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%.