Table 1.
Dice scores, contour distances in pixel and the standard deviation of Jacobian determinant of estimated deformation fields using different methods (for the Helen dataset). The standard deviation of Jacobian determinants of deformation fields show the smoothness of the deformation fields, where small values indicate more plausible, regular results. The mean of Jacobian negatives is the number of singular points in the estimated field divided by the total number of pixels. For B-Spline FlowNet, ours (without guidance) and ours (shared RegNet weights), we have implemented our own version of the method from the each reference (details in Section 3.2). Explicit shape regression (ESR) requires in addition corresponding manual landmarks for training. The experiment using pre-trained FlowNet was performed without fine-tuning and using downsampled images, which we first affine transformed based on the face landmarks. Approximated inference time is also given in seconds per image.
| Method | Dice (%) | Contour Distance (px) |
Jacobian Std. |
Jacobian Negatives |
Inference Time (s/img) |
|---|---|---|---|---|---|
| no registration | 23.0 | 15.55 | - | - | - |
| ESR ([22]) + CPD ([23]) | 65.6 | 1.96 | 0.154 | - | - |
| B-Spline FlowNet | 49.4 | 5.96 | 0.579 | 0.03124 | ≈0.007 |
| FlowNet w/ smaller images ([1]) | 30.6 | 12.83 | - | - | - |
| ours (without guidance, ∼[3]) | 55.5 | 5.41 | 0.257 | 0.00062 | ≈0.007 |
| ours (shared RegNet weights, ∼[2]) | 60.4 | 5.02 | 0.269 | 0.00061 | ≈0.007 |
| ours (diffeomorphic) | 52.0 | 5.66 | 0.240 | 0.00062 | ≈0.007 |
| ours (poly-affine) | 65.8 | 3.95 | 0.281 | 0.00093 | ≈0.024 |
| ours | 66.0 | 4.01 | 0.285 | 0.00106 | ≈0.007 |