Optimal circular fit to objects in two and three dimensions

This paper deals with the problem of optimal circular fit to simply connected objects in two and three dimensions. In two dimensions, the centroid of the object is chosen as the center of the fitting circle while the radius is chosen so that its area is equal to the area of the object. Similarly, in three dimensions, the centroid of the object surface is chosen as the center of the fitting sphere while its radius is chosen so that the surface area of the object is equal to that of the sphere. It is proved that these choices optimize a modified sum of squares objective function.