Andrew Bibitchev
2.1.5 Advantages and Drawbacks. Among advantages of described technique the following ones can be
accentuated:
high robustness;
* high tolerance, i.e. edge can be not exactly straight;
e step(d,a) can be treated as weight of L(d,o) ;
* generalization is allowed, i.e. one can construct functional step for any parametrized curve.
But the following drawbacks take place:
* step(d,a) is useful only for detection of contours with length comparable with image size, thus we must know
interest area for edge searching rather well;
e additional efforts are required to determine the end-points.
2.2 Correlation of 2d Edges
To enter the second part of desired functional let me consider the following auxiliary task.
2.2.1 Auxiliary Task. Suppose there are two different gray scale images of one and the same 3d scene: i? (x^, y°)
. . . S y . D D . . . . . D D
is "source" image of size s; xs$ and iP (P. Y) is "destination" image of size s, Xs . Furthermore, parameters of
internal, relative and optionally external orientation are assumed to be known, that is 2d image coordinates can be
transformed in 3d scene coordinates (X,Y, Z) and vise versa:
X=XbS,y°;xP,yP), y=rhS,y5;xP,yP), Z=ZhS,y5;xP,yP). (6)
4° =x(X,Y.Z), y =v"(X.Y.2); (7)
xP = 22 (X.Y,2y. vy? =yP XV. 2) (8)
Figure 4. Coordinate system in vicinities
Figure 3. “Source” (at the left) and “destination”
(at the right) images of 3d scene
And let we have 2d edge a^^? on the "source" image (see Figure 3). We need to match 2d edge a”b” on the
“destination” image, that is we need to find ab” such that a°hS and a”b” are projections of one and the same 3d
scene edge AB on “source” and “destination” images respectively.
To include (by indirection) 3d object model, we can require that there is parametrization œ of all possible AB
positions:
A- A?.55:0), B2 B(5,55:0), oe O, (9)
and thus
a? - a? (a? 55:0), AP - bP (5.55.0), oco. (10)
74 International Archives of Photogrammetry and Remote Sensing. Vol. XXXIII, Part B3. Amsterdam 2000.
M U2 C9) NN
If
ca
Sk
Fi
th
ad
