Publication Date:
2015-08-04
Description:
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 $lbrace Omega _irbrace$ 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 illustrated.
Print ISSN:
0162-8828
Electronic ISSN:
1939-3539
Topics:
Computer Science
