brief description of the drawings]
FIG. 1 is a flowchart showing an outline of a method of the present invention.
FIG. 2 is a diagram illustrating the principle of distortion correction by eyeball conversion.
FIG. 3 is a diagram for explaining the principle of distortion correction by eyeball conversion.
FIG. 4 is a diagram for explaining conversion of tomographic image pixel coordinates to coordinates on a projection plane in a method of constructing a three-dimensional image.
FIG. 5 is a diagram for deciphering conversion of pixel coordinates into coordinates on the projection plane for a plurality of tomographic images.
FIG. 6 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;
FIG. 7 is a block diagram showing a hardware configuration example to which the method of the present invention can be applied.
FIG. 8 is an explanatory diagram of eyeball projection.
FIG. 9 is an explanatory diagram of a center projection method and distortion.
[Explanation of symbols]
3 Projection sphere 4 Projection plane X, Y, Z Each 舳 O of the 3D coordinate system Origin 3 e of the 3D coordinate system Viewpoint h Distance between viewpoint e and projection plane 4 Radius P of projection sphere 3 Point on projection plane 4 (X1, Y1)
ψ Angle Q between straight line OP and X axis Point on projection sphere 3 corresponding to point P on projection plane 4 (intersection of line Pe and projection sphere 3)
θ Angle L formed by straight line Z1 Q and Z axis Arc OQ on projected spherical surface 3
L ′ Line segment on 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 the Y axis)
U Length of straight line eQ γ Length of straight line drawn perpendicularly to Z 舳 from angle w Q formed by line segment eP and Z axis

Claims (3)

  When a projection line is emitted from a viewpoint to a projection target that is a three-dimensional data group using a three-dimensional image constructing apparatus including a setting unit and first and second projection units, with the viewpoint as a vertex. In the three-dimensional image construction method based on the central projection method in which the projection target is projected onto a flat projection surface to obtain central projection data, and a three-dimensional image is constructed from the central projection data, the viewpoint and the projection are performed by the setting unit. A first step of setting a plane and a virtual sphere model between the viewpoint and the projection plane and in contact with each of the viewpoint and the projection plane at one point; and A second step of obtaining a spherical projection data by projecting a projection target viewed from the viewpoint onto a spherical surface of a set spherical model, and the obtained spherical projection data on the projection plane by the second projection means. Let it project Third step and three-dimensional image constructing method according to the central projection method which comprising the obtaining projection data obtained by correcting the positional distortion that depends on the projection direction occurring when the serial central projection data is projected.   When the spherical projection data obtained by projecting onto the spherical model in the third step is projected onto the projection plane, the projection is performed by enlarging the projection target image size. The method of constructing a three-dimensional image by the center projection method according to claim 1.   Using a three-dimensional image construction apparatus comprising a setting means, first and second projection point acquisition means, and a distance calculation means, a projection line is generated from the viewpoint to a three-dimensional projection object in a conical shape with the viewpoint as a vertex. In the 3D image construction method based on the central projection method in which the projection target is projected onto a flat projection surface to obtain projection data, and a 3D image is constructed from the projection data, the setting means is used to project the viewpoint and the projection. A first step of setting a plane and a spherical model between the viewpoint and the projection plane and in contact with the projection plane at one point; and the projection line is given by the first projection point acquisition means, and the projection is performed. A second step of projecting the projection target point onto the spherical surface of the spherical model and the projection plane where the lines intersect to obtain a projection point Q on the spherical surface and a projection point P on the projection plane; and the distance calculating means By means of the projection point Q and the spherical model Based on the third step of obtaining the distance L along the spherical surface with the shadow contact point and the angle L of the projection point P on the projection plane by the second projection point acquisition means, And a fourth step of obtaining a projection point G on the projection plane in which the positional distortion depending on the projection direction obtained in correspondence with the projection point Q is corrected. Method.

Images