Linear and Non-linear Geometric Object Matching with Implicit Representation

Authors:
Alex Leow;Ming-Chang Chiang;Hillary Protas;Paul Thompson;Luminita Vese;Henry S. C. Huang
Affiliations:
University of California, Los Angeles;University of California, Los Angeles;University of California, Los Angeles;University of California, Los Angeles;University of California, Los Angeles;University of California, Los Angeles
Venue:
ICPR '04 Proceedings of the Pattern Recognition, 17th International Conference on (ICPR'04) Volume 3 - Volume 03
Year:
2004

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Abstract

This paper deals with the matching of geometric objects including points, curves, surfaces, and subvolumes using implicit object representations in both linear and non-linear settings. This framework can be applied to feature-based non-linear image warping in biomedical imaging with the deformation constrained to be one-to-one, onto, and diffeomorphic. Moreover, a theoretical connection is established between the well known Hausdorff metric and the framework proposed in this paper. A general strategy for matching geometric objects in both 2D and 3D is discussed. The corresponding Euler-Lagrange equations are presented and gradient descent method is employed to solve the time dependent partial differential equations.