Professor Baddeley has done outstanding work in the difficult area of statistical analysis of digital images and spatial data. He has solved important practical problems using mathematical and statistical methods. The stereological measurement of such things as bone biopsies, skin samples and material fractures, has been fundamentally altered by his technique for measuring surface area from vertical sections. He has also introduced ways of measuring the `error' in image reconstruction, and has contributed to a broad range of other areas of spatial statistics and probability.
In brief, spatial statistics is about analysing spatial data (any kind of data that involve a spatial location, such as maps, weather station records, or satellite images) and statistical image analysis is more specifically about analysing digital pictures (from satellites, cameras, microscopes etc). Stereology or `quantitative microscopy' is a kind of sampling methodology used to draw statistical inferences from microscope images. Stochastic geometry is a branch of probability theory that deals with very general kinds of `random sets'. What these fields have in common is that they combine `geometry' (spatial or geometrical information) with `probability' (random processes and statistical inference).
Research in these fields is very important to the future of statistical science. Spatial data are increasingly common, thanks to GIS technology, digital imaging, GPS tagging, and other technologies. The statistical analysis of spatial data is not a trivial extension of classical statistical methods, and indeed it creates severe difficulties for classical methods. Research on spatial data has been a fertile source of new ideas in statistics. The fields of spatial statistics and statistical image analysis played a pivotal role in many of the big developments in statistical science between 1985 and 2005. Markov Chain Monte Carlo (MCMC) methods were first invented in spatial statistics. Bayesian methods using MCMC originated in statistical image analysis.
In collaboration with Richard Gill, an expert on survival analysis, Baddeley developed an important new approach to the problem of edge effects in spatial data, drawing a key connection between edge effects and censoring, developing the analogue of the Kaplan-Meier estimator for distance distributions, and establishing key properties of distance distributions. This pivotal work stimulated further activity in stochastic geometry and spatial statistics.
Baddeley introduced several important probability models for spatial point processes, including nearest-neighbour Markov models (with Jesper Moller) and area-interaction processes (with student Colette van Lieshout). He developed time-invariance methodology for parameter estimation in complex models, and showed that it provides a rigorous derivation of the pseudolikelihood of a point process.
Baddeley was one of the first statisticians to work on three-dimensional point patterns and replicated point patterns. With Van Lieshout, he used advanced techniques of point process theory (conditional intensity) to derive new nonparametric statistical measures of dependence in a spatial point pattern (J-functions), and elegant theoretical results about spatial interaction. Each of these theoretical advances was accompanied by the provision of free software to perform the calculations.
Over the last decade, Baddeley has been at the forefront of practical statistical methodology for spatial point patterns. With Rolf Turner he developed an efficient and flexible algorithm for fitting Gibbs point process models to spatial point pattern data, using maximum pseudolikelihood. Baddeley and Turner have implemented numerous practical techniques for spatial data analysis in open source software. In recent years, Baddeley and collaborators have analysed spatial point pattern data in geology, astronomy, public health, neuroscience and ecology.
Baddeley recently developed residual analysis for spatial point processes. This is a major advance in practical methodology for spatial point patterns. It was presented as a prestigious `Read Paper' to the Royal Statistical Society in London in 2005 with Moller, Turner and Hazelton.
Stereology is the science of interpreting microscope images. It deals with the geometrical complexities of interpreting a two-dimensional slice of a solid material (rock, metal, biological tissue) and the statistical challenges of drawing conclusions from a tiny sample of material.
Classical methods of stereology require that the cutting plane be randomly oriented. This is a severe restriction on the scope of applications. In 1983, Baddeley developed a new stereological method in which the cutting plane is `vertical' (parallel to a fixed axis, or perpendicular to a fixed surface). This made it possible to apply stereology to cylindrical core samples (e.g. bone biopsies in medicine, core samples in soil science), samples of flat materials (e.g. skin biopsies) and oriented samples (e.g. metal fracture profiles, longitudinal sections of muscle). This was publicised in a 1986 paper in the Journal of Microscopy which has over 600 citations. The discovery of vertical sections overturned one of the central assumptions in theoretical stereology, leading to a new branch of the discipline and a vast expansion of the scope of practical stereological methods.
Baddeley has been a leading advocate of statistical ideas in stereology. With Luis Cruz-Orive, he demonstrated the central role of the Horvitz-Thompson weighting principle in stereology, and proved the analogue of the classical Rao-Blackwell theorem for stereological methods. With Eva Vedel Jensen, he recently published a comprehensive treatise on the statistical foundations of stereology.
Baddeley and Van Lieshout formulated a statistical approach to object recognition in digital images (e.g. recognising objects in a scene, or recognising letters in a photograph of a document). They showed that the Hough Transform, popular in computer vision, is equivalent to the likelihood ratio test for a simple probability model. They improved the performance of existing object recognition algorithms using Bayesian methods, with Markov point processes as the prior distributions.
Baddeley has developed image metrics or measures of the `error' in an image processing technique, e.g. the inaccuracies in a CAT scan reconstruction of the human body. Using fundamental theory from stochastic geometry, Baddeley constructed a metric which has the right topological properties required for practical use (the Hausdorff metric topology) but is robust against noise. Baddeley's metric has proved to be useful in image processing, spatial statistics and weather prediction.
Prompted by a statistical consulting problem in clinical pathology, he introduced a new definition of surface curvature, developed fundamental theory, and applied it to practical measurement of the curvature of tubes from biopsies in human infertility research.
Baddeley and student Annoesjka Cabo developed new integral-geometric identities for plane sections of particles, applying them to the statistical analysis of volumes of individual biological cells observed in plane sections of tissue.