This text bases a comprehensive approach to visual representation on the notion of correspondence between proximal (internal) and distal similarities in objects. This leads to a computationally feasible and formally veridical representation of distal objects that addresses the needs of shape categorization and can be used to derive models of perceived similarity. The author discusses the representational needs of various visual recognition and surveys late-1990s theories of representation in this context. He then develops a theory of representation that is related to Shepard's notion of second-order isomorphism between representations and their targets. Shimon Edelman goes beyond Shepard by specifying the conditions under which the the representations can be made formally veridical. Edelman assesses his theory's performance in identification and categorization of 3D shapes and examines it in light of psychological and neurobiological data concerning the object-processing stream in primate vision. He also discusses the connections between his theory and other efforts to understand representation in the brain.