Local Symmetries of Shapes in Arbitrary Dimension

In [TSP], level curves of a function , called “the edge strength function,” defined for 2–dimensional shapes, are interpreted as successively smoother versions of the initial shape boundary. The local minima of the absolute gradient along the level curves of are shown to be a robust criterion for determining the shape skeleton. More generally, at an extremal point of along a level curve, the level curve is locally symmetric with respect to the gradient vector . That is, at such a point, the level curve is approximately a conic section whose one of the principal axes coincides with the gradient vector. Thus, the locus of the extremal points of along the level curves determines the axes of local symmetries of the shape. In this paper, we extend this method to shapes of arbitrary dimension and illustrate it by applying to 3D shapes.