## 2 Methods
### Evaluation
#### 2.4.2 Local Evaluation of Ventricle Segmentation  
This study aimed to assess the variation in anatomical differences, or segmentation errors, between the automatic segmentations and the manually delineated GT. To evaluate the variation in segmentation errors across this population, it is necessary to align all ventricle contours to a common reference orientation. A standardized ventricle OAR reference shape was used following the method proposed by [PERSON] et al. [PERSON] et al. (2019). For this purpose, a ventricle delineation with a volume close to the median volume over all patients was visually inspected on anatomical accuracy and consequently selected as the reference shape.  
The DL-based segmentations from both the nnU-Net and the SynthSeg models, as well as the manual GT contours, were converted into 3D discrete surface mesh models for each patient using the software AIQUALIS (Inpictura Ltd., Abingdon, England). These surface meshes were then registered to the reference ventricle surface mesh using a deformable shape-to-shape registration using an iterative closest point (ICP) algorithm [PERSON] et al. (2019). First, a rigid ICP was used to achieve a rough initial alignment to the reference shape, followed by a non-rigid registration to fine-tune the alignment and account for the anatomical differences across the population.  
The median and range (10 th-90 th percentiles) of the segmentation error of each vertex point of the 3D surface meshes were calculated over all patients within the test sets. Percentiles were used to be more robust to outliers within the distribution of segmentation errors for each vertex points. The conversion to 3D surface meshes, registration, and visualization of errors were all done using the software AIQUALIS (Inpictura Ltd., Abingdon, England). A low median segmentation error and low range suggest a general  
Figure 1: Illustration of the metrics used to evaluate the segmentations in this study, adapted from [PERSON] et al. (2019); [PERSON] et al. (2019). The solid line represents the manual ground truth segmentations (GT), while the dashed line depicts the automated segmentations (**A**). (**A**) shows the volumetric DSC, calculated as twice the overlap between two volumes (2 \(\times\) V\({}_{\text{overlap}}\)) divided by the sum of their volumes (V\({}_{\text{GT}}\) + V\({}_{\text{A}}\)). (**B**) illustrates the Hausdorff distance, defined as the maximum bidirectional nearest neighbor distance (orangearrows) between points on the two boundaries (max of HD(GT,A) and HD(A,GT)). (**C**) presents the surface DSC. Black arrow: the maximum deviation tolerated without penalty, set at 1 mm. Green: accepted surface parts (distance between surfaces \(<\) 1 mm). Red: unacceptable surface parts (distance between surfaces \(>\) 1 mm). The surface DSC reports the accepted surface parts (the surface parts within a tolerance of the true boundary) compared to the total surface (sum of automatic contour surface area and GT surface area). (**D**) demonstrates the added path length (APL) Green dashed line: accepted segmentation (distance between segmentations \(<\) 1 mm). Red dashed line: added path length which represents the length of the boundary in millimeters that required manual adjustment.  
acceptance of the DL contours. A high median error and low range could be interpreted as a systematic error in the DL contour. A low median error and high range suggest that at that location, the segmentation model performed well in general but that there are cases in which the segmentation failed or that it is a region with high interobserver variability in the GT delineations.