Two- and Three-Dimensional Coding Schemes for Wavelet and Fractal-Wavelet Image Compression

[摘要] This thesis presents two novel coding schemes and applications to both two- and three-dimensional image compression.Image compression can be viewed as methods of functional approximation under a constraint on the amount of information allowable in specifying the approximation. Two methods of approximating functions are discussed:Iterated function systems (IFS) and wavelet-based approximations.IFS methods approximate a function by the fixed point of an iterated operator, using consequences of the Banach contraction mapping principle.Natural images under a wavelet basis have characteristic coefficient magnitude decays which may be used to aid approximation. The relationshipbetween quantization, modelling, and encoding in a compression scheme is examined.Context based adaptive arithmetic coding is described. This encoding method is used in the coding schemes developed.A coder with explicit separation of the modelling and encodingroles is presented: an embedded wavelet bitplane coder based on hierarchical context in the wavelet coefficient trees.Fractal (spatial IFSM) and fractal-wavelet (coefficient tree), or IFSW,coders are discussed.A second coder is proposed, merging the IFSW approaches with the embedded bitplane coder.Performance of the coders, and applications to two- and three-dimensional images are discussed. Applications include two-dimensional still images in greyscale and colour, and three-dimensional streams (video).

[发布机构] University of Waterloo

[效力级别] image compression

[关键词] Mathematics;image compression;wavelets;fractal;arithmetic coding;hierarchical context model