JP3411665B2 - 3D image construction device - Google Patents
3D image construction deviceInfo
- Publication number
- JP3411665B2 JP3411665B2 JP08977094A JP8977094A JP3411665B2 JP 3411665 B2 JP3411665 B2 JP 3411665B2 JP 08977094 A JP08977094 A JP 08977094A JP 8977094 A JP8977094 A JP 8977094A JP 3411665 B2 JP3411665 B2 JP 3411665B2
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Description
【0001】[0001]
【産業上の利用分野】本発明は、コンピュータグラフィ
ックスに係り、特に中心投影の改良をはかる三次元装置
に関するものである。BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to computer graphics, and more particularly to a three-dimensional apparatus for improving central projection.
【0002】[0002]
【従来の技術】中心投影方法は、図9(a)に示すよう
に、一点(視点)eから円錐状に光線を発して、投影対
象を投影面4上に投影する方法である。この方法が断層
像の投影に応用され、三次元画像の構成に利用されてい
る(例えば、特願平6−3492号)。2. Description of the Related Art The central projection method is a method of projecting a projection target on a projection surface 4 by emitting a light beam in a conical shape from a point (viewpoint) e as shown in FIG. This method is applied to the projection of a tomographic image and is used to construct a three-dimensional image (for example, Japanese Patent Application No. 6-3492).
【0003】ところで従来、上記のような中心投影方法
(一般的中心投影方法)における投影面は、コンピュー
タグラフイックスに関する代表的な文献である「コンピ
ュータ・グラフイックス」(J.D.FOLEY &
A.VAN DAM著 今宮淳美訳 昭和59年7月1
5日 日本コンピュータ協会発行)の275〜316ペ
ージ等を見ても分かるように平面であった。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).
【0004】[0004]
【発明が解決しようとする課題】上記のように従来技術
では、中心投影方法における投影面は平面であった。こ
のため、次のような歪が発生した。図9(b)におい
て、投影対象40a,40bを投影面4に投影すると、
それぞれ投影像40A,40Bとなる。投影対象40a
と投影対象40bの長さ(図示左右方向の寸法)が同じ
であるとすると、投影対象40bは斜めから見ることに
なるので投影対象40aより短く見える筈である。As described above, in the prior art, the projection surface in the central projection method is a plane. Therefore, the following distortion was generated. In FIG. 9B, when the projection targets 40a and 40b are projected on the projection surface 4,
It becomes projected images 40A and 40B, respectively. Projection target 40a
If the projection target 40b has the same length (the size 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.
【0005】しかし、図9(b)から分かるように、そ
のようにはならず(逆に長くなり)、またこのような投
影方向に依存する歪は、視点eと投影面4との距離が小
さくなるほど大きくなるという問題点があった。However, as can be seen from FIG. 9 (b), this is not the case (longer conversely), and such distortion depending on the projection direction is caused by the distance between the viewpoint e and the projection surface 4. There was a problem that the smaller the size, the larger the size.
【0006】本発明の目的は、投影方向に依存する投影
像の歪をなくすことのできる三次元画像構成装置を提供
することにある。It is an object of the present invention to provide a three-dimensional image constructing apparatus capable of eliminating distortion of a projected image depending on the projection direction.
【0007】[0007]
【課題を解決するための手段】本発明は、視点を頂点と
して円錐状に投影線をその視点から三次元データ群であ
る投影対象へ発したときの、その投影対象を平面の投影
面に投影して中心投影データを得、中心投影データから
三次元画像を構成する中心投影法による三次元画像構成
装置において、前記視点と前記投影面との設定、及び視
点と投影面との間であって視点と投影面とのそれぞれに
一点で接する仮想的な球モデルを設定する設定手段と、
該設定された球モデルの球面上に前記視点から見た投影
対象を投影させ球面投影データを得る第1の投影手段
と、該得られた球面投影データを前記投影面に投影させ
て、前記中心投影データが投影されたときに生じた投影
方向に依存する位置歪みを補正した投影データを得る第
2の投影手段とを備えたことを特徴とする中心投影法に
よる三次元画像構成装置を開示する。According to the present invention, when a projection line is conically formed with a viewpoint as an apex from the viewpoint to a projection target which is a three-dimensional data group, the projection target is projected onto a flat projection surface. In the three-dimensional image construction device by the central projection method that obtains the central projection data and constructs a three-dimensional image from the central projection data, in the setting of the viewpoint and the projection plane, and between the viewpoint and the projection plane, Setting means for setting a virtual sphere model that is in contact with each of the viewpoint and the projection surface at one point,
First projection means for projecting a projection target viewed from the viewpoint onto the spherical surface of the set sphere model to obtain spherical projection data, and projecting the obtained spherical projection data onto the projection surface for the center. Disclosed is a three-dimensional image composing apparatus according to the central projection method, which comprises: a second projection unit that obtains projection data in which positional distortion depending on a projection direction generated when the projection data is projected is corrected. .
【0008】更に本発明は、前記第2の投影手段が前記
球面モデル上に投影して得た球面投影データを前記投影
面に投影させるさいに、その投影対象の画像サイズを拡
大させる手段を備えて拡大を行わせることを特徴とする
請求項1に記載の中心投影法による三次元画像構成装置
を開示する。The present invention further comprises means for expanding the image size of the projection target when the second projection means projects the spherical projection data obtained by projecting onto the spherical model on the projection surface. Disclosed is a three-dimensional image constructing apparatus according to the central projection method according to claim 1, which enlarges the image.
【0009】更に本発明は、視点を頂点として円錐状に
投影線をその視点から三次元の投影対象へ発したとき
の、その投影対象を平面の投影面に投影して投影データ
を得、この投影データから三次元画像を構成する中心投
影法による三次元画像構成装置において、視点と投影面
の設定、及び視点と投影面との間であって投影面に一点
で接する球モデルを設定する手段と、投影線を与えて、
この投影線が交わる前記球モデルの球面上と前記投影面
上に、前記投影対象の点を投影し球面上の投影点Qと投
影面上の投影点Pを得る手段と、前記投影点Qと球モデ
ルの投影面接点との球面に沿った距離Lを求める手段
と、この距離Lと投影面上での投影点Pの角度φとに基
づいて、前記投影点Qと対応させて得た投影方向に依存
する位置歪みを補正した前記投影面上の投影点Gを得る
手段とを備えたことを特徴とする中心投影法による三次
元画像構成装置を開示する。Further, according to the present invention, when a projection line having a conical shape with a viewpoint as a vertex is emitted from the viewpoint to a three-dimensional projection target, the projection target is projected onto a plane projection surface to obtain projection data. A means for setting a viewpoint and a projection surface, and a sphere model between the viewpoint and the projection surface, which is in contact with the projection surface at a single point, in a three-dimensional image forming apparatus by a central projection method for forming a three-dimensional image from projection data And give the projection line,
Means for projecting the point of the projection target on the spherical surface of the spherical model and the projection surface where the projection lines intersect to obtain a projection point Q on the spherical surface and a projection point P on the projection surface; and the projection point Q. Means for obtaining the distance L along the sphere with the projection plane contact point of the sphere model, and the projection obtained in correspondence with the projection point Q based on this distance L and the angle φ of the projection point P on the projection surface And a means for obtaining a projection point G on the projection plane in which positional distortion depending on a direction is corrected, and a three-dimensional image forming apparatus by the central projection method.
【0010】[0010]
【実施例】以下、図面を参照して本発明の実施例を説明
する。図1は、本発明による中心投影方法の一実施例を
示すフローチャートである。図1に示すように、本発明
による中心投影方法は、投影対象を、まず一般的な中心
投影方法によって平面からなる投影面(1次投影平面:
後述眼球変換による歪補正前の投影平面、すなわち従来
方法の投影平面)へ投影する(ステップ1)。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, according to the center projection method of the present invention, a projection target is first formed by a general center projection method as a projection plane (primary projection plane:
Projection is performed on a projection plane before distortion correction by eyeball conversion described later, that is, a projection plane of a conventional method) (step 1).
【0011】そして、その投影後又は投影時に、後述眼
球変換により前記投影平面(2次投影平面:後述眼球変
換による歪補正後の投影平面)に再投影し、前記投影対
象の投影像を得るものである(ステップ2)。After or at the time of projection, the projection image of the projection target is obtained by re-projecting onto 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).
【0012】ここで眼球変換とは、投影対象の、投影平
面への投影後又は投影時に、視線上に中心をもつ球面を
その中心位置において視線に直交する方向に2分割して
得られる2つの半球面のうち、視点に遠い側の半球面を
投影面とする該投影面(投影球面)への投影を介して
の、前記投影平面への再投影をいう。The term “eyeball conversion” as used herein means two values obtained by dividing a spherical surface having a center on the line of sight into two in the direction orthogonal to the line of sight after or at the time of projecting the projection target onto the projection plane. Of the hemispheres, it means reprojection onto the projection plane through projection onto the projection plane (projection sphere) whose projection surface is the hemisphere on the side far from the viewpoint.
【0013】すなわち本発明では、前記投影球面を投影
面として中心投影することとなるもので、この場合、投
影面である半球面に沿った各点(アドレス)がCRTの
表示画素(アドレス)に対応する。そして、前記投影球
面に投影したと同じ効果を平面(CRT画面)上で得る
ために眼球変換を行い、歪補正をするものである。That is, according to the present invention, the projection sphere is centrally projected as the projection surface, and in this case, each point (address) along the hemisphere which is the projection surface becomes a display pixel (address) of the CRT. Correspond. 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.
【0014】以下、図2及び図3を参照して上記本発明
方法の眼球変換による歪補正の原理について説明する。
まず図2を参照して説明すると、図2は視点eがh=2
Rの場合について示したものである。図2において、3
は視線(Z軸)上に中心をもつ球面をその中心位置にお
いて視線に直交する方向に2分割して得られる2つの半
球面I,IIのうち、視点に遠い側の半球面(半球面
I)からなる投影面(以下、投影球面という)である。
また、4は平面からなる投影面(以下、投影平面とい
う)で、眼球変換による歪補正前の投影平面、すなわち
従来方法の投影平面としての1次投影平面でもあり、か
つ眼球変換による歪補正後の投影平面としての2次投影
平面でもある。この投影平面4は、CRTの表示面であ
る画面に相当する。The principle of distortion correction by eyeball conversion of the method of the present invention will be described below with reference to FIGS. 2 and 3.
First, referring to FIG. 2, in FIG. 2, the viewpoint e is h = 2.
It shows the case of R. In FIG. 2, 3
Of two hemispheres I and II obtained by dividing a spherical surface having a center on the line of sight (Z axis) in the direction orthogonal to the line of sight at the center position, the hemisphere (hemisphere I ) Is a projection surface (hereinafter referred to as a projection spherical surface).
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 the screen that is the display surface of the CRT.
【0015】また、X,Y,Zは三次元座標系の各軸、
Oは三次元座標系の原点、eは視点、hは視点eと投影
平面4との距離、Rは投影球面3の半径、Pは投影平面
4上の点(X1,Y1)、ψは直線OPとX軸とのなす
角、Qは投影平面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は直線Z1 Qと
Z軸のなす角、Lは投影球面3上の円弧OQ、L´はL
と同じ長さをもった直線OP上の線分、ηはCRT表示
アドレス(X軸に平行にとる)、ξはCRT表示アドレ
ス(Y軸に平行にとる)、である。X, Y, 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).
【0016】これによれば、次の式が成り立つ。眼球に
対応した、h=2・Rのとき、
三角形e O Pについて、tan(θ/2)=sqrt(X
12+Y12)/2R
三角形X1 O Pについて、tan(ψ)=Y1/X1
が与えられる。According to this, the following equation holds. 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.
【0017】したがって、X1,Y1を指定すると、対応
するη1,ξ1 は、
ψ=arctan(Y1/X1)
θ=2・arctan[sqrt(X12+Y12)/2R]
L=R・θ
を使って、
η1=L・cos(ψ)
ξ1=L・sin(ψ)
となる。Therefore, when X1 and Y1 are specified, the corresponding η1 and ξ1 are obtained by using ψ = arctan (Y1 / X1) θ = 2 · arctan [sqrt (X1 2 + Y1 2 ) / 2R] L = R · θ Then, η1 = L · cos (ψ) ξ1 = L · sin (ψ).
【0018】このη1,ξ1が表示メモリ上の画素アドレ
スとなる。すなわち、投影平面4の(X1,Y1)の点
は、CRT画面上では点(η1,ξ1)に表示することに
なるもので、これにより眼球変換による歪補正が行われ
たことになる。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.
【0019】更に、この眼球変換により画像サイズは縮
小する(点Pから点(η1,ξ1)に縮む)。したがっ
て、歪補正後の投影平面4への投影像の画像サイズは、
眼球変換により補正して投影した像の画像サイズよりも
大きく投影可能となる。Further, the image size is reduced by this eyeball conversion (point P is reduced to 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.
【0020】次に、視点eがh=2R以外の場合につい
て図3により説明する。この図3(a),(b)におい
て、図2と同一符号は同一又は相当部分を示す。また、
Uは直線eQの長さ、γは線分ePとZ軸とのなす角、
wはQからZ軸に垂直に下ろした直線の長さ、である。Next, the case where the viewpoint e is other than h = 2R will be described with reference to FIG. In FIGS. 3A and 3B, the same reference numerals as those in FIG. 2 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.
【0021】これによれば、次の式が成り立つ。
U=sqrt[(h−R)2+R2−2・(h−R)・R・c
os(π−θ)]
とすると、
U・sinγ=R・sinθ
となる。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.
【0022】またγは、
tanγ=sqrt(X12+Y12)/h
で与えられる。これより、X1,Y1を指定するとθが求
まる。Γ is given by tan γ = sqrt (X1 2 + Y1 2 ) / h. From this, when X1 and Y1 are specified, θ can be obtained.
【0023】ψはtanψ=Y1/X1から求めると、L
=R・θであるので、
η1=L・cosψ
ξ1=L・sinψ
となる。Ψ is L when calculated from tan ψ = Y1 / X1
= R · θ, η1 = L · cosψ ξ1 = L · sinψ.
【0024】このη1,ξ1が表示メモリ上の画素アドレ
スとなる。すなわち、投影平面4の(X1,Y1)の点
は、CRT画面上では点(η1,ξ1)に表示することに
なるもので、これにより眼球変換による歪補正が行われ
たことになる。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.
【0025】投影対象はマウス等の入力装置により入力
したデータでもよく、また断層像(三次元計測によるボ
リューム画像を分解して得られた断層像も含む)等のよ
うな演算装置により演算した結果のデータでもよい。The projection target may be data input by an input device such as a mouse, or the result of calculation by a calculation device such as a tomographic image (including a tomographic image obtained by decomposing a volume image by three-dimensional measurement). Data may be used.
【0026】図4〜6は、複数の断層像から、一般的な
中心投影方法により三次元画像を構成する方法(特願平
6−3492号)につき表すが、このような場合におい
ても、中心投影をする以上、歪をなくすためは眼球変換
は必要になるもので、以下、三次元画像の構成方法に本
発明方法を適用した場合の一例を説明する。なお、図
5,図6いずれの場合においても、最初に平面からなる
X,Y投影面(投影平面)4上に断層像を投影し、次に
眼球変換によりη,ξ面に変換することになる。4 to 6 show a method of constructing a three-dimensional image from a plurality of tomographic images by a general center projection method (Japanese Patent Application No. 6-3492), even in such a case, As long as projection is performed, eyeball conversion is necessary to eliminate distortion, and an example of applying the method of the present invention to a method of constructing a three-dimensional image will be described below. In both cases of FIG. 5 and FIG. 6, 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.
【0027】まず、上記三次元画像の構成方法におい
て、中心投影による座標変換について述べる。中心投影
による投影面への各断層像の投影に当たっての、各断層
像の画素座標の投影面上の座標への変換は次のように行
われる。First, in the method of constructing the three-dimensional image, coordinate conversion by central projection will be described. When projecting each tomographic image on the projection surface by the central projection, conversion of pixel coordinates of each tomographic image into coordinates on the projection surface is performed as follows.
【0028】図4に示す例では、説明を簡単化するため
投影面と断層像面、更にはx−y面が各々平行であるよ
うに座標系をとっている。この図4において、x,y,
zは三次元座標系(x,y,z)の各軸、e点(x1,
y1,d1)は視点eの位置、P点(X,Y)は投影面
(表示画面に相当する)21上の点、S点(x0,y0,
d0)はe点(x1,y1,d1)とP点(X,Y)を通る
直線22と断層像23Aの交わる点、である。In the example shown in FIG. 4, 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. 4, x, y,
z is each axis of the three-dimensional coordinate system (x, y, z), and point e (x1,
y1, d1) is the position of the viewpoint e, point P (X, Y) is a point on the projection surface (corresponding to the display screen) 21, and point S (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.
【0029】また、Dは投影面21の投影面21の位置
(z軸上)で、任意に設定可能である。Further, D is the position of the projection surface 21 of the projection surface 21 (on the z-axis) and can be arbitrarily set.
【0030】d0は断層像23Aの位置(z軸上)で、
計測時に決まる。D0 is the position of the tomographic image 23A (on the z-axis),
Determined at the time of measurement.
【0031】d1は視点eのz座標、である。D1 is the z coordinate of the viewpoint e.
【0032】これによれば、次の式が成り立つ。According to this, the following equation holds.
【0033】
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)
投影された画像を投影面21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d0の断層像23A上では上掲
(3),(4)式によりx0,y0が決まり、どの点が投
影すべきかが決まる。断層像23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x0,y0が決まる。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 a projected image is displayed on a display screen (not shown) corresponding to the projection surface 21 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.
【0034】同様の座標系において、断層像23Aの他
にも断層像23B〜23Eを用意し、y軸方向から見た
図を図5(a)に示す。この図5(a)において、断層
像23A〜23Eは同一対象物について同一方向に等間
隔で得られた断層像(図示例では等間隔であるが、必ず
しも等間隔である必要はない)であり、断層像23Bに
は、臓器領域B1,B2,B3が強調して書いてある。臓
器領域B1,B2,B3を投影面21に投影するとB1´,
B2´,B3´となる。同様に、断層像23Cの臓器領域
C1,C2を投影面21に投影するとC1´,C2´とな
る。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. 5 (a). In FIG. 5A, the tomographic images 23A to 23E are tomographic images obtained at equal intervals in the same direction on the same object (equal intervals in the illustrated example, but not necessarily equal intervals). In the tomographic image 23B, the organ regions B1, B2, B3 are emphasized and written. When the organ areas B1, B2, B3 are projected on the projection surface 21, B1 ',
B2 'and B3'. Similarly, when the organ regions C1 and C2 of the tomographic image 23C are projected on the projection surface 21, they become C1 'and C2'.
【0035】ここで、投影データ(ここでは、B1´,
B2´,B3´;C1´,C2´)を表示メモリ(図示せ
ず)に書く時は、三次元的効果を出すために、視点eか
ら見てより遠くに存在する投影データを先に書き込み、
それより近くの投影データは後から上書きする。したが
ってここでは、投影データC1,C2より投影データB
1,B2,B3の方が視点eより遠くに存在するので、投
影データB1´,B2´,B3´を先に書いて、投影デー
タC1´,C2´は後から上書きすることになる。なお図
7(a)では、投影データB1´,B2´,B3´;C1
´,C2´は各々投影面21から離して示しているが、
これは表示メモリに書き込む投影データB1´,B2´,
B3´;C1´,C2´の順番を判り易くしたために過ぎ
ず、最初に書かれる投影データB1´,B2´,B3´
も、それに上書きされる投影データC1´,C2´も実際
には投影面21上に書かれる。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. ,
The projection data closer to it will be overwritten later. Therefore, here, the projection data B is calculated from the projection data C1 and 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. 7A, projection data B1 ', B2', B3 '; C1
′ And C2 ′ are shown separately from the projection plane 21,
This is the projection data B1 ', B2', which is written in the display memory.
The projection data B1 ', B2', B3 'written first is only for making the order of B3'; C1 ', C2' easier to understand.
Also, the projection data C1 'and C2' that are overwritten are actually written on the projection surface 21.
【0036】図5(b)は、図5(a)よりも一般化し
て示したもので、投影面と断層像面が平行でない場合の
例である。この場合は、断層像23A,23B,23C
…から補間演算で投影面21と平行な面に向けられた断
層像23a,23b,23c…を作っておく必要があ
る。その他は、図5(a)の場合と同様である。なお、
b1´;c1´,c2´;d1´は、補間演算された断層像
23b,23c,23d上の臓器領域b1;c1,c2;
d1の投影データである。FIG. 5B is a more generalized view than FIG. 5A 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, 23C
It is necessary to create the tomographic images 23a, 23b, 23c, ... Others are the same as in the case of FIG. In addition,
b1 ';c1', c2 ';d1' are organ regions b1; c1, c2; on the interpolated tomographic images 23b, 23c, 23d.
This is the projection data of d1.
【0037】図6は、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、断層像23上のS点(x0,z0,
y0)の投影結果が投影平面上のP点(x,y,z)に
なることを示す。FIG. 6 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, z0, on the tomographic image 23.
It shows that the projection result of (y0) becomes P point (x, y, z) on the projection plane.
【0038】この図6において、中心投影による投影平
面4への断層像23の投影に当たっての、断層像23の
画素座標の投影平面4上の座標への変換は次のように行
われる。ここで、aはx軸と投影平面4の交わる点、b
はy軸と投影平面4の交わる点、cはz軸と投影平面4
の交わる点、である。In the projection of the tomographic image 23 on the projection plane 4 by the central projection in FIG. 6, the pixel coordinates of the tomographic image 23 are converted into the coordinates on the projection plane 4 as follows. Where a is the intersection of the x-axis and the projection plane 4, b
Is the intersection of the y axis and the projection plane 4, and c is the z axis and the projection plane 4.
Is the point of intersection.
【0039】また、αは原点から投影平面4に下ろした
垂線をz−x面に投影した線がx軸となす角βは前記垂
線がx−z面となす角e点(x1,y1,z1)は視点e
の位置、P点(x,y,z)は投影面(表示画面に相当
する)4上の点、S点(x0,z0,y0)はe点(x1,
y1,z1)とP点(x,y,z) を通る直線22と断
層像23の交わる点、とすると、次の式が成り立つ。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 e point (x1, y1, y1) formed by the perpendicular line with the xz plane. z1) is 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 where the straight line 22 passing through the point P (x, y, z) and the tomographic image 23 intersect, the following formula is established.
【0040】まず、投影平面4は
(x/a)+(y/b)+(z/c)=1 …(5)
で表わされる。また、e点(x1,y1,z1)とP点
(x,y,z) を通る直線22は
(x0−x)/(x1−x)=(y0−y)/(y1−y)=(z0−z)/(z1
−z) …(6)
で与えられる。First, the projection plane 4 is expressed by (x / a) + (y / b) + (z / c) = 1 (5). A straight line 22 passing through the point e (x1, y1, z1) and the point P (x, y, z) is (x0-x) / (x1-x) = (y0-y) / (y1-y) = (Z0-z) / (z1-z) (6)
【0041】投影平面4がC1点(xc1,yc1,zc
1)を通るとき、
k1=sinα
k2=cosα/sinβ
k3=cosα・cosβ/sinβ
ai=1/a
bi=1/b
ci=1/c
として、
z=[X・k1−Y・k2−yc1・k3−{(ci・k3・zc1)/bi}+{
(ai・k3・X)/(bi・cosα)}−{(ai・k3・xc1)/bi}
]/[1−{(ci・k3)/bi}+{(ai・k3・sinα)/(bi・c
osα)}] …(7)
x=(X−z・sinα)/cosα …(8)
y=[yc1+{−ci・(z−zc1)−ai・(x−xc1)}]/bi
…(9)
ここで、上記C1点(xc1,yc1,zc1)には、例え
ば、視点e(x1,y1,z1)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、
zc1=z1+−[h/sqrt{1+(c2/a2)+(c2/b2)}]
(「z1+−」の「−」はz0<zc1のとき) …(10)
xc1=x1+{c・(z1−zc1)/a} …(11)
yc1=y1+{c・(z1−zc1)/b} …(12)
を使ってもよい。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)}] ( "z1 + -" in "-" when the z0 <zc1) ... (10) xc1 = x1 + {c · (z1-zc1) / A} (11) yc1 = y1 + {c · (z1−zc1) / b} (12) may be used.
【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。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. Listed above for each X and Y (7),
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 coordinate x0 of the pixel S point on the tomographic image of y0 = d0,
z0 is determined.
【0043】
x0={(d0−y)/(y1−y)}×(x1−x)+x …(13)
z0={(d0−y)/(y1−y)}×(z1−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x0,y0が決まる。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.
【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。Note that R in FIG. 6 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 the 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,
Since it corresponds to the point (ξ), the pixel value is stored at the point (η, ξ).
【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。The above coordinate conversion is performed for all points on the projection plane 4 corresponding to the display screen. In addition, all tomographic images 23 are performed. Furthermore, even if the three-dimensional image that is the resultant image is constructed,
It may be performed for each tomographic image.
【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。FIG. 7 is a block diagram showing a hardware configuration example to which the method of the present invention can be applied. In this 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 and a program for performing calculation of the method of the present invention.
【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。The CPU 50 reads out these plural tomographic images and the 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 is displayed. Mouse 56 connected to mouse controller 55
Specifies the viewpoint position and the like when performing calculations such as eyeball conversion.
The image that has undergone eyeball conversion and distortion correction is stored in the magnetic disk 52 as necessary.
【0048】[0048]
【発明の効果】以上説明したように本発明によれば、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。As described above, according to the present invention, the distortion of the projected image depending on the projection direction is corrected and the projection data (length or size) is prevented from being different due to the difference in the projection direction. The effect is that you can do it.
【図1】本発明方法の概略を示すフローチャートであ
る。FIG. 1 is a flow chart showing an outline of the method of the present invention.
【図2】眼球変換による歪補正の原理説明図である。FIG. 2 is a diagram illustrating the principle of distortion correction by eye conversion.
【図3】同じく眼球変換による歪補正の原理説明図であ
る。FIG. 3 is a diagram illustrating the principle of distortion correction by eyeball conversion.
【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。FIG. 4 is a diagram for explaining conversion of tomographic image pixel coordinates into coordinates on a projection plane in a method of constructing a three-dimensional image.
【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説明するための図である。FIG. 5 is a diagram for explaining conversion of pixel coordinates of a plurality of tomographic images into coordinates on the projection surface.
【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。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.
【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。FIG. 7 is a block diagram showing a hardware configuration example to which the method of the present invention can be applied.
【図8】眼球投影の説明図である。FIG. 8 is an explanatory diagram of eyeball projection.
【図9】中心投影方法と歪の説明図である。FIG. 9 is an explanatory diagram of a center projection method and distortion.
3 投影球面
4 投影平面
X,Y,Z 三次元座標系の各軸
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軸に垂直に下ろした直線の長さ3 Projection sphere 4 Projection plane X, Y, Z Each axis of the three-dimensional coordinate system O Origin of the three-dimensional coordinate system viewpoint h The distance between the viewpoint e and the projection plane 4 R The radius of the projection sphere 3 P The point on the projection plane 4 (X1, Y1) ψ Angle Q formed by the straight line OP and the X axis Point on the projection spherical surface 3 corresponding to point P on the projection plane 4 (intersection point of the straight line Pe and the projection spherical surface 3) θ Straight line Z1 Q of the Z axis Formed angle L A line segment on a straight line OP having the same length as the arc OQ L'L on the projection spherical surface 3 η CRT display address (taken in parallel with X axis) ξ CRT display address (taken in parallel with Y axis) U Length of straight line eQ γ Length of straight line lowered perpendicularly to Z axis from angle w Q formed by line segment eP and Z axis
───────────────────────────────────────────────────── フロントページの続き (56)参考文献 特開 平6−96191(JP,A) 特開 平6−21305(JP,A) 特開 平5−181980(JP,A) 特開 平4−167078(JP,A) 特開 平4−153894(JP,A) 特開 平3−113305(JP,A) 実開 平4−31175(JP,U) (58)調査した分野(Int.Cl.7,DB名) G06T 15/00 100 G06T 1/00 290 JICSTファイル(JOIS)─────────────────────────────────────────────────── ─── Continuation of the front page (56) Reference JP-A-6-96191 (JP, A) JP-A-6-21305 (JP, A) JP-A-5-181980 (JP, A) JP-A-4- 167078 (JP, A) JP-A-4-153894 (JP, A) JP-A-3-113305 (JP, A) Actual development 4-31175 (JP, U) (58) Fields investigated (Int.Cl. 7 , DB name) G06T 15/00 100 G06T 1/00 290 JISST file (JOIS)
Claims (3)
視点から三次元データ群である投影対象へ発したとき
の、その投影対象を平面の投影面に投影して中心投影デ
ータを得、中心投影データから三次元画像を構成する中
心投影法による三次元画像構成装置において、前記視点
と前記投影面との設定、及び視点と投影面との間であっ
て視点と投影面とのそれぞれに一点で接する仮想的な球
モデルを設定する設定手段と、該設定された球モデルの
球面上に前記視点から見た投影対象を投影させ球面投影
データを得る第1の投影手段と、該得られた球面投影デ
ータを前記投影面に投影させて、前記中心投影データが
投影されたときに生じた投影方向に依存する位置歪みを
補正した投影データを得る第2の投影手段とを備えたこ
とを特徴とする中心投影法による三次元画像構成装置。1. When a projection line having a conical shape with a viewpoint as an apex is emitted from the viewpoint to a projection target which is a three-dimensional data group, the projection target is projected onto a plane projection surface to obtain central projection data, In a three-dimensional image forming apparatus by a central projection method for forming a three-dimensional image from central projection data, in the setting of the viewpoint and the projection surface, and between the viewpoint and the projection surface, each of the viewpoint and the projection surface. Setting means for setting a virtual sphere model contacting at one point, first projection means for projecting a projection target viewed from the viewpoint onto the spherical surface of the set sphere model, and obtaining the projection data, Second projection means for projecting spherical projection data onto the projection surface to obtain projection data in which positional distortion depending on the projection direction generated when the central projection data is projected is corrected. Characteristic center throw 3D image composition device by shadow method.
に投影して得た球面投影データを前記投影面に投影させ
るさいに、その投影対象の画像サイズを拡大させる手段
を備えて拡大を行わせることを特徴とする請求項1に記
載の中心投影法による三次元画像構成装置。2. When the second projection means projects the spherical projection data obtained by projecting onto the spherical model onto the projection surface, it is provided with means for enlarging the image size of the projection target. The three-dimensional image construction apparatus according to the central projection method according to claim 1, wherein the three-dimensional image construction apparatus is performed.
視点から三次元の投影対象へ発したときの、その投影対
象を平面の投影面に投影して投影データを得、この投影
データから三次元画像を構成する中心投影法による三次
元画像構成装置において、視点と投影面の設定、及び視
点と投影面との間であって投影面に一点で接する球モデ
ルを設定する手段と、投影線を与えて、この投影線が交
わる前記球モデルの球面上と前記投影面上に、前記投影
対象の点を投影し球面上の投影点Qと投影面上の投影点
Pを得る手段と、前記投影点Qと球モデルの投影面接点
との球面に沿った距離Lを求める手段と、この距離Lと
投影面上での投影点Pの角度φとに基づいて、前記投影
点Qと対応させて得た投影方向に依存する位置歪みを補
正した前記投影面上の投影点Gを得る手段とを備えたこ
とを特徴とする中心投影法による三次元画像構成装置。3. When a projection line having a conical shape with a viewpoint as an apex is emitted from the viewpoint to a three-dimensional projection target, the projection target is projected onto a plane projection surface to obtain projection data, and from this projection data In a three-dimensional image constructing apparatus for forming a three-dimensional image by a central projection method, means for setting a viewpoint and a projection surface, and a sphere model between the viewpoint and the projection surface and contacting the projection surface at one point, Means for giving a line and projecting a point of the projection target on the spherical surface of the spherical model and the projection surface where the projection line intersects to obtain a projection point Q on the spherical surface and a projection point P on the projection surface; Corresponding to the projection point Q on the basis of means for obtaining the distance L along the spherical surface between the projection point Q and the projection surface contact point of the sphere model, and the distance L and the angle φ of the projection point P on the projection surface. On the projection surface corrected for positional distortion depending on the projection direction obtained by Three-dimensional image constructing apparatus according to the central projection, characterized in that it comprises a means for obtaining a projection point G.
Priority Applications (4)
Application Number | Priority Date | Filing Date | Title |
---|---|---|---|
JP08977094A JP3411665B2 (en) | 1994-04-27 | 1994-04-27 | 3D image construction device |
US08/374,088 US5694530A (en) | 1994-01-18 | 1995-01-18 | Method of constructing three-dimensional image according to central projection method and apparatus for same |
US08/708,959 US5900878A (en) | 1994-01-18 | 1996-09-06 | Method of constructing pseudo-three-dimensional image for obtaining central projection image through determining view point position by using parallel projection image and apparatus for displaying projection image |
US08/856,675 US5953013A (en) | 1994-01-18 | 1997-04-29 | Method of constructing three-dimensional image according to central projection method and apparatus for same |
Applications Claiming Priority (1)
Application Number | Priority Date | Filing Date | Title |
---|---|---|---|
JP08977094A JP3411665B2 (en) | 1994-04-27 | 1994-04-27 | 3D image construction device |
Related Child Applications (1)
Application Number | Title | Priority Date | Filing Date |
---|---|---|---|
JP2002340774A Division JP3706098B2 (en) | 2002-11-25 | 2002-11-25 | 3D image construction method |
Publications (2)
Publication Number | Publication Date |
---|---|
JPH07296184A JPH07296184A (en) | 1995-11-10 |
JP3411665B2 true JP3411665B2 (en) | 2003-06-03 |
Family
ID=13979929
Family Applications (1)
Application Number | Title | Priority Date | Filing Date |
---|---|---|---|
JP08977094A Expired - Lifetime JP3411665B2 (en) | 1994-01-18 | 1994-04-27 | 3D image construction device |
Country Status (1)
Country | Link |
---|---|
JP (1) | JP3411665B2 (en) |
Families Citing this family (4)
Publication number | Priority date | Publication date | Assignee | Title |
---|---|---|---|---|
JP3770280B2 (en) * | 1996-03-29 | 2006-04-26 | 株式会社日立メディコ | 3D image display method and apparatus |
JP3712145B2 (en) * | 1996-06-25 | 2005-11-02 | 株式会社日立メディコ | Three-dimensional image construction method and apparatus |
WO1998015226A1 (en) | 1996-10-08 | 1998-04-16 | Hitachi Medical Corporation | Method and apparatus for forming and displaying image from a plurality of sectional images |
JP5745947B2 (en) * | 2011-06-20 | 2015-07-08 | 株式会社日立メディコ | Medical image processing apparatus and medical image processing method |
-
1994
- 1994-04-27 JP JP08977094A patent/JP3411665B2/en not_active Expired - Lifetime
Also Published As
Publication number | Publication date |
---|---|
JPH07296184A (en) | 1995-11-10 |
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