Pose estimation from a single image using tensor decomposition and an algebra of circulants

Abstract

Dimensionality reduction and object classification (recognition and pose estimation) serve as important tools in robotics, robotic vision, and industrial automation. The current paper presents a new approach to dimensionality reduction and object classification of three-dimensional rigid objects. The approach is based upon recent developments in tensor decompositions and a newly defined algebra of circulants. In particular, it is shown that under the right tensor multiplication operator, a third order tensor can be written as a product of third order tensors in which the left and right tensors are tensor-orthogonal and the inner-tensor is a diagonal tensor of singular-tuples. This new development allows for a proper tensor singular value decomposition (SVD) to be defined and has natural extension to tensor principal component analysis (PCA). Comparisons are made with traditional PCA and it is shown that the current approach is capable of recovering significantly more information from an image sequence using a much smaller subspace dimension. Further, it is shown that for most objects, accurate pose estimation can be performed from a single subspace dimension.

Fast Sparse PCA via Positive Semidefinite Projection for Unsupervised Feature Selection

“…In terms of performing linear projection, the current TPCA methods can be roughly divided into two types: 1) Tuckersbased TPCA [12], [26], [27]: TPCA based on the directionunfolding products defined by Tucker decomposition and its variation, and 2) T-SVDs-based TPCA [28]- [30]: TPCA based on the ⋆ M product defined by T-SVD and its generalization T-SVDM [31]. These two types of TPCA methods perform truncated SVD on different levels of a tensor to obtain factor matrices.…”