Name
Abstract | ||
|---|---|---|
Computations on tensors have become common with the use of DT-MRI. But the classical Euclidean framework has many defects, and affine-invariant Riemannian metrics have been proposed to correct them. These metrics have excellent theoretical properties but lead to complex and slow algorithms. To remedy this limitation, we propose new metrics called Log-Euclidean. They also have excellent theoretical properties and yield similar results in practice, but with much simpler and faster computations. Indeed, Log-Euclidean computations are Euclidean computations in the domain of matrix logarithms. Theoretical aspects are presented and experimental results for multilinear interpolation and regularization of tensor fields are shown on synthetic and real DTI data. |
Year | DOI | Venue |
|---|---|---|
2005 | 10.1007/11566465_15 | MICCAI |
Keywords | Field | DocType |
affine-invariant riemannian metrics,log-euclidean computation,excellent theoretical property,log-euclidean framework,simple calculus,matrix logarithm,theoretical aspect,classical euclidean framework,new metrics,euclidean computation,faster computation | Applied mathematics,Tensor,Matrix (mathematics),Computer science,Interpolation,Artificial intelligence,Euclidean geometry,Multilinear map,Discrete mathematics,Pattern recognition,Tensor field,Matrix exponential,Bilinear interpolation | Conference |
Volume | Issue | ISSN |
8 | Pt 1 | 0302-9743 |
ISBN | Citations | PageRank |
3-540-29327-2 | 100 | 7.11 |
References | Authors | |
4 | 4 | |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Vincent Arsigny | 1 | 733 | 50.69 |
| P Fillard | 2 | 1238 | 75.70 |
| Xavier Pennec | 3 | 5021 | 357.08 |
| Nicholas Ayache | 4 | 10804 | 1654.36 |