SlowGuess/NeurIPS_2023_OCR huggingface dataset:
$$
\operatorname {M A E} (\mathrm {R}) = \frac {1}{3} \left\| \tilde {R} - R ^ {g t} \right\| _ {1}, \tag {17}
$$
$$
\mathrm {R M S E} (\mathrm {R}) = \frac {1}{\sqrt {3}} | | \tilde {R} - R ^ {g t} | | _ {2},
$$
Figure 7: An example of surface segmentation over the point cloud of a bottle broken into 7 major pieces. Fracture points are marked with green in the predicted result of our method (left) and red in the ground-truth (right).
Table 4: Comparison of training and influence time with Tesla V100 GPUs. For Jigsaw, the time used in the forward is 1.30s/batch and the rest of the time is used on Hungarian and global alignment.
Jigsaw	Predator[16]	DGL [33]	LSTM [33]	Global [33]
Training Time / GPUs	120H / 4	96H / 4	11H / 1	16H /1	21H / 1
Influence Speed (s/batch) / batch size	7.67(1.30) / 8	1.28 / 28	2.46 / 32	1.63 / 32	1.65 / 32
Table 5: Detailed quantitative results of Jigsaw on Breaking Bad dataset (mean and STD by 3 runs).
Method	RMSE (R) ↓ degree	MAE (R) ↓ degree	RMSE(T) ↓ ×10-2	MAE (T) ↓ ×10-2	PA ↑ %
Results on the everyday object subset.
Jigsaw	42.3 ± 0.03	36.3 ± 0.06	10.7 ± 0.02	8.7 ± 0.02	57.3 ± 0.012
Results on the artifact object subset.
Jigsaw	52.4 ± 0.09	45.4 ± 0.14	22.2 ± 0.05	19.3 ± 0.04	45.6 ± 0.015
for each piece, where  $\tilde{R}$  and  $R^{gt}$  were predicted rotation and ground-truth rotation represented in Euler angles. The error over each object was computed as the mean error of all the pieces and the total error was the mean error of all the object. For translation, MAE(T) and RMSE(T) were computed in the same way
$$
\operatorname {M A E} (\mathrm {T}) = \frac {1}{3} | | \tilde {\boldsymbol {t}} - \boldsymbol {t} ^ {g t} | | _ {1},
$$
$$
\operatorname {R M S E} (\mathrm {T}) = \frac {1}{\sqrt {3}} \left\| \tilde {\boldsymbol {t}} - \boldsymbol {t} ^ {g t} \right\| _ {2}, \tag {18}
$$
where  $\tilde{t}$  and  $t^{gt}$  were the predicted translation and ground-truth translation.
D.1 Additional Configuration of parameters
For PREDATOR [16], we carefully follow the parameters presented in its open sourced code, and the threshold for overlap recall to add saliency loss is set to be 0.3. For Jigsaw, we start training with only the segmentation loss. We add matching loss after first 10 epochs, and rigidity loss after 200 epochs.
D.2 Running time
Our framework is implemented in Pytorch. All methods are trained over Tesla V100-SXM2-32GB GPUs and distributed data parallel strategy is applied for multi-GPU training. The training and influence time for Jigsaw and baseline methods are shown in Table 4.
E.1 Detailed Quantitative Results
Fig. 8 gives a detailed distribution of each error metric with respect to the number of fractured pieces. Our approach exhibits a clear advantage in each of the metrics evaluated, and this advantage becomes more pronounced as the number of pieces decreases.
In addition, we present the mean and standard deviation (STD) of three runs of our method in Table 5. These values demonstrate the stability of our method across different random seeds and variations in the sampled point cloud. The consistent performance and low standard deviation affirm the robustness of our proposed approach.
Figure 8: Detailed analysis of the quantitative results obtained by each method on the everyday object subset. We provide results for each metric, categorized by the number of pieces involved. The shadowed area in the figures represents the distribution of each metric across the corresponding number of pieces. The horizontal line indicates the mean value of the metric for that specific number of pieces. Different hues represent different methods.
E.2 More Qualitative Results
We collect additional visualizations of the assembled objects in Fig. 9. Even with a large number of pieces to assemble, our method remains robust in restoring major pieces to their original pose.
E.3 Additional Registration Baseline
We have received advice to consider GeoTransformer [30] as a state-of-the-art baseline for low overlap registration. However, training GeoTransformer proves to be exceedingly slow (about 15 days over 4 V100 GPUs), primarily due to the significant scale of Breaking-Bad in comparison to the 3D registration datasets on which it was originally tested. On pairwise transformations GeoTransformer achieves MAE(R) = 72.4 (degree), RMSE(R) = 84.8 (degree), RMSE(T) = 14.3 (×10 $^{-2}$ ), MAE(T) = 11.6 (×10 $^{-2}$ ), PA = 3.1%. These findings align with the claims we've put forth in our paper, and we believe that presenting the full results of PREDATOR adequately reflects how registration baselines perform on the assembly task.
Figure 9: More visualization of assembly results.