Minimum perimeter convex hull of imprecise points in convex regions

Abstract

Imprecise points are points in R2 whose exact location is unknown. For each point, we only know it is contained in a region of R2, which is called the uncertainty region of the point. The research we present in this video focuses on the problem of finding the minimum perimeter convex hull of a set of imprecise points, where each uncertainty region is closed, convex, and the regions may intersect. We first present and animate our theoretical findings: as each point moves inside its uncertainty region, the perimeter of the resulting convex hull is a convex function on the position of the points; as a consequence, any local minimum of the perimeter is a global minimum. We then show the possible positions of imprecise points inside their uncertainty region. Finally, we demonstrate an algorithm for finding the minimum perimeter convex hull of a set of imprecise points.