ISPRS Commission II, Vol.34, Part 3A „Photogrammetric Computer Vision‘, Graz, 2002
- F(P) (1)
In the case of stereo images I, and I, , we have two functions,
F,(P) for I, , and F,(P) for I,
2) Transformation functions from Image coordinates p(x, y) to
3D coordinates P(X, Y, Z) , under the condition that one of the
coordinates (X, Y, Z) is known:
P - Gx(p, X)
7 Gy(p. Y)
P - Gz(p, Z) Q2)
Similar to function (1), we have two sets of the functions,
Gx,, Gy,, Gz, for I, , and Gx,, Gy,, Gz, for I,
3) Transformation functions from a stereo pair of image coordi-
nates p,(x,,y,) and Pp,(x,,y,) to 3D coordinates
P(X, Y.Z):
pz
G, (Pgs p) (3)
Plane A ^
Figure 1. The target problem
2.2 Basic Strategy
Assuming that plane A can be described by a set of parameters
D = |», D, D,| . The matching function H , which gives match-
ing point p,; for a given point p,, within a polygon A,
depends on parameter D :
p, = H(p,; D) (4)
To determinate D by stereo matching, least square method can
be applied to minimize the following evaluation function xX(D) :
x(D) - Y e (5)
e;(D) = L,(H(p,;. D)) - Hl (p,,) (6)
where summation in equation (5) is computed for all pixels in
polygon A.
3. DEFINITION OF PARAMETER D
Suppose that Q,, Q,, Q; are projected onto P1(1)>P1(2)>P1(3)
in I, and P2(1)>P2(2)>P2(3) in L , respectively. Also suppose
that points P^) P^) are on the epipolar line of py,
points P22) and P22) are on the epipolar line of p,(;,, and
points p’ 2(3) and p^ 2(3) ON the epipolar Tine P1) Wii a set
of parameters D = p, D ? Dj; Pa): P^2;0): P20): P^20:
p 2(3) and p” 2(3)> P2(1)> P2@) and P2(3) can be described by
the following equations:
Pau) ^ (1-D): pa; *Di: p^;ay
P22) = (1- Dj): p; * D: p^;
P2(3) ^ (1- D): p * D4: p^;(3j (7)
A set of D determines three corresponding point pairs and three
3-D points on plane A can be computed by equation (3). Since
three non-colinear points determine a unique plane, D deter-
mines geometry of plane À .
Here we call pairs of corresponding points “control pairs”.
Epipolar Line of p,
INCL E
Face A 2 d
/ Plane A
Q,
Figure 2. Definition of Planar Parameter D
4. DERIVATION OF FUNCTION H
It is well known that correspondence between p, — (x,, y,) on
I, and p, = (X,,y,) on I,, where Point Q on plane A is
projected, can be described by projective transformation (or 2-D
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