Detection of generalized principal axes in rotationally symmetric shapes

摘要

Automatic detection of the principal axes of given shapes with known symmetry properties is studied in this paper. The inapplicability of a well-known equation, which is used to compute the direction of the principal axis of a given shape using moment functions, to a class of so-called degenerate shapes is first pointed out. Rotationally symmetric shapes often encountered in real applications are shown to belong to this class. This problem is solved by extending the notion of principal axis to higher order ones in terms of higher order moment functions. Analytic equations for computing the direction of high-order principal axes are derived. They include the well-known equation for computing the direction of the (second-order) principal axis as a special case. Some experimental results are included finally to show the effectiveness of the derived analytic equations.