Title page for ETD etd-07082004-104919


Type of Document Master's Thesis
Author Hossain, Imtiaz
Author's Email Address imtiaz@math.lsu.edu
URN etd-07082004-104919
Title Query by Image Content Using Wavelets and Gibbs-Markov Random Fields
Degree Master of Science (M.S.)
Department Mathematics
Advisory Committee
Advisor Name Title
Gestur Olafsson Committee Chair
George Cochran Committee Member
Vibhas Aravamuthan Committee Member
Keywords
  • multiresolution
  • wavelet
  • texture
  • markov random field
  • gibbs distribution
Date of Defense 2003-12-05
Availability unrestricted
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.

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