Distance Metric on Multidimensional Spatial Objects

A distance metric for spatially extended objects provides a formal basis for analytical work in transformation-based multidimensional spatial access methods, including locality preservation of the underlying transformation, statistical analyses of the transformation-effect on spatial parameters and distribution, and distance-based spatial queries. We study the Hausdorff distance metric on the space of closed and bounded subsets in a multidimensional Euclidean space, and its restriction to convexity results in an explicit formulation in computation based on their boundary subsets.