Information Geometry for Landmark Shape Analysis: Unifying Shape Representation and Deformation

posted by Michal Frystacky on Thu, 02/09/2012 - 10:04
TitleInformation Geometry for Landmark Shape Analysis: Unifying Shape Representation and Deformation
Publication TypeJournal Article
Year of Publication2009
AuthorsPeter, AM, Rangarajan, A
JournalIEEE Trans. Pattern Anal. Mach. Intell.
Volume31
Pagination337-350
KeywordsInformation Geometry Shape Analysis
AbstractThis paper proposes a new affine registration algorithm for matching two point sets in IR2 or IR3. The input point sets are represented as probability density functions, using either Gaussian mixture models or discrete density models, and the problem of registering the point sets is treated as aligning the two distributions. Since polynomials transform as symmetric tensors under an affine transformation, the distributions’ moments, which are the expected values of polynomials, also transform accordingly. Therefore, instead of solving the harder problem of aligning the two distributions directly, we solve the softer problem of matching the distributions’ moments. By formulating a least-squares problem for matching moments of the two distributions up to degree three, the resulting cost function is a polynomial that can be efficiently optimized using techniques originated from algebraic geometry: the global minimum of this polynomial can be determined by solving a system of polynomial equations. The algorithm is robust in the presence of noises and outliers, and we validate the proposed algorithm on a variety of point sets with varying degrees of deformation and noise.
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