Geometric Structures for Efficient Shape Analysis

Statistical shape models have been established as one of the most successful methods for understanding the geometric variability in shape populations. There is increasing evidence that intrinsic approaches, which account for the non-Euclidean structure inherent to shapes, are essential to faithfully capture the large variability. This talk presents a nonlinear, rigid motion invariant approach for shape analysis based on concepts from differential geometry of smooth surfaces. Performing geodesic calculus on this representation allows for fast computations opening up the potential in large shape databases accessible through longitudinal and multi-site imaging studies. The rich structure of the derived shape space yields highly differentiating shape descriptors providing a compact representation that is amenable to learning algorithms. The advantages over alternative approaches will be demonstrated on the example of shape-based assessment and classification of morphological disorders.