Determining the Geometry of Boundaries of Objects from Medial Data

摘要

We consider a region Ω in R2 or R3 with generic smooth boundary B and Blum medial axis M, on which is defined a multivalued “radial vector field” U from points x on M to the points of tangency of the sphere at x with B. We introduce a “radial shape operator” Srad and an “edge shape operator” S E which measure how U bends along M. These are not traditional differential geometric shape operators, nonetheless we derive all local differential geometric invariants of B from these operators.