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A useful discrete distribution (the Conway-Maxwell-Poisson distribution) is revived and its statistical and probabilistic properties are introduced and explored. This distribution is a two-parameter extension of the Poisson distribution that generalizes some well-known discrete distributions (Poisson, Bernoulli and geometric). It also leads to the generalization of distributions derived from these discrete distributions (i.e. the binomial and negative binomial distributions). We describe three methods for estimating the parameters of the Conway-Maxwell-Poisson distribution. The first is a fast simple weighted least squares method, which leads to estimates that are sufficiently accurate for practical purposes. The second method, using maximum likelihood, can be used to refine the initial estimates. This method requires iterations and is more computationally intensive. The third estimation method is Bayesian. Using the conjugate prior, the posterior density of the parameters of the Conway-Maxwell-Poisson distribution is easily computed. It is a flexible distribution that can account for overdispersion or underdispersion that is commonly encountered in count data. We also explore two sets of real world data demonstrating the flexibility and elegance of the Conway-Maxwell-Poisson distribution in fitting count data which do not seem to follow the Poisson distribution. Copyright 2005 Royal Statistical Society.

This paper presents the theory, design principles, implementation and performance results of PicHunter, a prototype content-based image retrieval (CBIR) system. In addition, this document presents the rationale, design and results of psychophysical experiments that were conducted to address some key issues that arose during PicHunter's development. The PicHunter project makes four primary contributions to research on CBIR. First, PicHunter represents a simple instance of a general Bayesian framework which we describe for using relevance feedback to direct a search. With an explicit model of what users would do, given the target image they want, PicHunter uses Bayes's rule to predict the target they want, given their actions. This is done via a probability distribution over possible image targets, rather than by refining a query. Second, an entropy-minimizing display algorithm is described that attempts to maximize the information obtained from a user at each iteration of the search. Third, PicHunter makes use of hidden annotation rather than a possibly inaccurate/inconsistent annotation structure that the user must learn and make queries in. Finally, PicHunter introduces two experimental paradigms to quantitatively evaluate the performance of the system, and psychophysical experiments are presented that support the theoretical claims.

Computational color constancy is the task of estimating the true reflectances of visible surfaces in an image. In this paper we follow a line of research that assumes uniform illumination of a scene, and that the principal step in estimating reflectances is the estimation of the scene illuminant. We review recent approaches to illuminant estimation, firstly those based on formulae for normalisation of the reflectance distribution in an image -so-called grey-world algorithms, and those based on a Bayesian formulation of image formation.In evaluating these previous approaches we introduce a new tool in the form of a database of 568 high-quality, indoor and outdoor images, accurately labelled with illuminant, and preserved in their raw form, free of correction or normalisation. This has enabled us to establish several properties experimentally. Firstly automatic selection of grey-world algorithms according to image properties is not nearly so effective as has been thought. Secondly, it is shown that Bayesian illuminant estimation is significantly improved by the improved accuracy of priors for illuminant and reflectance that are obtained from the new dataset.