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.