Format

Send to

Choose Destination
See comment in PubMed Commons below
IEEE Trans Pattern Anal Mach Intell. 2013 Sep;35(9):2284-97. doi: 10.1109/TPAMI.2012.275.

WESD--Weighted Spectral Distance for measuring shape dissimilarity.

Author information

1
Athinoula A. Martinos Center for Biomedical Imaging, Massachusetts General Hospital/Harvard Medical School, Cambridge, MA 02144, USA. ender.konukoglu@gmail.com

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.

PMID:
23868785
DOI:
10.1109/TPAMI.2012.275
[Indexed for MEDLINE]
PubMed Commons home

PubMed Commons

0 comments
How to join PubMed Commons

    Supplemental Content

    Full text links

    Icon for IEEE Engineering in Medicine and Biology Society
    Loading ...
    Support Center