An affine shape constraint for geometric active contours - Emerging Trends in Image Processing, Computer Vision, and Pattern Recognition - page 425

(16)
Then to estimate matrix A' s parameters (Equation 14 ) , we have to resolve a system with 2 N
equations and four unknown parameters that can be writen as
(17)
The solution of the system (Equation 16 ) can be obtained by
(18)
So we have to minimize the quadratic error e by using the pseudoinverse of K . We show
by the following figure an example of affine motion estimation between two synthetic curves
after contours resampling ( Figure 3 ). The final result of curves alignment after affine motion
estimation is presented by Figure 4 . The estimated motion parameters are presented in Table
2 .
FIGURE 3 Two different shapes after affine deformations ((a) and (c)) and curve resampling
((b) and (d)).
FIGURE 4 Results of affine shape alignment.