# Back to the Metrics: Exploration of Distance Metrics in Anomaly Detection
## 3 Experiments
### Performance Comparison
#### 3.4.2 Anomaly Segmentation on MVTec-3D AD  
To compare the anomaly scoring (AS) performance, we evaluated BTM against several 3D, RGB, and RGB + 3D multimodal methods on the MVTec-3D dataset. As shown in Table 2, under the RGB + 3D multimodal setting, BTM achieved an average AUPRO performance of 96.9%, surpassing M3 DM and BTF by 0.8% and 0.5%, respectively. This superiority was also evident when examining individual categories. In the RGB and 3D \begin{table}
\begin{tabular}{l l c c c c c c c c c c} \hline \hline \multicolumn{1}{c}{\multirow{2}{*}{**Method**}} & \multirow{2}{*}{**Bagel**} & \multicolumn{2}{c}{**Cable**} & \multirow{2}{*}{**Carrot**} & \multirow{2}{*}{**Cookie**} & \multirow{2}{*}{**Dowel**} & \multirow{2}{*}{**Foam**} & \multirow{2}{*}{**Peach**} & \multirow{2}{*}{**Potato**} & \multirow{2}{*}{**Rope**} & \multirow{2}{*}{**Tire**} & \multirow{2}{*}{**Mean**} \\  & & & **Gland** & & & & & & & & & & \\ \hline \multirow{9}{*}{**0.5**} & Depth GAN [40] & 0.538 & 0.372 & 0.580 & 0.603 & 0.430 & 0.534 & 0.642 & 0.601 & 0.443 & 0.577 & 0.532 \\  & Depth AE [40] & 0.648 & 0.502 & 0.650 & 0.488 & 0.805 & 0.522 & 0.712 & 0.529 & 0.540 & 0.552 & 0.595 \\  & Depth VM [40] & 0.513 & 0.551 & 0.477 & 0.581 & 0.617 & 0.716 & 0.450 & 0.421 & 0.598 & 0.623 & 0.555 \\  & Voxel GAN [40] & 0.680 & 0.324 & 0.565 & 0.399 & 0.497 & 0.482 & 0.566 & 0.579 & 0.601 & 0.482 & 0.517 \\  & Voxel AE [40] & 0.510 & 0.540 & 0.384 & 0.693 & 0.446 & 0.632 & 0.550 & 0.494 & 0.721 & 0.413 & 0.538 \\  & Voxel VM [40] & 0.553 & 0.772 & 0.484 & 0.701 & 0.751 & 0.578 & 0.480 & 0.466 & 0.689 & 0.611 & 0.609 \\  & 3D-ST & 0.862 & 0.484 & 0.832 & 0.894 & 0.848 & 0.663 & 0.763 & 0.687 & 0.958 & 0.486 & 0.748 \\  & M3 DM [44] & **0.941** & **0.651** & **0.965** & **0.969** & **0.905** & **0.760** & **0.880** & **0.974** & **0.926** & **0.765** & **0.874** \\  & FPFH (BTF) [43] & 0.820 & 0.533 & 0.877 & 0.769 & 0.718 & 0.574 & 0.774 & 0.895 & 0.990 & 0.582 & 0.753 \\  & **FPFH (BTM)** & 0.939 & 0.553 & 0.916 & 0.844 & 0.823 & 0.588 & 0.718 & 0.928 & 0.976 & 0.633 & 0.792 \\ \hline \multirow{9}{*}{**0.5**} & PatchCore [44] & 0.876 & 0.880 & 0.791 & 0.682 & 0.912 & 0.701 & 0.695 & 0.618 & 0.841 & 0.702 & 0.770 \\  & M3 DM [44] & **0.944** & **0.918** & **0.896** & **0.749** & 0.959 & **0.767** & **0.919** & **0.648** & **0.938** & **0.767** & **0.850** \\  & RGB Net (BTF) [43] & 0.854 & 0.840 & 0.824 & 0.687 & 0.974 & 0.716 & 0.713 & 0.593 & 0.920 & 0.724 & 0.785 \\  & **RGB \#Net (BTM)** & 0.909 & 0.895 & 0.838 & 0.745 & **0.975** & 0.714 & 0.79 & 0.605 & 0.93 & 0.759 & 0.816 \\ \hline \multirow{9}{*}{**0.5**} & Depth GAN [40] & 0.530 & 0.376 & 0.607 & 0.603 & 0.497 & 0.484 & 0.595 & 0.489 & 0.536 & 0.521 & 0.523 \\  & Depth AE [40] & 0.468 & 0.731 & 0.497 & 0.673 & 0.534 & 0.417 & 0.485 & 0.549 & 0.564 & 0.546 & 0.546 \\  & Depth VM [40] & 0.510 & 0.542 & 0.469 & 0.576 & 0.609 & 0.699 & 0.450 & 0.419 & 0.668 & 0.520 & 0.546 \\  & Voxel GAN [40] & 0.383 & 0.623 & 0.474 & 0.639 & 0.564 & 0.409 & 0.617 & 0.427 & 0.663 & 0.577 & 0.537 \\  & Voxel AE [40] & 0.693 & 0.425 & 0.515 & 0.790 & 0.494 & 0.558 & 0.537 & 0.484 & 0.639 & 0.583 & 0.571 \\  & Voxel VM [40] & 0.750 & 0.747 & 0.613 & 0.738 & 0.823 & 0.693 & 0.679 & 0.652 & 0.609 & 0.690 & 0.699 \\  & M3 DM * & **0.998** & **0.894** & 0.96 & 0.963 & 0.954 & **0.901** & 0.958 & 0.868 & 0.962 & 0.797 & 0.926 \\  & BTF [43] & 0.938 & 0.765 & 0.972 & 0.888 & 0.960 & 0.664 & 0.904 & 0.929 & 0.982 & 0.726 & 0.873 \\
**BTM** & 0.980 & 0.860 & **0.980** & **0.963** & **0.978** & 0.726 & **0.958** & **0.953** & **0.980** & **0.926** & **0.930** \\ \hline \hline \end{tabular}  
* Denotes results obtained by employing pre-trained parameters provided by the original studies. Unannotated results are directly excerpted from the corresponding literature. The bold method is the method proposed by this paper. The bold number represents the best performance metric in the current modality and category.  
\end{table} 
Table 1: **I-AUROC** score for anomaly detection of all categories of MVTec-3D AD.