# 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

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.