Unsupervised Clustering Using Diffusion Maps for Local Shape Modelling

Understanding the biological variability of anatomical objects is essential for statistical shape analysis and to distinguish between healthy and pathological structures. Statistical Shape Modelling (SSM) can be used to analyse the shapes of sub-structures aiming to describe their variation across individual objects and between groups of them [1]. However, when the shapes exhibit self-similarity or are intrinsically fractal, such as often encountered in biomedical problems, global shape models result in highly non-linear shape spaces and it can be difficult to determine a compact set of modes of variation. In this work, we present a method for local shape modelling and analysis that uses Diffusion Maps [2] for non-linear, spectral clustering to build a set of linear shape spaces for such analysis. The method uses a curvature scale-space (CSS) description of shape to partition them into sets of self-similar parts and these are then linearly mixed to more compactly model the global shape.