DocumentCode

Title

Semi-Continuity of Skeletons in Two-Manifold and Discrete Voronoi Approximation

Author

Liu, Yong-Jin

Author_Institution

Tsinghua National Laboratory for Information Science and Technology, the Department of Computer Science and Technology, Tsinghua University, Beijing, China

Volume

Issue

fYear

2015

fDate

Sept. 1 2015

Firstpage

1938

Lastpage

1944

Abstract

The skeleton of a 2D shape is an important geometric structure in pattern analysis and computer vision. In this paper we study the skeleton of a 2D shape in a two-manifold $mathcal {M}$

, based on a geodesic metric. We present a formal definition of the skeleton $S(\\Omega )$

for a shape $\\Omega$

in $mathcal {M}$

and show several properties that make $S(\\Omega )$

distinct from its Euclidean counterpart in $mathbb {R}^2$

. We further prove that for a shape sequence $\\lbrace \\Omega _i\\rbrace$

that converge to a shape $\\Omega$

in $mathcal {M}$

, the mapping $\\Omega \\righta- row \\overline {S}(\\Omega )$

is lower semi-continuous. A direct application of this result is that we can use a set $P$

of sample points to approximate the boundary of a 2D shape $\\Omega$

in $mathcal {M}$

, and the Voronoi diagram of $P$

inside $\\Omega \\subset mathcal {M}$

gives a good approximation to the skeleton $S(\\Omega )$

. Examples of skeleton computation in topography and brain morphometry are illu

Keywords

Approximation methods; Computer vision; Manifolds; Measurement; Pattern analysis; Shape; Skeleton; 2-manifold; 2D shape sequence; Voronoi skeleton; geodesic; two-manifold;

fLanguage

English

Journal_Title

Pattern Analysis and Machine Intelligence, IEEE Transactions on

Publisher

ieee

ISSN

0162-8828

Type

jour

DOI

10.1109/TPAMI.2015.2430342

Filename

7102776

Link To Document

https://search.isc.ac/dl/search/defaultta.aspx?DTC=49&DC=54616