Shape From Moments - An Estimation Perspective
July 12th, 2002
The SIAM 50th Anniversary Meeting - Invited Talk

This talk discusses the problem of recovering a planar polygon from its measured moments. The moments correspond to an indicator function defined over the polygon’s support. Previous work on this problem gave necessary and sufficient conditions for such successful recovery process and focused mainly on the case of exact measurements being given. In this talk we describe an extension of these results treating the same problem in the case where a longer than necessary series of noise corrupted moments is given.

Leaning on similar problems in array processing, system identification, and signal processing, we discuss a set of possible estimation procedures which are based on the Prony and the Pencil methods, relate them one to the other, and compare them through simulations. We then present an improvement over these methods based on the direct use of the Maximum-Likelihood estimator, exploiting the above methods as initialization. Finally, we show how regularization, and thus Maximum A-posteriori Probability estimator could be applied to reflect prior knowledge about the recovered polygon.

Joint work with Peyman Milanfar, Professor at Electrical Engineering, University of California - Santa-Cruz, and Gene Golub, Professor at Stanford University - Computer Science Department.