<title>Efficient representation of shape variability using surface-based free-vibration modes</title>

Abstract

The efficient representation of shape and shape variability is a key issue in computerized 3D image processing. One of the common goals is the ability to express as much shape variability as necessary with as few parameters as possible. In this paper we focus on the capture of shape variability on the basis of free surface vibration modes. We do not model the interior of an elastic object, but rather its triangulated surface. As in the case of 3D statistical point-distribution models (PDM) we assume that the shape of an anatomical object can efficiently be approximated by a weighted sum of a mean shape and a number of variation modes. The variation modes are in our case Eigenvectors of a stiffness-matrix. Based on a given surface triangulation we define a physical model by placing mass points at the vertices and coil- and leaf-spring elements at the edge positions of the triangulation. Ordered by wavelength, the resulting free vibration modes can be used to efficiently approximate shape variability in a coarse to fine manner, similar to a Fourier decomposition. As real-object examples from the medical image-processing domain, we applied the method to triangulated surfaces of segmented lumbar vertebra and femor-head from CT data sets. A comparison to corresponding statistical shape models shows, that natural variability of anatomical shape can efficiently be approximated by free surface vibration modes.