An affine shape constraint for geometric active contours - Emerging Trends in Image Processing, Computer Vision, and Pattern Recognition - page 421

(5)
where , θ is chosen to satisfy Equation (6) and minimize f ( θ , t 0 )
where t 0 is one of the roots of Equation (5) .
(6)
Having the value of θ and t 0 that minimize f ( θ , t 0 ), the scaling factor is given by
(7)
Based on Nyquist-Shannon theorem and B-spline approximation of the g ( t )'s curve, Persoon
and Fu [ 19 ] proposed the first implementation of this method of shape alignment and its ap-
plication in rigid motion estimation for video compression. In Figure 1 , we give an example of
two aligned curves with the used method.
FIGURE 1 Example of two curves before (a) and after (b) shape alignment.
The estimated motion's parameters are presented in Table 1 . The associated g ( t )'s curve is
presented in Figure 2 . The zeros of g ( t ) are drawn with circles.