Clippingdale, Simon (1988) Multiresolution image modelling and estimation. PhD thesis, University of Warwick.

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Abstract

Multiresolution representations make explicit the notion of scale in images, and facilitate the combination of information from different scales. To date, however, image modelling and estimation schemes have not exploited such representations and tend rather to be derived from two- dimensional extensions of traditional one-dimensional signal processing techniques. In the causal case, autoregressive (AR) and ARMA models lead to minimum mean square error (MMSE) estimators which are two-dimensional variants of the well-established Kalman filter. Noncausal approaches tend to be transform-based and the MMSE estimator is the two- dimensional Wiener filter. However, images contain profound nonstationarities such as edges, which are beyond the descriptive capacity of such signal models, and defects such as blurring (and streaking in the causal case) are apparent in the results obtained by the associated estimators.

This thesis introduces a new multiresolution image model, defined on the quadtree data structure. The model is a one-dimensional, first-order gaussian martingale process causal in the scale dimension. The generated image, however, is noncausal and exhibits correlations at all scales unlike those generated by traditional models. The model is capable of nonstationary behaviour in all three dimensions (two position and one scale) and behaves isomorphically but independently at each scale, in keeping with the notion of scale invariance in natural images.

The optimal (MMSE) estimator is derived for the case of corruption by additive white gaussian noise (AWGN). The estimator is a one-dimensional, first-order linear recursive filter with a computational burden far lower than that of traditional estimators. However, the simple quadtree data structure leads to aliasing and 'block' artifacts in the estimated images. This could be overcome by spatial filtering, but a faster method is introduced which requires no additional multiplications but involves the insertion of some extra nodes into the quadtree. Nonstationarity is introduced by a fast, scale-invariant activity detector defined on the quadtree. Activity at all scales is combined in order to achieve noise rejection. The estimator is modified at each scale and position by the detector output such that less smoothing is applied near edges and more in smooth regions. Results demonstrate performance superior to that of existing methods, and at drastically lower computational cost. The estimation scheme is further extended to include anisotropic processing, which has produced good results in image restoration. An orientation estimator controls anisotropic filtering, the output of which is made available to the image estimator.

Item Type:	Thesis (PhD)
Subjects:	Q Science > QA Mathematics > QA76 Electronic computers. Computer science. Computer software
Library of Congress Subject Headings (LCSH):	Image processing, Signal processing, Estimation theory, Stochastic processes
Official Date:	September 1988
Dates:	Date Event September 1988 Submitted
Institution:	University of Warwick
Theses Department:	Department of Computer Science
Thesis Type:	PhD
Publication Status:	Unpublished
Supervisor(s)/Advisor:	Wilson, Roland, 1949-
Format of File:	pdf
Extent:	234 leaves : illustrations, charts
Language:	eng

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