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This article presents a new distance for measuring shape dissimilaritybetween objects. Recent publications introduced the use of eigenvalues of theLaplace operator as compact shape descriptors. Here, we revisit the eigenvaluesto define a proper distance, called Weighted Spectral Distance (WESD), forquantifying shape dissimilarity. The definition of WESD is derived throughanalysing the heat-trace. This analysis provides the proposed distance anintuitive meaning and mathematically links it to the intrinsic geometry ofobjects. We analyse the resulting distance definition, present and prove itsimportant theoretical properties. Some of these properties include: i) WESD isdefined over the entire sequence of eigenvalues yet it is guaranteed toconverge, ii) it is a pseudometric, iii) it is accurately approximated with afinite number of eigenvalues, and iv) it can be mapped to the [0,1) interval.Lastly, experiments conducted on synthetic and real objects are presented.These experiments highlight the practical benefits of WESD for applications invision and medical image analysis.

WESD - Weighted Spectral Distance for Measuring Shape Dissimilarity