Identifier

etd-07082004-104919

Degree

Master of Science (MS)

Department

Mathematics

Document Type

Thesis

Abstract

The central theme of this thesis is the application of Wavelets and Random Processes to content-based image query (on texture patterns, in particular). Given a query image, a content-based search extracts a certain representative measure (or signature) from the query image and likewise for all the target images in the search archive. A good representative measure is one that provides us with the ability to differentiate easily between different patterns. A distance measure is computed between the query properties and the properties of each of the target images. The lowest distance measure gives us the best target match for the particular query. Typically, the measure extraction on the target archive is performed as a pre-processing step. The thesis features two different methods of measure extraction. The first one is a wavelet based measure extraction method. It builds upon a previously documented method, but adds subtle modifications to it so that it now lends much much more effectiveness to pattern matching on texture patterns and on images of unequal sizes. The modified algorithm as well as the mathematics behind it is presented. The second method uses a Markov Random Field to model the texture properties of regions within an image. The parameters of the model serve as the texture measure or signature. Wavelet-based multiresolution is then used to speed up the search. The theory of Markov Random Fields, their equivalence with Gibbs Random Fields, the Hammerseley-Clifford theorem and parameter estimation techniques are presented. In addition to pattern matching these texture signatures have also be used for controlled image smoothing and texture generation. The results from both methods are encouraging. One hopes that these methods find widespread use in image query applications.

Date

2004

Document Availability at the Time of Submission

Release the entire work immediately for access worldwide.

Committee Chair

Gestur Olafsson

DOI

10.31390/gradschool_theses.655

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