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 small 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 a regular grid. 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 |
|---|---|---|
2006 | 10.1007/11784012_15 | WBIR |
Keywords | Field | DocType |
log-euclidean polyaffine,affine deformation,polyaffine fusion,affine registration,novel framework,general framework,polyaffine transformation,log-euclidean polyaffine framework,affine component,small number,log-euclidean polyaffine transformation,coordinate system,degree of freedom,magnetic resonance imaging,lie groups | Coordinate system,Affine transformation,Inverse,Topology,Mathematical optimization,Regular grid,Parametrization,Computer science,Algorithm,Invariant (mathematics),Invertible matrix,Euclidean geometry | Conference |
Volume | ISSN | ISBN |
4057 | 0302-9743 | 3-540-35648-7 |
Citations | PageRank | References |
17 | 3.02 | 14 |
Authors | ||
4 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Vincent Arsigny | 1 | 733 | 50.69 |
| Olivier Commowick | 2 | 505 | 39.81 |
| Xavier Pennec | 3 | 5021 | 357.08 |
| Nicholas Ayache | 4 | 10804 | 1654.36 |