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Correcting curvature-density effects in the Hamilton-Jacobi skeleton

Hancock, E.R. and Torsello, A. (2006) Correcting curvature-density effects in the Hamilton-Jacobi skeleton. IEEE Transactions on Image Processing. pp. 877-891. ISSN 1057-7149

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Abstract

The Hainilton-Jacobi approach has proven to be a powerful and elegant method for extracting the skeleton of two-dimensional (2-D) shapes. The approach is based on the observation that the normalized flux associated with the inward evolution of the object boundary at nonskeletal points tends to zero as the size of the integration area tends to zero, while the flux is negative at the locations of skeletal points. Nonetheless, the error in calculating the flux on the image lattice is both limited by the pixel resolution and also proportional to the curvature of the boundary evolution front and, hence, unbounded near endpoints. This makes the exact location of endpoints difficult and renders the performance of the skeleton extraction algorithm dependent on a threshold parameter. This problem can be overcome by using interpolation techniques to calculate the flux with subpixel precision. However, here, we develop a method for 2-D skeleton extraction that circumvents the problem by eliminating the curvature contribution to the error. This is done by taking into account variations of density due to boundary curvature. This yields a skeletonization algorithm that gives both better localization and less susceptibility to boundary noise and parameter choice than the Hamilton-Jacobi method.

Item Type: Article
Copyright, Publisher and Additional Information: Copyright © 2006 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE.
Keywords: curvature, Hamilton-Jacobi equations, shape-description, two-dimensional (2-D) skeleton
Academic Units: The University of York > Computer Science (York)
Depositing User: Repository Officer
Date Deposited: 21 Feb 2007
Last Modified: 17 Oct 2013 14:19
Published Version: http://dx.doi.org/10.1109/TIP.2005.863951
Status: Published
Refereed: Yes
Related URLs:
URI: http://eprints.whiterose.ac.uk/id/eprint/1997

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