Table I.
Approximation Errors in Various Algorithms
| Riem. μ | Riem. σ | Forb. μ | Forb. σ | |
|---|---|---|---|---|
| Euc. Geodesic Appr. | 12.2023 | 10.5576 | 37.2502 | 51.8160 |
| Log-Euc Geodesic Appr. | 6.5117 | 7.3565 | 7.7040 | 31.4381 |
| Riem. Geodesic Appr. | 6.5115 | 7.3563 | 7.7037 | 31.4378 |
| PDE interpolation | 8.8490 | 6.5481 | 6.3611 | 29.4992 |
| Non-Robust Tensor Spline | 3.8652 | 2.7202 | 0.5082 | 0.8581 |
| Approximation errors using robust function | ||||
| Robust Euc. Geodesic Appr. | 8.6782 | 0.7521 | 0.9201 | 0.1002 |
| Robust Log-Euc Geodesic Appr. | 3.8912 | 2.3191 | 0.6328 | 0.928 |
| Robust Riem. Geodesic Appr. | 3.4711 | 2.2534 | 0.6192 | 0.795 |
| Robust Tensor Spline Appr. | 0.1373 | 0.0463 | 0.0015 | 0.0006 |
| Approximation errors of robust splines using different metrics | ||||
| Robust Euc. Spline Appr. | 7.4655 | 0.4931 | 0.0988 | 0.0927 |
| Robust Log-Euc Spline Appr. | 1.4651 | 0.9996 | 0.0328 | 0.0318 |
| Robust Tensor Spline Appr. | 0.1373 | 0.0463 | 0.0015 | 0.0006 |