Julian Ernst Besag, 26 March 1945 -- 6 August 2010, a biographical memoir

Julian Besag was an outstanding statistical scientist, distinguished for his pioneering work on the statistical theory and analysis of spatial processes, especially conditional lattice systems. His work has been seminal in statistical developments over the last several decades ranging from image analysis to Markov chain Monte Carlo methods. He clarified the role of auto-logistic and auto-normal models as instances of Markov random fields and paved the way for their use in diverse applications. Later work included investigations into the efficacy of nearest neighbour models to accommodate spatial dependence in the analysis of data from agricultural field trials, image restoration from noisy data, and texture generation using lattice models.Comment: 26 pages, 14 figures; minor revisions, omission of full bibliograph

CDDT: Fast Approximate 2D Ray Casting for Accelerated Localization

Localization is an essential component for autonomous robots. A well-established localization approach combines ray casting with a particle filter, leading to a computationally expensive algorithm that is difficult to run on resource-constrained mobile robots. We present a novel data structure called the Compressed Directional Distance Transform for accelerating ray casting in two dimensional occupancy grid maps. Our approach allows online map updates, and near constant time ray casting performance for a fixed size map, in contrast with other methods which exhibit poor worst case performance. Our experimental results show that the proposed algorithm approximates the performance characteristics of reading from a three dimensional lookup table of ray cast solutions while requiring two orders of magnitude less memory and precomputation. This results in a particle filter algorithm which can maintain 2500 particles with 61 ray casts per particle at 40Hz, using a single CPU thread onboard a mobile robot.Comment: 8 pages, 14 figures, ICRA versio

Agent-based pedestrian modelling

When the focus of interest in geographical systems is at the very fine scale, at the level of streets and buildings for example, movement becomes central to simulations of how spatial activities are used and develop. Recent advances in computing power and the acquisition of fine scale digital data now mean that we are able to attempt to understand and predict such phenomena with the focus in spatial modelling changing to dynamic simulations of the individual and collective behaviour of individual decision-making at such scales. In this Chapter, we develop ideas about how such phenomena can be modelled showing first how randomness and geometry are all important to local movement and how ordered spatial structures emerge from such actions. We focus on developing these ideas for pedestrians showing how random walks constrained by geometry but aided by what agents can see, determine how individuals respond to locational patterns. We illustrate these ideas with three types of example: first for local scale street scenes where congestion and flocking is all important, second for coarser scale shopping centres such as malls where economic preference interferes much more with local geometry, and finally for semi-organised street festivals where management and control by police and related authorities is integral to the way crowds move