MATLAB Implementation of Hausdorff Distance Calculation

The Hausdorff distance is a mathematical method used to measure similarity between two point sets, with extensive applications in computer vision and image processing. This distance metric is particularly suitable for comparing shape or contour similarities, such as in medical image analysis and object recognition scenarios. The core implementation approach in MATLAB involves: first calculating the shortest distance from each point in set A to set B, then taking the maximum of these distances. Specifically, the algorithm can be divided into two main steps: For each point in set A, compute the minimum distance to all points in set B, and record the maximum value among these minimum distances. Repeat the same operation for each point in set B, recording the maximum value similarly. The final Hausdorff distance is the larger of these two maximum values. This asymmetric property enables Hausdorff distance to capture the "most dissimilar" portions between two point sets. In MATLAB implementation, efficient computation can be achieved using matrix operations and the built-in `pdist2` function for pairwise distance calculations. Through vectorization techniques, explicit loops can be avoided, significantly improving computational performance. For implementation, the code typically involves: - Using `pdist2(A,B)` to compute all pairwise distances between sets A and B - Applying `min` function along the appropriate dimension to find minimum distances - Taking `max` of the resulting distance vectors - Comparing the two directional distances using `max` to obtain the final Hausdorff distance For large-scale point sets, performance optimization can be achieved through approximate algorithms or spatial partitioning data structures like KD-trees. The MATLAB implementation can leverage `KDTreeSearcher` for efficient nearest-neighbor searches when dealing with high-dimensional data. Hausdorff distance demonstrates sensitivity to noise and outliers, which may require combining with smoothing techniques or robust improvement methods in practical applications. This characteristic also makes it advantageous over other distance metrics (like Euclidean distance) in certain scenarios, particularly when measuring shape similarity under partial matching conditions. The implementation should consider adding optional preprocessing steps like outlier removal or distance thresholding for improved robustness.