Chu-Yin Chang's PhD Thesis Abstract

Eigenspace Methods for Correlated Images

Ph.D., Purdue University, Dec. 1999

Major Professor: Anthony A. Maciejewski

A fundamental problem in computer vision is the recognition and localization of three­dimensional objects from two­dimensional images. ``Eigenspace methods'' represent one promising approach to this problem. However, the off­line computation required to perform the eigendecomposition of correlated images for this approach is generally expensive. In addition, the on­line performance of eigenspace methods degrades in the presence of occlusion and background noise in an image.

In the first part of this work, a computationally efficient algorithm for the eigenspace decomposition of correlated images is presented. This approach is motivated by the fact that for a set of planar rotated images, analytical expressions can be given for the eigendecomposition, based on the theory of circulant matrices. These analytical expressions turn out to be good first approximations of the eigendecomposition, even for three­dimensional objects performing smooth motions. This observation was used to automatically determine the dimension of the subspace required to represent an image with a guaranteed user­specified accuracy, as well as to quickly compute a basis for the subspace. Examples show that the algorithm performs very well on a number of test cases ranging from images of three­dimensional objects rotated about a single axis to arbitrary video sequences.

The second part of this work presents a solution to the pose detection problem, based on eigenspace methods, for cases where occlusion and background noise are present in an image. The proposed algorithm is based purely on the appearance of the objects and requires no feature detection. The computational requirements of the algorithm are a function of the difficulty of the problem, i.e., less computation time is required for images with less occlusion. Test results show that the algorithm performs reasonably efficiently and accurately for occlusions of up to 50%.