Geometry and Shape Analysis in Biological Sciences (8-9 June 2017)
Tutorial 4: Comparing biological shapes (2)
Now that we have described discrete surfaces and the concept of conformal mapping, we will study in more detail the problem of defining a standard correspondence, or map, between two surfaces, sometimes called a parameterization. Such a map allows a mesh, or triangulation representing one of the surfaces to be transported to the second surface. We will describe approaches to this problem through circle packing and Ricci flow. The methods described so far for comparing two shapes focus on the differences in the geometry of a pair of shapes. An alternative approach is to attempts to capture the cost of deforming one shape into the other. We will describe one implementation of this approach, based on the idea of a variational distance that generalizes the concept of Euclidean distance.
Slides of the presentation
Particle Dynamics Animation
The small animation illustrates the dynamics of an elastic network representing a shape.