An Incremental Hausdorff Distance Calculation Algorithm

The Hausdorff distance is commonly used as a similarity measure between two point sets. Using this measure, a set X is considered similar to Y iff every point in X is close to at least one point in Y . Formally, the Hausdorff distance HAUSDIST(X, Y ) can be computed as the MAX-MIN distance from X to Y , i.e., find the maximum of the distance from an element in X to its nearest neighbor (NN) in Y . Although this is similar to the closest pair and farthest pair problems, computing the Hausdorff distance is a more challenging problem since its MAX-MIN nature involves both maximization and minimization rather than just one or the other. A traditional approach to computing HAUSDIST(X, Y ) performs a linear scan over X and utilizes an index to help compute the NN in Y for each x in X. We present a pair of basic solutions that avoid scanning X by applying the concept of aggregate NN search to searching for the element in X that yields the Hausdorff distance. In addition, we propose a novel ...

• Type: Journal
• Year: 2011
• Where: PVLDB
• Authors: Sarana Nutanong, Edwin H. Jacox, Hanan Samet
• Keywords: Applied Computing, Hausdorff Distance, Linear Scan, PVLDB 2011, Similarity Measure