# Normalizing Flows for Out-of-Distribution Detection: Application to Coronary Artery Segmentation
## 3 Results and Discussion  
### Evaluation on Synthetic Mask Perturbations  
First, we evaluated the baseline and the proposed networks trained on original (unperturbed) data. We applied the synthetic perturbations on the testset in increasing levels of severity and measured how well the models can distinguish between log-probs of original and log-probs of perturbed samples. At each perturbation level, we computed the area under the RoC curve. Figures 6-8 display the AUROC values for translation, zooming and morphing perturbations, respectively. We use AuRoC as a metric for assessing how well two individual data distributions can be separated by using a probability threshold. A value close to 1 indicates that there are probability thresholds which yield near 100% accuracy in detecting perturbations, while values close to 0.5 indicate that the probabilities of the two data distributions have high overlap and are therefore indistinguishable by simple thresholding. Hence, the closer the AuRoC values are to 1, the better is the performance of the method. Zoom level 1.0\(\times\) and translate level 0 do not have any effect on the test data, so naturally the AuRoC is 0.5 since it is comparing the same distribution against itself. Figure 4: Example of mask morphing perturbation in the left-to-right direction. Top row shows dilations (the mask is prolonged), bottom row shows erosions (the mask is shortened). Only the mask contour is shown. Figure 5: Example of mask translation perturbation in the topLeft-bottomRight direction. Only the mask contour is shown. Figure 3: Example of zoom perturbation on lumen mask. Only the mask contour is shown. It is observed that the proposed model has superior performance across all perturbation types and levels. Zooming under 1.0\(\times\) actually yields higher log-probs for the baseline model, resulting in AuRoC values under 0.5. Even at small mask perturbation levels (e.g., 0.9\(\times\)/1.1\(\times\) zooming, \(\pm\)2 pixels translation), the proposed model has much larger sensitivity in detecting the mask alterations (even though it was not trained explicitly to do so) in contrast to the baseline model, where the log-probs start to decrease more significantly only at larger perturbation levels. The mask morphing is the hardest to detect since part of the mask remains the same. Thus, the baseline model is largely insensitive to this type of perturbation as the maximum AuRoC at a high perturbation level of 60% is under 0.65. In comparison, the AuRoC for the proposed network has a much faster variation for increasing perturbation severity, achieving values over 0.9 for some directions at 60% morphing. Next, we evaluated the test-time sensitivity against synthetic perturbations after training using the augmented trainset and loss from Equation (3). We employed the following perturbation levels to generate OoD samples for training:  
* translation (in all 4 directions) of \(\pm\)3 or \(\pm\)4 pixels;
* zooming levels of 0.65\(\times\), 0.8\(\times\), 1.2\(\times\), and 1.35\(\times\);
* morphing (in all 4 directions, erosions/dilations) levels of 0.2 and 0.35 (ratio of initial mask size). Figure 8: AuRoC performance for the baseline and proposed architecture when tested against mask morphing in various directions. Training done only on original data. Figure 6: AuRoC performance for the baseline and proposed architecture when tested against mask translation in various directions. Training done only on original data. Figure 7: AuRoC performance for the baseline and proposed architecture when tested against mask zooming. Training done only on original data. Any OoD sample had only one type of perturbation applied to it. In addition, given the fact that each sample is a 3D volume consisting of 8 2D slices, the perturbation could be applied on each slice following some preset variation for its severity/level along the slice axis (see Figure 9 for the employed severity variation types).