Much of the reading of medical images is in terms of figures: objects or object components. We focus on the part of the visual process in which the viewer attentively scrutinizes objects to determine their shape and their geometry relative to other nearby objects. We propose and give evidence that figures are represented in terms of their middles and widths by a mechanisms that separates information at various levels of detail. Important figural properties, as well as inter-figure relationships, appear directly in or are easily derived from this representation by a set of cores. Cores are traces in scale space that are derived from a value called medialness. Medialness is, in turn, derived from boundariness values, which are multiscale graded measurements derived directly from the image intensities. Core formation is guided by attention which directs processing to an approximate location and size (scale), i.e., about here, about this width. This paper gives justification for the model and discusses its usefulness in modeling various visual tasks that are performed when viewing medical images.