Given discrete event data, we wish to produce a probability density that can model the relative probability of events occurring in a spatial region. Common methods of density estimation, such as Kernel Density Estimation, do not incorporate geographical information. Using these methods could result in nonnegligible portions of the support of the density in unrealistic geographic locations. For example, crime density estimation models that do not take geographic information into account may predict events in unlikely places such as oceans, mountains, and so forth. We propose a set of Maximum Penalized Likelihood Estimation methods based on Total Variation and H 1 Sobolev norm regularizers in conjunction with a priori high resolution spatial data to obtain more geographically accurate density estimates. We apply this method to a residential burglary data set of the San Fernando Valley using geographic features obtained from satellite images of the region and housing density information.

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In this paper 1 , we describe a hybrid human-machine system for searching and detecting Objects of Interest (OI) in imagery. Automated methods for OI detection based on models of human visual attention have received much interest, but are inherently bottom-up and driven by features. Humans fixate on regions of imagery based on a much stronger top-down component. While it may be possible to include some aspects of top-down cognition into these methods, it is difficult to fully capture all aspects of human cognition into an automated algorithm. Our hypothesis is that combination of automated methods with human fixations will provide a better solution than either alone. In this work, we describe a Brain-Enhanced Synergistic Attention (BESA) system that combines models of visual attention with real-time eye fixations from a human for accurate search and detections of OI. We describe two different BESA schemes and provide implementation details. Preliminary studies were conducted to determine the efficacy of the system and initial results are promising. Typical applications of this technology are in surveillance, reconnaissance and intelligence analysis.

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