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

-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. Shape normalization Moment Rotational symmetry Principal axis Fourier transform