On Modelling Nonlinear Variation

in Discrete Appearances of ObjectsUppsala Dissertations from the Faculty

of Science & Technology No. 54

By Felix Wehrmann

August 2004

Uppsala University Press

ISBN: 915545951X

140 pages, Illustrated, 6 ½" x 9 ½"

$44.00 Paper Original

This is a Ph.D. dissertation. Mathematical models of classes of objects can significantly contribute to the analysis of digital images. A major problem in modeling is to establish suitable descriptions that cover not only a single object but also the variation that is usually present within a class of objects. The objective of this thesis is to develop more general modeling strategies than commonly used today.

In particular, the impact of the human factor in the model creation process should be minimized. It is presumed that the human ability of abstraction imposes undesired constraints on the description. In comparison, common approaches are discussed from the viewpoint of generality. The technique considered introduces appearance space as a common framework to represent both shapes and images. In appearance space, an object is represented by a single point in a high-dimensional vector space. Accordingly, objects subject to variation appear as nonlinear manifolds in appearance space.

These manifolds are often characterized by only a few intrinsic dimensions. A model of a class of objects is therefore considered equal to the mathematical description of this manifold. The presence of nonlinearity motivates the use of artificial auto-associative neural networks in the modeling process. The network extracts nonlinear modes of variation from a number of training examples. The procedure is evaluated on both synthetic and natural data of shapes and images and shows promising results as a general approach to object modeling.

Digital Imaging; Statistics

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