Table 3. Rotation-only registration results for corresponding point sets with anisotropic noise present in both sets of points. (Experiment 1C).
| Rot. (deg.) | Alg. | Iter. | Runtime | RE | Inst. |
|---|---|---|---|---|---|
| [0, 15] | Isotropic | 1.0 | 0.0000 | 0.304 | 0 |
| Kanatani | 4.0 | 0.0025 | 0.279 | 0 | |
| Proposed | 3.8 | 0.0013 | 0.278 | 0 | |
| [15, 45] | Isotropic | 1.0 | 0.0000 | 0.292 | 0 |
| Kanatani | 4.0 | 0.0025 | 0.283 | 0 | |
| Proposed | 4.4 | 0.0015 | 0.269 | 0 | |
| [45, 90] | Isotropic | 1.0 | 0.0000 | 0.295 | 0 |
| Kanatani | 4.0 | 0.0025 | 0.313 | 0 | |
| Proposed | 5.1 | 0.0017 | 0.271 | 0 | |
| [90, 150] | Isotropic | 1.0 | 0.0000 | 0.292 | 0 |
| Kanatani | 4.5 | 0.0028 | 0.323 | 0 | |
| Proposed | 6.3 | 0.0020 | 0.265 | 0 | |
| [150, 180] | Isotropic | 1.0 | 0.0000 | 0.286 | 0 |
| Kanatani | 6.1 | 0.0038 | 0.360 | 10 | |
| Proposed | 8.7 | 0.0028 | 0.263 | 0 |
Results report the efficiency (number of iterations and runtime (seconds)), registration error (RE) (mm), and instability (% of trials) of the GTLS method proposed in this paper (modified to computer only rotation) compared to the closed-form isotropic solution [26] and the prior GTLS rotation estimation method of Ohta and Kanatani [28]. The tests are binned according to the magnitude of initial misalignment in rotation (degrees) with translational misalignment being zero; each bin represents average values measured over 1000 randomized trials.