# Back to the Metrics: Exploration of Distance Metrics in Anomaly Detection
## 3 Experiments
### Performance of kNN Reweight Metrics on BTF  
We conducted experiments on computing AD anomaly scores using BTF with a kNN re-weighting approach (Equation (11)) on the MVTec-3D AD dataset. As shown in Figure 8, the AD performance is lowest when \(k=1\). Subsequently, as \(k\) increases, the influence of weight w decreases, and the AD performance gradually approaches our optimal performance. \begin{table}
\begin{tabular}{c c c c c c c c c c c c} \hline \hline \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**} \\ \cline{1-1} \cline{6-11}  & & & & & & & & & & & & \\ \hline \multirow{8}{*}{**C**} & Depth GAN [40] & 0.111 & 0.072 & 0.212 & 0.174 & 0.160 & 0.128 & 0.003 & 0.042 & 0.446 & 0.075 & 0.143 \\  & Depth AE [40] & 0.147 & 0.069 & 0.293 & 0.217 & 0.207 & 0.181 & 0.164 & 0.066 & 0.545 & 0.142 & 0.203 \\  & Depth VM [40] & 0.280 & 0.374 & 0.243 & 0.526 & 0.485 & 0.314 & 0.199 & 0.388 & 0.543 & 0.385 & 0.374 \\  & Voxel GAN [40] & 0.440 & 0.453 & 0.875 & 0.755 & 0.782 & 0.378 & 0.392 & 0.639 & 0.775 & 0.389 & 0.583 \\  & Voxel AE [40] & 0.260 & 0.341 & 0.581 & 0.351 & 0.502 & 0.234 & 0.351 & 0.658 & 0.015 & 0.185 & 0.348 \\  & Voxel VM [40] & 0.453 & 0.343 & 0.521 & 0.697 & 0.680 & 0.284 & 0.349 & 0.634 & 0.616 & 0.346 & 0.492 \\  & 3D-ST [41] & 0.950 & 0.483 & **0.986** & 0.921 & 0.905 & 0.632 & 0.945 & **0.988** & 0.976 & 0.542 & 0.833 \\  & M3 DM [44] & 0.943 & 0.818 & 0.977 & 0.882 & 0.881 & **0.743** & 0.958 & 0.974 & 0.95 & 0.929 & 0.906 \\  & FPFH (BTF) [43] & 0.972 & 0.849 & 0.981 & **0.939** & **0.963** & 0.693 & 0.975 & 0.981 & **0.980** & **0.949** & **0.928** \\  & **FPFH (BTM)** & **0.974** & **0.861** & 0.981 & 0.937 & 0.959 & 0.661 & **0.978** & 0.983 & 0.98 & 0.947 & 0.926 \\ \hline \multirow{8}{*}{**C**} & PatchCore [44] & 0.901 & 0.949 & 0.928 & 0.877 & 0.892 & 0.563 & 0.904 & 0.932 & 0.908 & 0.906 & 0.876 \\  & M3 DM [44] & **0.952** & **0.972** & **0.973** & 0.891 & 0.932 & **0.843** & **0.97** & **0.956** & **0.968** & **0.966** & **0.942** \\  & RGB iNet (BTF) [43] & 0.898 & 0.948 & 0.927 & 0.872 & 0.927 & 0.555 & 0.902 & 0.931 & 0.903 & 0.899 & 0.876 \\  & **RGB iNet (BTM)** & 0.901 & 0.958 & 0.942 & **0.905** & **0.951** & 0.615 & 0.906 & 0.938 & 0.927 & 0.916 & 0.896 \\ \hline \multirow{8}{*}{**C**} & Depth GAN [40] & 0.421 & 0.422 & 0.778 & 0.696 & 0.494 & 0.252 & 0.285 & 0.362 & 0.402 & 0.631 & 0.474 \\  & Depth AE [40] & 0.432 & 0.158 & 0.808 & 0.491 & 0.841 & 0.406 & 0.262 & 0.216 & 0.716 & 0.478 & 0.481 \\  & Depth VM [40] & 0.388 & 0.321 & 0.194 & 0.570 & 0.408 & 0.282 & 0.244 & 0.349 & 0.268 & 0.331 & 0.335 \\  & Voxel GAN [40] & 0.664 & 0.620 & 0.766 & 0.740 & 0.783 & 0.332 & 0.582 & 0.790 & 0.633 & 0.483 & 0.639 \\  & Voxel AE [40] & 0.467 & 0.750 & 0.808 & 0.550 & 0.765 & 0.473 & 0.721 & 0.918 & 0.019 & 0.170 & 0.564 \\  & Voxel VM [40] & 0.510 & 0.331 & 0.413 & 0.715 & 0.680 & 0.279 & 0.300 & 0.507 & 0.611 & 0.366 & 0.471 \\  & M3 DM * & 0.966 & 0.971 & 0.978 & 0.949 & 0.941 & **0.92** & 0.977 & 0.967 & **0.971** & 0.973 & 0.961 \\  & BTF [43] & 0.976 & 0.967 & 0.979 & 0.974 & 0.971 & 0.884 & 0.976 & 0.981 & 0.959 & 0.971 & 0.964 \\  & **BTM** & **0.979** & **0.972** & **0.980** & **0.976** & **0.977** & 0.905 & **0.978** & **0.982** & 0.968 & **0.975** & **0.969** \\ \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 2: **AUPRO** score for anomaly detection of all categories of MVTec-3D AD.