PhD, Colorado State University, August 2006
Major Professor: Anthony A. Maciejewski
Eigendecomposition-based techniques play an important role in numerous image processing and computer vision applications. The advantage of these techniques is that they are purely appearance based and require few online computations. All eigenspace methods take advantage of the fact that a set of highly correlated images can be approximately represented by a small set of eigenimages. However, the offline calculation required to determine both the appropriate number of eigenimages as well as the eigenimages themselves can be prohibitively expensive. This thesis considers two issues associated with the calculation of the eigendecomposition of correlated images, i.e., the effect of spatial resolution reduction and correlations associated with three-dimensional pose estimation.
The first part of this thesis addresses the issue of computing the eigendecomposition of one-dimensional correlated images. It is well known that the computation of an eigendecomposition can become prohibitively expensive when dealing with very high-resolution images. While reducing the resolution of the images will reduce the computational expense, it is not known a priori how this will affect the quality of the resulting eigendecomposition. This work provides an analysis of how different resolution reduction techniques affect the eigendecomposition. A computationally efficient algorithm for calculating the eigendecomposition based on this analysis is also presented. Examples show that this algorithm performs very well on images of objects rotated along a single axis and on arbitrary video sequences.
The second part of this thesis considers the computation of the eigendecomposition of general three-dimensional image sets that can be used in pattern recognition applications; specifically in the three-dimensional pose estimation of objects. Previous work has shown that the correlation associated with one-dimensional pose estimation can be used to accelerate the computation of the eigendecomposition. In this work, it is shown how this algorithm can be extended to take advantage of the correlations in three-dimensional pose estimation.