A critical review of Luneburg's model with regard to global structure of visual space.

Visual space (VS) is a coherent self-organized dynamic complex that is structured into objects, backgrounds, and the self. As a concrete example of geometrical properties in VS, experimental results on parallel and (equi) distance alleys in a frameless VS were reviewed, and Luneburg's interpretation on the discrepancy between these 2 alleys was sketched with emphasis on the 2 hypotheses involved: VS is a Riemannian space of constant curvature (RCC) and the a priori assumed correspondence between VS and the physical space in which stimulus points are presented. Dissociating these 2 assumptions, the author tried to see to what extent the global structure of VS under natural conditions is in accordance with the hypothesis of RCC and to make explicit the logic underlying RCC. Several open questions about the geometry of VS per se have been enumerated.