Patrice Koehl
Department of Computer Science
Genome Center
Room 4319, Genome Center, GBSF
451 East Health Sciences Drive
University of California
Davis, CA 95616
Phone: (530) 754 5121

Geometry and Shape Analysis in Biological Sciences (8-9 June 2017)

Tutorial 4: Comparing biological shapes (2)

Venue: IMS, National University of Singapore



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

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Particle Dynamics Animation

The small animation illustrates the dynamics of an elastic network representing a shape.


  Page last modified 9 June 2017