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Chu-Yin Chang's PhD Thesis Abstract

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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%.