A week ago, Carlos and I were sent off to Hong Kong to attend Solid and Physical Modeling 2014. Carlos was there to present his poster on edge length interpolation.
In general, it was very motivational to see so many works that are very directly relevant to your research topic, if not directly attacking the same problem. Here are some notes.
Congenital hand deformities classification by conformal module.
Here’s the paper. Sadly, none of the authors came, so they got collaborator Ying He to present as proxy. Basically, they mark sulci associated with the disease, cut them to create genus-0 surface with some holes, conformally map the sphere, and define a shape space signature based on geodesic lengths of the boundaries, which they use to classify. Clearly, their dataset was very small as it was mentioned as a limitation, and the size was not even mentioned.
Spoke with possible collaborator Ying He
He’s an associate professor at Nanyang Tech in Singapore who got his PhD from Stony Brook and worked with David Gu. He is working not so much on conformal maps and biomedical applications that David Gu tends to do, but more on intrinsic distances: their paper is about computing Voronoi diagram intrinsically.
Michael Kazhdan talk on geometric flow
He demo’d how you can hack on the mean curvature flow equation to do mesh editing. He showed a visualization of flowing a genus-0 surface to the round sphere - the end result is conformal but not the transition states. I remember when a SIGGRAPH reviewer pointed to this method and said that what we did to visualize a conformal map was already done? Well, they’re wrong because it’s not a conformal transition, only the end state! But there is a 2013 paper by Crane, Pinkall, and Schroeder that does do the conformal flow.
Shape space talk by Max Wardetsky
In addition to talking about his shape space paper, Max made a few remarks in his talk about shape space:
Connection between existing shape space methods
Wardetzky posets Amenta- and Winkler-like fast methods as approximations to full-fledged geodesics in high-dimensional shape space, though I have no clue how one would formally establish the connection.
Curvature of shape space
If we could only know the curvature of shape space, we could better be able to understand things like rigidity e.g. are there lots of ways a shape can change or is it pretty limited?
Isometric shape interpolation paper
His approach is just like ours. Seung-Yeob Stephen Baek is a postdoc who is more interested in modeling and has no plans for future work on this, but he basically achieved what we wanted to do: efficient, many-model interpolation based on local frames. The difference is in the shape representation: instead of just the length at each edge, he stores two angles that rotates the local frame of the face into alignment with the opposite face. Read the paper.
All the papers from SPM: http://www.sciencedirect.com/science/journal/00104485/58
All the papers from SMI: http://www.sciencedirect.com/science/journal/00978493