An affine shape constraint for geometric active contours - Emerging Trends in Image Processing, Computer Vision, and Pattern Recognition - page 427

(20)

In Ref. [ 20 ], the author introduced two sets of invariant descriptors I and J which are, re-
spectively, given by (Equations 21 and 22 ) .

(21)

(22)

In Refs. [ 21 , 22 ] , the authors have shown experimentally that such descriptors are complete
and stable. The completeness guarantees the uniqueness of matching. The stability gives ro-
bustness under nonlinear shape distortions and numerical errors. In Ref. [ 20 ] , the author
demonstrates that the shape space S can be considered as a metric space with a set of metrics.
Hence, the Euclidean distance (Equation 23 ) between the set of the presented invariants can be
used to compare the evolving curve and the available templates.

(23)

For any real number p such that p > 1. Where f and h are two normalized affine arc
length reparametrization of two objects having, respectively, the shapes F and H . The shape
having the minimum distance according to the evolving active contour is used as template.