Automatic symmetry determination and normalization for rotationally symmetric 2D shapes and 3D solid objects

摘要

Determination of the rotational symmetry of a shape is useful for object recognition and shape analysis in computer vision application. However, the usual normalization methods are inapplicable when the shape is N-fold rotationally-symmetric (N > = 3). In this paper, an efficient and reliable new method using modified Fourier transform is introduced to normalize such a 2D rotationally-symmetric shape. Furthermore, we extend this new method to the normalization of a N-fold axial rotationally-symmetric 3D object. There are two obvious advantages when using this new method: (1) it prevents the high computation load and the difficulty in normalizing the shape's orientation which occurred in the old methods using full matching or correlation functions; and (2) the weakness introduced by the old methods using data reduction (from 2D data to 1D data) is remedied. Experiments will show the validity of our method.