A Discrete Global Minimization Algorithm for
Continuous Variational Problems
There are many applications where one needs to search for a "function"
that has "minimal energy" while satisfying some boundary constraints. As a simple example, consider the problem of finding the minial area soap bubble surface that spans a wireframe boundary. Numerical methods are typically only good at finding local minima to such varational problems.
In this talk, we show how global optima can be found as the limit of a set of purely combinatorial problems. These combinatorial problems can be thought of as higher dimensional analogues of the "shortest path in planar graph" problems. For example, when the problem dimension is 3, the combinatorial problem is to find a "discrete minimal surface" in a volumetric cellular complex. We then show how these combinatorial problems can be solved in polynomial time by reducing them to instances of MIN-CUT.
We will then explore an application of these ideas to 3-camera stereo vision.
About the Speaker:
Steven (aka Shlomo) Gortler is the Robert I. Goldman Professor of Computer Science at Harvard University. Shlomo's main area of research is computer graphics, specializing in rendering and geometry, but is often convinced to work on other things as well.
Thursday, October 6, 2005
JEC 3117 - 4:00 p.m. to 5:00 p.m.
Refreshments at 3:30 p.m.