Browsing by Author "Wohlberg, Brendt"

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    Designing hypothesis tests for digital image matching
    (2000) Cox, Gregory Sean; Wohlberg, Brendt; Nicolls, Fred; De Jager, Gerhard
    Image matching in its simplest form is a two class decision problem. Based on the evidence in two sensed images, a matching procedure must decide whether they represent two views of the same scene, or views of two different scens. Previous solutions to this problem were either based on an intuitive notion of image similarity, or were modelled on solutions to the superficially similar problem of target detection in images. This research, in contrast, uses a decision theoretic formulation of the problem, with the image pair as unit of observation and probability of error in the match/mismatch decision as performance criterion. A stochastic model is proposed for the image pair, and the optimal test of match and mismatch hypotheses for samples of this random process is derived. The test is written conveniently in terms of a statistic of the two images and a scalar decision threshold. The analytical advantages of a solution derived from first principles are illustrated with the derivation of hypothesis conditional probability distributions, optimal decision thresholds, and expessions for the probability of error in the decision.
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    Fractal image compression and the self-affinity assumption : a stochastic signal modelling perspective
    (1996) Wohlberg, Brendt; De Jager, Gerhard
    Fractal image compression is a comparatively new technique which has gained considerable attention in the popular technical press, and more recently in the research literature. The most significant advantages claimed are high reconstruction quality at low coding rates, rapid decoding, and "resolution independence" in the sense that an encoded image may be decoded at a higher resolution than the original. While many of the claims published in the popular technical press are clearly extravagant, it appears from the rapidly growing body of published research that fractal image compression is capable of performance comparable with that of other techniques enjoying the benefit of a considerably more robust theoretical foundation. . So called because of the similarities between the form of image representation and a mechanism widely used in generating deterministic fractal images, fractal compression represents an image by the parameters of a set of affine transforms on image blocks under which the image is approximately invariant. Although the conditions imposed on these transforms may be shown to be sufficient to guarantee that an approximation of the original image can be reconstructed, there is no obvious theoretical reason to expect this to represent an efficient representation for image coding purposes. The usual analogy with vector quantisation, in which each image is considered to be represented in terms of code vectors extracted from the image itself is instructive, but transforms the fundamental problem into one of understanding why this construction results in an efficient codebook. The signal property required for such a codebook to be effective, termed "self-affinity", is poorly understood. A stochastic signal model based examination of this property is the primary contribution of this dissertation. The most significant findings (subject to some important restrictions} are that "self-affinity" is not a natural consequence of common statistical assumptions but requires particular conditions which are inadequately characterised by second order statistics, and that "natural" images are only marginally "self-affine", to the extent that fractal image compression is effective, but not more so than comparable standard vector quantisation techniques.