Hausdorff Distance

A spatial overlap metric measuring the similarity between two binary segmentation masks, ranging from 0 (no overlap) to 1 (perfect agreement). Unlike Hausdorff Distance, which captures worst-case boundary error, DSC is a global overlap measure that is insensitive to small, localized deviations. It is calculated as twice the intersection area divided by the sum of the areas. A DSC above 0.90 is generally considered excellent agreement in most anatomical segmentation tasks.

The mean of all Euclidean distances from each point on the predicted surface to the closest point on the ground truth surface, and vice versa. While Hausdorff Distance reports the maximum error, ASSD provides a more robust summary of overall boundary fit. It is less sensitive to outliers than Hausdorff Distance, making it a complementary metric for evaluating segmentation quality in the presence of minor annotation noise.

A robust variant of the standard Hausdorff Distance that uses the 95th percentile of surface distances instead of the absolute maximum. This metric is widely preferred in medical imaging challenges because it retains sensitivity to boundary errors while eliminating the influence of extreme outliers caused by annotation artifacts or insignificant spurious voxels. HD95 is the primary boundary metric in benchmarks such as the Medical Segmentation Decathlon.

A voxel-wise visualization that encodes the Euclidean distance from each point on one surface to the nearest point on another surface. This map provides spatially localized error information that summary metrics like Hausdorff Distance cannot convey. Clinicians and engineers use these maps to identify specific anatomical regions where a segmentation algorithm systematically underperforms, such as thin vessel walls or organ boundaries with low contrast.

Measures of the geometric fidelity of the polygonal surface extracted from a segmentation mask, including triangle aspect ratio, Jacobian determinant, and dihedral angle. Poor mesh quality can artificially inflate Hausdorff Distance measurements by introducing jagged surface artifacts. Preprocessing steps such as Laplacian smoothing or Taubin smoothing are often applied to segmentation masks before computing surface distance metrics to ensure the mesh accurately represents the underlying anatomical boundary.

A metric that measures the local perpendicular distance between corresponding points on two surfaces, often computed using correspondence matching algorithms. Unlike Hausdorff Distance, which is a global extremum, boundary displacement error provides a distribution of local errors. This is particularly useful for evaluating deformable registration algorithms and for identifying systematic biases in segmentation models, such as consistent over-segmentation of convex anatomical structures.