Table 1. Rigid-body registration results for corresponding point sets with anisotropic noise present in both sets of points. (Experiment 1A).
| Trans. (mm) | [10, 20] | [90, 100] | ||||||||
|---|---|---|---|---|---|---|---|---|---|---|
| Rot. (deg.) | Alg. | Iter. | Runtime | RE | Inst. | Alg. | Iter. | Runtime | RE | Inst. |
| [0, 15] | Isotropic | 1.0 | 0.0001 | 0.439 | 0 | Isotropic | 1.0 | 0.0001 | 0.442 | 0 |
| Estepar | 15.1 | 0.0106 | 0.423 | 0 | Estepar | 15.1 | 0.0106 | 0.424 | 0 | |
| Balach. | 28.1 | 0.0060 | 0.423 | 0 | Balach. | 32.9 | 0.0068 | 0.424 | 0 | |
| Proposed | 3.8 | 0.0014 | 0.422 | 0 | Proposed | 3.8 | 0.0013 | 0.423 | 0 | |
| [15, 45] | Isotropic | 1.0 | 0.0001 | 0.443 | 0 | Isotropic | 1.0 | 0.0001 | 0.442 | 0 |
| Estepar | 17.2 | 0.0120 | 0.432 | 0 | Estepar | 17.2 | 0.0120 | 0.431 | 0 | |
| Balach. | 34.1 | 0.0070 | 0.428 | 0 | Balach. | 37.5 | 0.0076 | 0.427 | 0 | |
| Proposed | 4.4 | 0.0015 | 0.424 | 0 | Proposed | 4.4 | 0.0015 | 0.423 | 0 | |
| [45, 90] | Isotropic | 1.0 | 0.0001 | 0.442 | 0 | Isotropic | 1.0 | 0.0001 | 0.435 | 0 |
| Estepar | 18.8 | 0.0131 | 0.456 | 0 | Estepar | 18.8 | 0.0130 | 0.450 | 0 | |
| Balach. | 38.1 | 0.0078 | 0.442 | 0 | Balach. | 40.3 | 0.0081 | 0.436 | 0 | |
| Proposed | 5.1 | 0.0017 | 0.424 | 0 | Proposed | 5.1 | 0.0017 | 0.416 | 0 | |
| [90, 150] | Isotropic | 1.0 | 0.0001 | 0.446 | 0 | Isotropic | 1.0 | 0.0001 | 0.439 | 0 |
| Estepar | 22.9 | 0.0154 | 0.469 | 2 | Estepar | 23.3 | 0.0157 | 0.466 | 2 | |
| Balach. | 39.4 | 0.0080 | 0.448 | 0 | Balach. | 41.9 | 0.0084 | 0.444 | 0 | |
| Proposed | 6.3 | 0.0021 | 0.430 | 0 | Proposed | 6.3 | 0.0021 | 0.421 | 0 | |
| [150, 180] | Isotropic | 1.0 | 0.0001 | 0.444 | 0 | Isotropic | 1.0 | 0.0001 | 0.442 | 0 |
| Estepar | 28.0 | 0.0184 | 0.475 | 60 | Estepar | 27.6 | 0.0181 | 0.477 | 59 | |
| Balach. | 42.0 | 0.0085 | 0.439 | 0 | Balach. | 44.5 | 0.0088 | 0.441 | 0 | |
| Proposed | 8.8 | 0.0028 | 0.424 | 0 | Proposed | 8.7 | 0.0028 | 0.426 | 0 | |
Results report the efficiency (number of iterations and runtime (seconds)), registration error (RE) (mm), and instability (% of trials) of the GTLS registration method proposed in this paper compared to the closed-form isotropic solution [26] and the prior GTLS methods of Estepar et al. [10] and Balachandran and Fitzpatrick [31]. The tests are binned according to the magnitude of initial misalignment in translation (mm) and rotation (degrees); each bin represents average values measured over 1000 randomized trials.