Surface matching via currents (2005)
| Venue: | Proceedings of Information Processing in Medical Imaging (IPMI 2005), number 3565 in Lecture Notes in Computer Science |
| Citations: | 36 - 1 self |
BibTeX
@INPROCEEDINGS{Vaillant05surfacematching,
author = {Marc Vaillant and Joan Glaunès},
title = {Surface matching via currents},
booktitle = {Proceedings of Information Processing in Medical Imaging (IPMI 2005), number 3565 in Lecture Notes in Computer Science},
year = {2005},
pages = {381--392}
}
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Abstract
Abstract. We present a new method for computing an optimal deformation between two arbitrary surfaces embedded in Euclidean 3-dimensional space. Our main contribution is in building a norm on the space of surfaces via representation by currents of geometric measure theory. Currents are an appropriate choice for representations because they inherit natural transformation properties from differential forms. We impose a Hilbert space structure on currents, whose norm gives a convenient and practical way to define a matching functional. Using this Hilbert space norm, we also derive and implement a surface matching algorithm under the large deformation framework, guaranteeing that the optimal solution is a one-to-one regular map of the entire ambient space. We detail an implementation of this algorithm for triangular meshes and present results on 3D face and medical image data. 1
