WESD--Weighted Spectral Distance for measuring shape dissimilarity.

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Title: WESD--Weighted Spectral Distance for measuring shape dissimilarity.
Authors: Konukoglu, E
Glocker, B
Criminisi, A
Pohl, KM
Item Type: Journal Article
Abstract: This paper presents a new distance for measuring shape dissimilarity between objects. Recent publications introduced the use of eigenvalues of the Laplace operator as compact shape descriptors. Here, we revisit the eigenvalues to define a proper distance, called Weighted Spectral Distance (WESD), for quantifying shape dissimilarity. The definition of WESD is derived through analyzing the heat trace. This analysis provides the proposed distance with an intuitive meaning and mathematically links it to the intrinsic geometry of objects. We analyze the resulting distance definition, present and prove its important theoretical properties. Some of these properties include: 1) WESD is defined over the entire sequence of eigenvalues yet it is guaranteed to converge, 2) it is a pseudometric, 3) it is accurately approximated with a finite number of eigenvalues, and 4) it can be mapped to the ([0,1)) interval. Last, experiments conducted on synthetic and real objects are presented. These experiments highlight the practical benefits of WESD for applications in vision and medical image analysis. © 1979-2012 IEEE.
Issue Date: 31-Dec-2012
URI: http://hdl.handle.net/10044/1/13907
DOI: http://dx.doi.org/10.1109/TPAMI.2012.275
Start Page: 2284
End Page: 2297
Journal / Book Title: IEEE Trans Pattern Anal Mach Intell
Volume: 35
Issue: 9
Copyright Statement: © 2013 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.
Conference Place: United States
Appears in Collections:Computing

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