Name
Abstract | ||
|---|---|---|
In this article, we focus on the parameterization of non-rigid geometrical deformations with a small number of flexible degrees of freedom. In previous work, we proposed a general framework called polyaffine to parameterize deformations with a finite number of rigid or affine components, while guaranteeing the invertibility of global deformations. However, this framework lacks some important properties: the inverse of a polyaffine transformation is not polyaffine in general, and the polyaffine fusion of affine components is not invariant with respect to a change of coordinate system. We present here a novel general framework, called Log-Euclidean polyaffine, which overcomes these defects.We also detail a simple algorithm, the Fast Polyaffine Transform, which allows to compute very efficiently Log-Euclidean polyaffine transformations and their inverses on regular grids. The results presented here on real 3D locally affine registration suggest that our novel framework provides a general and efficient way of fusing local rigid or affine deformations into a global invertible transformation without introducing artifacts, independently of the way local deformations are first estimated. |
Year | DOI | Venue |
|---|---|---|
2009 | 10.1007/s10851-008-0135-9 | Journal of Mathematical Imaging and Vision |
Keywords | Field | DocType |
Locally affine transformations,Medical imaging,ODE,Diffeomorphisms,Polyaffine transformations,Log-Euclidean,Non-rigid registration | Affine transformation,Coordinate system,Topology,Inverse,Mathematical optimization,Finite set,Algorithm,Invariant (mathematics),Euclidean geometry,SIMPLE algorithm,Invertible matrix,Mathematics | Journal |
Volume | Issue | ISSN |
33 | 2 | 0924-9907 |
Citations | PageRank | References |
55 | 2.18 | 16 |
Authors | ||
4 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Vincent Arsigny | 1 | 733 | 50.69 |
| Olivier Commowick | 2 | 505 | 39.81 |
| Nicholas Ayache | 3 | 10804 | 1654.36 |
| Xavier Pennec | 4 | 5021 | 357.08 |