Comparing LAS Files: A Chamfer Distance Approach

LAS (LIDAR data exchange format) files have become indispensable tools in solving real-world problems, particularly in fields like geology, forestry, urban planning, and autonomous vehicles. They contain precise 3D spatial data captured by LIDAR (Light Detection and Ranging) sensors, making them valuable for various applications. In this article, we’ll explore a method to compare LAS files and determine their similarity using the Chamfer distance computation.

What is a LAS file?

Before we dive into the comparison methods, let’s briefly understand what LAS files are and why they matter in real-world scenarios. LAS files are repositories of point cloud data, where each point represents a precise 3D coordinate in space. These files find applications in creating digital elevation models, mapping terrains, and monitoring environmental changes over time. Comparing LAS files enables us to detect alterations in landscapes, track construction progress, or identify anomalies for safety and security.

Chamfer vs. Hausdorff Distance Metrics

When comparing LAS files, two popular distance metrics are Chamfer distance and Hausdorff distance. Both metrics measure the similarity between two point clouds but with different approaches.

Hausdorff Distance:

Pros:

1. It considers the maximum distance between the closest points of two point clouds.
2. Robust against outliers.

Cons:

1. Sensitive to the presence of outliers, making it less suitable for noisy data.
2. Computationally expensive.

Chamfer Distance:

Pros:

1. More robust to outliers compared to Hausdorff distance. Computationally efficient.
2. Easier to implement.

Cons:

1. May underestimate distances in cases where points are sparse.

Using Chamfer Distance for Comparison

To compute the similarity score between two LAS files using Chamfer distance, follow these steps:

Step 1: Install Necessary Libraries

pip install pykdtree laspy numpy scipy

Step 2: Define the Chamfer Distance Function

from pykdtree.kdtree import KDTree
from scipy.spatial.distance import cdist

import laspy
import numpy as np


def chamfer_distance_with_kdtree(las_file_path1, las_file_path2):
    """
    Compute the Chamfer distance between two LAS files using KD-Tree.

    Args:
        las_file_path1 (str): File path to the LAS file 1.
        las_file_path1 (str): File path to the LAS file 2.

    Returns:
        float: Chamfer distance between the two point clouds.
    """
    # Load the LAS file using laspy
    las_file1 = laspy.read(las_file_path1)
    las_file2 = laspy.read(las_file_path2)

    # Extract XYZ coordinates from the PLY file
    xyz1 = np.vstack((las_file1.x, las_file1.y, las_file1.z)).T
    xyz2 = np.vstack((las_file2.x, las_file2.y, las_file2.z)).T

    # Build KD-Tree for point_cloud2
    tree2 = KDTree(xyz2)

    # Calculate distances from each point in point_cloud1 to the nearest point in point_cloud2
    min_distances1, _ = tree2.query(xyz1)

    # Build KD-Tree for point_cloud1
    tree1 = KDTree(xyz1)

    # Calculate distances from each point in point_cloud2 to the nearest point in point_cloud1
    min_distances2, _ = tree1.query(xyz2)

    # Compute the Chamfer distance
    chamfer_dist = np.sum(min_distances1) + np.sum(min_distances2)

    return chamfer_dist

Step 3: Visualize LAS Files

# Create a figure for visualization
fig = plt.figure()
ax = fig.add_subplot(111, projection='3d')

# Plot the first point cloud in blue
ax.scatter(xyz1[:, 0], xyz1[:, 1], xyz1[:, 2], c='blue', label='LAS File 1')

# Plot the second point cloud in red
ax.scatter(xyz2[:, 0], xyz2[:, 1], xyz2[:, 2], c='red', label='LAS File 2')

# Visualize the correspondence between points using lines
for i in range(len(xyz1)):
    closest_point_idx = np.argmin(cdist(xyz1[i].reshape(1, -1), xyz2))
    closest_point = xyz2[closest_point_idx]
    ax.plot([xyz1[i, 0], closest_point[0]], 
            [xyz1[i, 1], closest_point[1]], 
            [xyz1[i, 2], closest_point[2]], 
            c='green', linestyle='--')

# Set labels and legend
ax.set_xlabel('X')
ax.set_ylabel('Y')
ax.set_zlabel('Z')
ax.legend()

# Show the 3D plot
plt.show()

This code snippet will generate a 3D scatter plot of the two LAS files, allowing you to explore and analyze the point cloud data visually.

Conclusion

Comparing LAS files is crucial for various applications, and the choice of distance metric matters. While both Chamfer and Hausdorff distances have their pros and cons, Chamfer distance often outperforms Hausdorff distance, especially when dealing with noisy or sparse point clouds. Implementing Chamfer distance is relatively straightforward, and visualizing the results in 3D can aid in understanding the differences between LAS files effectively. Whether you’re monitoring environmental changes or ensuring the accuracy of autonomous vehicle sensors, understanding and utilizing these techniques can be invaluable in your work.

References

[1]: Huffman, Landis, Josh Finken, Amey Aroskar, and Sumedh Rasal. “Point cloud creation.” U.S. Patent Application 17/074,452, filed April 21, 2022.