Given an N N grid of squares, where each square has a count and an underlying population, our goal is to find the square region with the highest density, and to calculate its significance by randomization. Any density measure D, dependent on the total count and total population of a region, can be used. For example, if each count represents the number of disease cases occurring in that square, we can use Kulldorff's spatial scan statistic D

Given an N N grid of squares, where each square has a count and an underlying population,our goal is to find the square region with the highest density, and to calculate its significance by randomization. Any density measure D, dependent on the total count and total population of a region, canbe used. For example, if each count represents the number of disease cases occurring in that square, we can use Kulldorff's spatial scan statistic D

Sketch maps are an important spatial representation used in many geospatial-reasoning tasks. This article describes techniques we have developed that enable software to perform humanlike reasoning about sketch maps. We illustrate the utility of these techniques in the context of nuSketch Battlespace, a research system that has been successfully used in a variety of experiments. After an overview of the nuSketch approach and nuSketch Battlespace, we outline the representations of glyphs and sketches and the nuSketch spatial reasoning architecture.

Sketch maps are an important spatial representation used in many geospatial-reasoning tasks. This article describes techniques we have developed that enable software to perform humanlike reasoning about sketch maps. We illustrate the utility of these techniques in the context of nuSketch Battlespace, a research system that has been successfully used in a variety of experiments. After an overview of the nuSketch approach and nuSketch Battlespace, we outline the representations of glyphs and sketches and the nuSketch spatial reasoning architecture. We describe the use of qualitative topology and Voronoi diagrams to construct spatial representations, and explain how these facilities are combined with analogical reasoning to provide a simple form of enemy intent hypothesis generation.

Reasoning about spatial data is a key task in many applications, including geographic information systems, meteorological and fluid-flow analysis, computer-aided design, and protein structure databases. Qualitative spatial reasoning (QSR) provides representational primitives (a spatial "vocabulary") and inference mechanisms for these tasks. It then turns to the data-rich case, where the goal is to derive and manipulate qualitative spatial representations that efficiently and correctly abstract important spatial aspects of the underlying data for use in subsequent tasks. This article focuses on how a particular QSR system, SPATIAL AGGREGATION, can help answer spatial queries for scientific and engineering data sets.

Reasoning about spatial data is a key task in many applications, including geographic information systems, meteorological and fluid-flow analysis, computer-aided design, and protein structure databases. Such applications often require the identifi- cation and manipulation of qualitative spatial representations, for example, to detect whether one object will soon occlude another in a digital image or efficiently determine relationships between a proposed road and wetland regions in a geographic data set. Qualitative spatial reasoning (QSR) provides representational primitives (a spatial "vocabulary") and inference mechanisms for these tasks. This article first reviews representative work on QSR for data-poor scenarios, where the goal is to design representations that can answer qualitative queries without much numeric information. It then turns to the data-rich case, where the goal is to derive and manipulate qualitative spatial representations that efficiently and correctly abstract important spatial aspects of the underlying data for use in subsequent tasks. This article focuses on how a particular QSR system, SPATIAL AGGREGATION, can help answer spatial queries for scientific and engineering data sets. A case study application of weather analysis illustrates the effective representation and reasoning supported by both data-poor and data-rich forms of QSR

This article describes a method for building a cognitive map of a virtual urban environment. Our routines enable virtual humans to map their environment using a realistic model of perception. We based our implementation on a computational framework proposed by Yeap and Jefferies (1999) for representing a local environment as a structure called an absolute space representation (ASR). Their algorithms compute and update ASRs from a 2-1/2-dimensional (2-1/2D) sketch of the local environment and then connect the ASRs together to form a raw cognitive map.1 Our work extends the framework developed by Yeap and Jefferies in three important ways. First, we implemented the framework in a virtual training environment, the mission rehearsal exercise (Swartout et al. 2001). Second, we developed a method for acquiring a 2- 1/2D sketch in a virtual world, a step omitted from their framework but that is essential for computing an ASR. Third, we extended the ASR algorithm to map regions that are partially visible through exits of the local space. Together, the implementation of the ASR algorithm, along with our extensions, will be useful in a wide variety of applications involving virtual humans and agents who need to perceive and reason about spatial concepts in urban environments.

Most models of spatial representations in the cortex assume cells with limited receptive fields that are defined in a particular egocentric frame of reference. However, cells outside of primary sensory cortex are either gain modulated by postural input or partially shifting. We show that solving classical spatial tasks, like sensory prediction, multi-sensory integration, sensory-motor transformation and motor control requires more complicated intermediate representations that are not invariant in one frame of reference. We present an iterative basis function map that performs these spatial tasks optimally with gain modulated and partially shifting units, and tests it against neurophysiological and neuropsychological data. In order to perform an action directed toward an object, it is necessary to have a representation of its spatial location.

We present a computational model of the neural mechanisms in the parietal and temporal lobes that support spatial navigation, recall of scenes and imagery of the products of recall. Long term representations are stored in the hippocampus, and are associated with local spatial and object-related features in the parahippocampal region. Viewer-centered representations are dynamically generated from long term memory in the parietal part of the model. The model thereby simulates recall and imagery of locations and objects in complex environments. After parietal damage, the model exhibits hemispatial neglect in mental imagery that rotates with the imagined perspective of the observer, as in the famous Milan Square experiment [1]. Our model makes novel predictions for the neural representations in the parahippocampal and parietal regions and for behavior in healthy volunteers and neuropsychological patients.

Most models of spatial representations in the cortex assume cells with limited receptive fields that are defined in a particular egocentric frame of reference. However, cells outside of primary sensory cortex are either gain modulated by postural input or partially shifting. We show that solving classical spatial tasks, like sensory prediction, multi-sensory integration, sensory-motor transformation and motor control requires more complicated intermediate representations that are not invariant in one frame of reference. We present an iterative basis function map that performs these spatial tasks optimally with gain modulated and partially shifting units, and tests it against neurophysiological and neuropsychological data. In order to perform an action directed toward an object, it is necessary to have a representation of its spatial location.