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Regularization Methods in Non-Rigid Registration :II. Isotropic Energies, Filters and Splines

Pascal Cachier 1 Nicholas Ayache
1 EPIDAURE - Medical imaging and robotics
CRISAM - Inria Sophia Antipolis - Méditerranée
Abstract : The goal of this report is to propose some new regularization and filtering techniques specific to vector fields. Indeed, most of vectorial regularization energies used in the domain of image or feature matching are in fact scalar energies applied independently on each component of the transformation. The only common exception is the elastic energy, which enables cross-effects between components. In this report, we first propose a technique to find all isotropic differential quadratic forms (IDQF) of any order on vector fields, and give results in the case of order 1 and 2. The dense quadratic approximation induced by these energies give birth to a new class of vector filters, which are applied in practice in the Fourier domain. We also propose a family of isotropic and separable vector filters that generalize scalar Gaussian filtering to vectors and enables efficient isotropic smoothing without using Fourier transform, using recursive filtering in the real domain. We also study the splines induced by these energies in the context of spare point motion interpolation or approximation. These splines are generalization to vectors of the scalar Laplacian splines, such as the thin-plate spline. We finally propose to merge dense and sparse approximation problems, yielding solutions that mix convolution filter and splines. This enables to introduce naturally sparse geometric constraints into an intensity-based registration algorithm.
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Contributor : Rapport de Recherche Inria <>
Submitted on : Tuesday, May 23, 2006 - 8:28:44 PM
Last modification on : Saturday, January 27, 2018 - 1:31:24 AM
Long-term archiving on: : Sunday, April 4, 2010 - 11:04:45 PM


  • HAL Id : inria-00072344, version 1



Pascal Cachier, Nicholas Ayache. Regularization Methods in Non-Rigid Registration :II. Isotropic Energies, Filters and Splines. RR-4243, INRIA. 2001. ⟨inria-00072344⟩



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