Flux Invariants for Shape

Flux Invariants for Shape (2003)

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by Pavel Dimitrov , James N. Damon , Kaleem Siddiqi

Venue:	In CVPR
Citations:	26 - 3 self

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Datum	Value	Source
TITLE	Flux Invariants for Shape	INFERENCE
AUTHOR NAME	Pavel Dimitrov	SVM HeaderParse 0.2
AUTHOR AFFIL	† School of Computer Science; § Department of Mathematics; McGill University University of North Carolina, Chapel Hill	SVM HeaderParse 0.2
AUTHOR ADDR	Montreal, Canada Chapel Hill, North Carolina, USA	SVM HeaderParse 0.2
AUTHOR NAME	James N. Damon	SVM HeaderParse 0.2
AUTHOR AFFIL	† School of Computer Science; § Department of Mathematics; McGill University University of North Carolina, Chapel Hill	SVM HeaderParse 0.2
AUTHOR ADDR	Montreal, Canada Chapel Hill, North Carolina, USA	SVM HeaderParse 0.2
AUTHOR NAME	Kaleem Siddiqi	SVM HeaderParse 0.2
AUTHOR AFFIL	† School of Computer Science; § Department of Mathematics; McGill University University of North Carolina, Chapel Hill	SVM HeaderParse 0.2
AUTHOR ADDR	Montreal, Canada Chapel Hill, North Carolina, USA	SVM HeaderParse 0.2
ABSTRACT	We consider the average outward flux through a Jordan curve of the gradient vector field of the Euclidean distance function to the boundary of a 2D shape. Using an alternate form of the divergence theorem, we show that in the limit as the area of the region enclosed by such a curve shrinks to zero, this measure has very different behaviours at medial points than at non-medial ones, providing a theoretical justification for its use in the Hamilton-Jacobi skeletonization algorithm of [7]. We then specialize to the case of shrinking circular neighborhoods and show that the average outward flux measure also reveals the object angle at skeletal points. Hence, formulae for obtaining the boundary curves, their curvatures, and other geometric quantities of interest, can be written in terms of the average outward flux limit values at skeletal points. Thus this measure can be viewed as a Euclidean invariant for shape description: it can be used to both detect the skeleton from the Euclidean distance function, as well as to explicitly reconstruct the boundary from it. We illustrate our results with several numerical simulations. 1.	SVM HeaderParse 0.2
YEAR	2003	INFERENCE
VENUE	In CVPR	INFERENCE
VENUE TYPE	CONFERENCE	INFERENCE
PAGES	835--841	INFERENCE
VOLUME	2003	INFERENCE
TECH	M.Sc. thesis	INFERENCE
CITATIONS	2 found	ParsCit 1.0