Shape analysis of carpal bones using spectral graph wavelets

Abstract

Graph signal processing is an emerging field that provides powerful tools for analyzing signals defined on graphs. In this chapter, we present a graph signal processing approach to shape analysis of carpal bones of the human wrist by exploiting local structure information among shape features for the purpose of quantitative shape comparison. We represent the cortical surface of a carpal bone in the spectral geometric setting using the Laplace-Beltrami operator and spectral graph wavelets. We propose a global spectral graph wavelet (GSGW) descriptor that is isometric invariant, efficient to compute, and combines the advantages of both low-pass and band-pass filters. We perform experiments on shapes of the carpal bones of ten women and ten men from a publicly-available database of wrist bones. Using one-way multivatiate analysis of variance (MANOVA) and permutation testing, our extensive results that the proposed GSGW framework gives a much better performance compared to the graph spectral signature (GPS) embedding approach for comparing shapes of the carpal bones across populations.