Point Set Matching Algorithm Based on Hausdorff Distance with Code Implementation

The Hausdorff distance is a classical mathematical definition for measuring the distance between two point sets, originally introduced by mathematician Felix Hausdorff in 1914. This distance metric quantifies the maximum distance between two point sets by considering their mutual correspondence relationships while incorporating shape and geometric characteristics. Our algorithm leverages the Hausdorff distance to evaluate the similarity between point sets and outputs matching results through systematic point correspondence identification.

The implementation involves several key computational steps: first calculating pairwise distances between all points in both sets, then determining the maximum minimum distance between sets using vectorized operations for efficiency. The algorithm employs optimization techniques to handle edge cases and ensure robustness. Key functions include distance matrix computation, bidirectional Hausdorff distance calculation, and greedy point matching with threshold validation. By implementing this algorithm, users can rapidly and accurately match point sets with practical applications across multiple domains including computer vision, geographic information systems, and pattern recognition.

The code structure features modular design with separate functions for distance computation, maximum distance identification, and point pair matching. Algorithm efficiency is enhanced through precomputation of distance matrices and optimized search strategies for finding corresponding point pairs. The implementation includes error handling for irregular point distributions and provides configurable similarity thresholds for flexible matching criteria.