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Discrete Approach to Curve and Surface Evolution. Longin Jan Latecki Dept. of Computer and Information Science Temple University Philadelphia Email: latecki@temple.edu.
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Discrete Approach to Curve and Surface Evolution Longin Jan Latecki Dept. of Computer and Information Science Temple University Philadelphia Email: latecki@temple.edu
Discrete Curve Evolution P=P0, ..., PmPi+1 is obtained from Pi by deleting the vertices of Pi that have minimal relevance measure K(v, Pi) = K(u,v,w) = |d(u,v)+d(v,w)-d(u,w)| v v w w u u
Discrete Curve Evolution: Preservation of position, no blurring
Parts of Visual Form (Siddiqi, Tresness, and Kimia 1996) = maximal convex arcs
Discete Cureve Evolution is used in shape similarity retrieval in image databases
Shape similarity measure based on correspondence of visual parts
A video sequence is mapped to a trajectory in a high dimensional space,e.g. by mapping each frame to a feature vector in R37Discrete curve evolution allows us to determine key frames
2379 vertices 20 vertices Trajectory Simplification
The 10 most relevant frames in Mr. Beanwww.videokeyframes.de
Discrete Surface Evolution: repeated removal of least relevant vertices
(Lyche and Morken in late 80s): Surface patch f:R2 -> R is represented with radial base splines Sgiven a set of knots T:||f – G(T)(f)|| = min{||f - g||: g in S}Surface evolution by knot removalRelevance measure of the knot:r(t) = ||f – G(T – {t})(f)||