Algorithm 1 LA-EAD inference process

Input: input image I, EfficientAD model $EAD$, proposed extractor E, precomputed covariance matrix $\mathsf{\Sigma }$, precomputed feature vector $f_m$, precomputed normalization parameters ${\mu }_p$, ${\sigma }_p$, ${\mu }_u$ and ${\sigma }_u$

Output: final anomaly score $s_{\mathrm{final}}$

1:Extract features from the proposed extractor E   2:Get output feature of the proposed extractor for I:   3:    $f_{c,w,h}=E\left(I\right)$   4:Compute global average pooled feature vector:   5:    $f_{test}={\left(HW\right)}^{-1}{\sum }_{h=1}^H{\sum }_{w=1}^W{f}_{c,w,h}(\mathrm{as}\mathrm{Equation}\left(4\right))$   6:Calculate anomaly score $s_u$ of the logical anomaly detection module:   7:Compute Mahalanobis distance using precomputed $f_m$ and $f_{test}$:   8:    $s_u=\sqrt{{(f_{test}-f_m)}^T{\mathsf{\Sigma }}^{-1}(f_{test}-f_m)}(\mathrm{as}\mathrm{Equation}\left(8\right))$   9:Get anomaly score $s_p$ from EfficientAD 10:Feed the image I into EfficientAD for the inference process and obtain the anomaly score: 11:    $s_p=EAD\left(I\right)$ 12:Normalize and fuse scores 13:Perform separate normalization on the $s_p$ and $s_u$, with the normalization parameters (mean and variance) calculated from the inference results of the validation subset. (following PUAD [24]) 14:    $s_p^{\mathrm{norm}}={\displaystyle \frac{s_p-{\mu }_p}{{\sigma }_p}},s_u^{\mathrm{norm}}={\displaystyle \frac{s_u-{\mu }_u}{{\sigma }_u}}$ 15:Compute final anomaly score: 16:    $s_{\mathrm{final}}=s_p^{\mathrm{norm}}+s_u^{\mathrm{norm}}$ 17:return $s_{\mathrm{final}}$