Measuring the Geometric Similarities of Shapes: Applications in Biology

Finding efficient algorithms to describe, measure and compare shapes is a central problem in numerous disciplines that generate extensive quantitative and visual information. Among these, biology occupies a central place. Registration of brain anatomy for example is essential to many studies in neurobiology; at a molecular level, comparison of protein shapes is a key step in understanding the relationships between their functions.In this talk I will introduce different methods for comparing such shapes when they are described by their (discrete) surfaces. In particular, I will focus on a method derived from computational geometry, in which the distance between two surfaces is computed as the difference between the optimal conformal mapping between the two surfaces, and an isometry, as well as on a physics-based method, in which the distance is measured as the cost of deforming one surface onto the other. I will show that these approaches lead to the definition of metrics in the space of shapes. I will describe the implementations of these approaches and their applicationson biological examples, from protein surface matching to 3D morphometrics on bones of primates.