hausdorff

The hausdorff command is used to compute the Hausdorff distance between two point clouds. In this context, the Hausdorff distance is the greatest of all Euclidean distances from a point in one point cloud to the closest point in the other point cloud.

More formally, for two non-empty subsets \(X\) and \(Y\), the Hausdorff distance \(d_H(X,Y)\) is

\[d_H(X,Y) = \operatorname*{max} \big\{ \operatorname*{sup}_{x \in X} \operatorname*{inf}_{y \in Y} d(x,y), \operatorname*{sup}_{y \in Y} \operatorname*{inf}_{x \in X} d(x,y)\big\}\]

where \(\operatorname*{sup}\) and \(\operatorname*{inf}\) are the supremum and infimum respectively.

$ pdal hausdorff <source> <candidate>

--source arg     Source filename
--candidate arg  Candidate filename

The algorithm makes no distinction between source and candidate files (i.e., they can be transposed with no affect on the computed distance).

The command returns 0 along with a JSON-formatted message summarizing the PDAL version, source and candidate filenames, and the Hausdorff distance. Identical point clouds will return a Hausdorff distance of 0.

$ pdal hausdorff source.las candidate.las
{
  "filenames":
  [
    "\/path\/to\/source.las",
    "\/path\/to\/candidate.las"
  ],
  "hausdorff": 1.303648726,
  "pdal_version": "1.3.0 (git-version: 191301)"
}

Note

The hausdorff is computed for XYZ coordinates only and as such says nothing about differences in other dimensions or metadata.