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Summary form only given. This talk builds around three challenges: fusing heterogeneous and uncertain sources of information, extracting and tracking geometry, and dealing with computational complexity. In the first of these it is briefly describe the work being done in the group (and led by Dr. John Fisher) on machine learning/information-theoretic methods, with illustrations in audio/video fusion and in association of signals subject to propagation distortion. The second topic focuses on so-called curve evolution methods, their probabilistic interpretation, and some of the methods being developed in the group that incorporate both information-theoretic methods for "blind" segmentation and prior modeling of shapes for segmentation in complex imagery. Illustrations would be given to two problems of profound societal importance: automatic segmentation of the prostate (for prostate brachytherapy) and automatic segmentation of photos of zebras when you have no idea what a zebra is. The third topic deals with research in the group on large-scale problems of statistical inference specified in terms of so-called graphical models. The paper briefly describe some of the significant theoretical successes we have had in developing methods that exploit embedded tractable graphical structures to solve both large-scale estimation problems and large integer programming problems such as arise in data association. Finally, two really big challenges-very large-scale data assimilation for geophysical fields and fusion of large numbers of distributed and individually very limited sensors is briefly commented. Addressing each of these challenges requires much more than the union of the topics addressed in this talk, but asking a few questions that suggest how research in these areas might evolve to contribute to these very large and very interesting challenges.