📦 3D Metrics

Chamfer Distance §

Chamfer distance measures the distance between two point clouds as the squared distance between nearest-neighbor point correspondences. Formally,

Hausdorff Distance §

Hausdorff distance measures the distance between two sets (point clouds) as the maximum distance we need to travel from one set to another,

Unidirectional Hausdorff Distance (UHD) §

In 3D shape completion, it’s useful to measure the “faithfulness” of the outputted complete shape with a partial input point cloud. In this case, we only want to measure the Hausdorff distance in one direction—from partial to completed shape—which gives us UHD on input and output ,

Total Mutual Difference (TMD) §

TMD measures the measures diversity across multiple 3D shapes. This is commonly used in shape generation and is defined for shapes as

the sum of average Chamfer distances from each of the shapes.