Measuring the geometric similarities of shapes: Applications in Biology

Abstract:
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 applications
on biological examples, from protein surface matching to 3D morphometrics on bones of primates.


Biography:
Patrice Koehl, based at the University of California, Davis, has made fundamental contributions to computational biology through innovative applications of physics, geometry, and algorithmic design to problems in structural biology and molecular biophysics. His work has advanced our understanding of protein structure, molecular shape, and biomolecular dynamics, while also giving rise to computational methods used in structural prediction, macromolecular modeling, and the analysis of high-dimensional biological data. A hallmark of his research is the development of mathematically principled, computationally efficient algorithms that bridge physics, computer science, and the life sciences.