How to compute HD95 (95th-percentile Hausdorff distance) in Python¶

HD95 is the 95th percentile of the symmetric surface distances between a predicted and a ground-truth segmentation. It is preferred over the maximum Hausdorff distance (HD) because it is far less sensitive to a single outlier voxel, which is why Metrics Reloaded recommends it for most segmentation tasks.

With segauge:

import segauge as sg

metrics = sg.surface_metrics(pred_mask, gt_mask, spacing=(1.0, 1.0, 3.0))
print(metrics["hd95"])   # 95th-percentile Hausdorff distance, in mm
print(metrics["hd"])     # maximum Hausdorff distance
print(metrics["assd"])   # average symmetric surface distance

pred_mask and gt_mask are boolean (or 0/1) 3D NumPy arrays. spacing is the physical voxel size in the same axis order as the arrays; it matters, because HD95 is a physical distance.

Why segauge's HD95 is different¶

Most libraries compute Hausdorff distance on the voxel grid: they take the surface voxels and measure distances between voxel centres. That bakes in discretization error, which is largest for thick-slice (anisotropic) data.

segauge extracts the object surface with marching cubes at the true voxel spacing and measures distances over that surface, following the MeshMetrics method. In benchmarking on data with a known answer, this reduces HD95 error under anisotropic spacing.

From files (NIfTI / DICOM-SEG)¶

import segauge as sg

result = sg.evaluate([sg.Case("p1", pred="pred.nii.gz", gt="gt.nii.gz")])
print(result.summary()["hd95"])   # HD95 with a bootstrap confidence interval

Confidence intervals¶

When you evaluate more than one case, every metric (including HD95) comes back with a bootstrap confidence interval, so you can report HD95 honestly.