Shape Analysis in Evolutionary Biology
How much can we learn about biology by looking at anatomical surfaces? Potentially a lot, but there are many preprocessing issues to deal with before we can.
Summary
Experts in many realms of biology have grown interested in the role of the shape of objects of interest. There are many questions that one can ask: exactly what can the shape of an object determine about it? If there are a collection of shapes of the same basic type (i.e. crowns from the same type of molar), are there natural ways in which they cluster? How does this relate to genetic information?
Rigid shapes coming from evolutionary history (e.g. bones and teeth) provide an interesting challenge for mathematics. Shapes of the same basic type coming from multiple different species can exhibit a much wider amount of variation (i.e. are much less isometric) than those coming from just humans. In some cases, this increased variation renders standards tools and methods for computing features, registrations, and shape statistics useless. The goal of this project is to fix these issues and develop new tools that can be used in place of these.
Projects
Eyes on the Prize: Improving Registration via Forward Propagation
Fully automated registration of shapes can prove to be extremely challenging if the shapes have clearly corresponding parts but wildly different features. Read more
SAMS: Shape Alignment, Mapping, and Statistics
Fully automated methods for statistical shape analysis are needed in order to do high-resolution analysis of large amounts of data. Existing methods primarily focus on the case when shapes are topological spheres and have little variation. SAMS is a package that will work on all simply-connected shapes and can robustly handle higher variability of data. Read more
Distlets: Building Flexible, Interpretable Dictionaries for Shape Data
The geometric and topological properties of spaces of shapes are not well understood, let alone those of anatomical surfaces. However, those of other spaces (e.g. Hilbert spaces) are. If we were able to embed shapes into a nicer, lower dimensional space, we could use pullbacks of tools on the nicer spaces to learn more about shape spaces. Sparse dictionaries provide a natural, interpretable way to do this. Read more