discrete approach to curve and surface evolution
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Discrete Approach to Curve and Surface Evolution. Longin Jan Latecki Dept. of Computer and Information Science Temple University Philadelphia Email: [email protected]. - PowerPoint PPT PresentationTRANSCRIPT
Discrete Approach Discrete Approach to Curve and Surface Evolutionto Curve and Surface Evolution
Longin Jan Latecki
Dept. of Computer and Information Science
Temple University
Philadelphia
Email: [email protected]
Discrete Curve EvolutionDiscrete Curve Evolution P=P P=P00, ..., P, ..., Pmm
PPi+1i+1 is obtained from P is obtained from Pii by deleting the by deleting the vertices of Pvertices of Pii that have minimal relevance that have minimal relevance
measure measure K(v, PK(v, Pii) = K(u,v,w) = |d(u,v)+d(v,w)-d(u,w)|) = K(u,v,w) = |d(u,v)+d(v,w)-d(u,w)|
u
v
w u
v
w
Discrete Curve EvolutionDiscrete Curve Evolution: : Preservation of position, no blurringPreservation of position, no blurring
Discrete Curve EvolutionDiscrete Curve Evolution: : robustness with respect to noiserobustness with respect to noise
Discrete Curve EvolutionDiscrete Curve Evolution: : extraction of linear segmentsextraction of linear segments
Parts of Visual Form (Siddiqi, Tresness, and Parts of Visual Form (Siddiqi, Tresness, and Kimia 1996) = maximal convex arcsKimia 1996) = maximal convex arcs
Discete Cureve Discete Cureve Evolution is uEvolution is used sed
in shape in shape similarity retrieval similarity retrieval
in image in image databasesdatabases
Shape similarity measure based on Shape similarity measure based on correspondence of visual partscorrespondence of visual parts
A video sequence is mapA video sequence is mappped to a ed to a trajectory in a high dimensional space,trajectory in a high dimensional space,
e.g. by mapping each frame to a feature e.g. by mapping each frame to a feature vector in Rvector in R3737
Discrete curve evolution allows us to Discrete curve evolution allows us to determine key framesdetermine key frames
The 10 most relevant framesThe 10 most relevant frames in Mr. Bean in Mr. Bean
www.videokeyframes.dewww.videokeyframes.de
Detection of unpredictable events in Detection of unpredictable events in videosvideos::
Mov3.mpgMov3.mpg
Detection of unpredictable events in Detection of unpredictable events in videosvideos::
seciurity1.mpgseciurity1.mpg
Two most unpredictable frames extracted Two most unpredictable frames extracted fromfrom Mov3.mpg Mov3.mpg
Two most unpredictable frames extracted Two most unpredictable frames extracted from security1.mpgfrom security1.mpg
(Lyche and Morken in late 80s): (Lyche and Morken in late 80s):
Surface patch f:RSurface patch f:R22 -> R is represented -> R is represented with radial base splines Swith radial base splines S
given a set of knots T:given a set of knots T:
||f – G(T)(f)|| = min{||f - g||: g in S}||f – G(T)(f)|| = min{||f - g||: g in S}
Surface evolution by knot removalSurface evolution by knot removal
Relevance measure of the knot:Relevance measure of the knot:
r(t) = ||f – G(T – {t})(f)||r(t) = ||f – G(T – {t})(f)||