Graduate Exam Abstract
August 18, 2008, 1:00
Pose Estimation of Spherically Correlated Images Using Eigendecomposition in Conjunction with Spectral Theory
Abstract: Determining the pose of three-dimensional objects from two-dimensional images has become an important issue in many computer vision, robotics, and industrial automation applications. Eigendecomposition represent one computationally efficient approach for dealing with object detection and pose estimation, as well as other vision-based problems and has been applied to sets of correlated images for this purpose. The major drawback in using eigendecomposition is the off-line computational expense incurred by computing the desired subspace. This off-line expense increases drastically as the number of correlated images becomes large (which is the case when doing fully general 3-D pose estimation). Previous work has shown that for data correlated on $S^1$, Fourier analysis can help reduce the computational burden of this off-line expense. This report presents a method for extending this technique to data correlated on $S^2$ as well as $SO(3)$ by sampling the sphere appropriately. An algorithm is then developed for reducing the off-line computational burden associated with computing the eigenspace by exploiting the spectral information of this spherical data set using spherical harmonics and Wigner-$D$ functions. Experimental results are presented to compare the proposed algorithm to the true eigendecomposition, as well as assess the computational savings.
Adviser: Anthony A. Maciejewski
Non-ECE Member: Chris Peterson, Mathematics
Member 3: Edwin K. Chong, ECE
Addional Members: Rodney G. Roberts, ECE Florida A&M - Florida Tech.
Program of Study: