3-D Object matching using phase correlation method

In this paper, we propose a novel method of calculating the degree of similarity between 3-D objects considering translation and rotation along x, y, and z axes using the phase correlation method. The phase correlation method has been used to estimate the translation and rotation between similar images on the 2-D plane. We extend the phase correlation method to estimate the rotations along three axes and the translation in 3-D space. Because a 3-D object is often represented by a polygon mesh, we consider a 3-D object represented by the polygon mesh, and transform the polygon mesh to the surface function. Then the surface function is transformed by 3-D Fourier transform, and its amplitudes are represented in a cylindrical coordinate. By applying the phase correlation method to the amplitudes for two 3-D objects, the rotations between objects along the height axis of the cylindrical coordinate is obtained. The rotations remaining along two axes perpendicular to it are obtained by changing the height axis of the cylindrical coordinate to its orthogonal one. The translation of a 3-D object is estimated by applying the phase correlation method to the 3-D objects which were corrected by estimated rotations. The experimental results show that the proposed method performs 3-D object matching more accurately than the object matching scheme using range image matching.