Representing images of a rotating object with cyclic permutation for view-based pose estimation

In this paper, we propose a novel approach using a cyclic group to model the appearance change in an image sequence of an object rotated about an arbitrary axis (1DOF out-of-plane rotation). In the sequence, an image x_j is followed by an image x_j+1. We represent the relationship between images by a cyclic group as x_j+1=Gx_j, and obtain the matrix G by real block diagonalization. Then, G to the power of a real number is used to represent the image sequence and also for pose estimation. Two estimation methods are proposed and evaluated with real image sequences from the COIL-20, COIL-100, and ALOI datasets, and also compared to the Parametric Eigenspace method. Additionally, we discuss the relationship of the proposed approach to the pixel-wise Discrete Fourier Transform (DFT) and to linear regression, and also outline several extensions.