The Hausdorff Distance is a measure used in mathematics to determine how far two subsets of a metric space are from each other. It quantifies the greatest distance from a point in one set to the closest point in the other set. This distance helps in comparing shapes, patterns, or point clouds in various fields, including computer vision and shape analysis. To calculate the Hausdorff Distance, one typically uses the maximum of two values: the distance from each point in one set to the nearest point in the other set. This concept is named after the mathematician Felix Hausdorff, who contributed significantly to topology and set theory.