The out-of-roundness measurement of a circular profile undertakes different schemes depending on the type of center specified. The most common standard recommended by the American National Standards Institute (ANSI) is the minimum radial separation center. In this paper, we introduce another standard, called the minimum area difference center. Although the two centers are different in characteristics, the approach to finding both centers shares many commonalities. We present an O(n log n + k) time algorithm to compute the minimum radial separation center, and the minimum area difference center of a simple polygon G, where n is the number of vertices of G, and k is the number of intersection points of the medial axis (or the nearest neighbor Voronoi polygons of all skeleton region elements) and the farthest neighbor Voronoi diagram of G.
