This chapter lays out one approach to describing the inferential problem encountered when integrating multiple different cues that may arise from many different objects. By switching representations from a set of discrete single-valued cues to a spatial representation based on attribute and cue "maps," it was possible naturally to model observers' behavior in some simple multiobject and multicue settings, and provide a natural, tractable approach to approximation within these settings. But while effective in these simple cases, the framework is still far from providing a complete description of perceptual inference and integration in cluttered scenes. The framework developed here works best when the cues used for inference are inherently localized in space (in the visual case) or with respect to some other dimension important for determining grouping.