chamfer

Warning

As of PDAL v2.6.0, the chamfer command is marked as DEPRECATED. It will be removed from the default install in PDAL v2.7 and removed completely in PDAL v2.8.

The following Python code can be used with the PDAL Python bindings to compute the chamfer distance.

import pdal
import numpy as np

def chamfer_distance(arr1, arr2):
    distance_1_to_2 = 0
    distance_2_to_1 = 0

    points1 = np.column_stack((arr1['X'], arr1['Y'], arr1['Z']))
    points2 = np.column_stack((arr2['X'], arr2['Y'], arr2['Z']))

    # Compute distance from each point in arr1 to arr2
    for p1 in points1:
        distances = np.sqrt(np.sum((points2 - p1)**2, axis=1))
        min_distance = np.min(distances)
        distance_1_to_2 += min_distance

    # Compute distance from each point in arr2 to arr1
    for p2 in points2:
        distances = np.sqrt(np.sum((points1 - p2)**2, axis=1))
        min_distance = np.min(distances)
        distance_2_to_1 += min_distance

    return (distance_1_to_2 + distance_2_to_1) / (len(arr1) + len(arr2))

pipeline1 = pdal.Reader("/path/to/input1.laz").pipeline()
pipeline1.execute()
arr1 = pipeline1.array[0]

pipeline2 = pdal.Reader("/path/to/input2.laz").pipeline()
pipeline2.execute()
arr2 = pipeline2.array[0]

# Compute Chamfer distance
result = chamfer_distance(arr1, arr2)
print("Chamfer Distance:", result)

Popular Python packages such as scipy and sklearn have functions to compute the pairwise distance between points and can be used to simplify the above somewhat.

Note that the provided code does not match exactly the output of PDAL’s original implementation, which summed the square of the distance to the nearest neighbor. We have elected not to update the PDAL implementation at this time.

The chamfer command is used to compute the Chamfer distance between two point clouds. The Chamfer distance is computed by summing the squared distances between nearest neighbor correspondences of two point clouds.

More formally, for two non-empty subsets \(X\) and \(Y\), the Chamfer distance \(d_{CD}(X,Y)\) is

\[ d_{CD}(X,Y) = \sum_{x \in X} \operatorname*{min}_{y \in Y} ||x-y||^2_2 + \sum_{y \in Y} \operatorname*{min}_{x \in X} ||x-y||^2_2 \]

$ pdal chamfer <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 Chamfer distance. Identical point clouds will return a Chamfer distance of 0.

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

Note

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