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Representation of shape is a fundamental problem in vision science. Neurophysiological studies of macaque have reported that neurons in the primary visual cortex (V1) respond to Medial Axis (MA) of 2D surface, and that those in higher cortex (IT) respond to surfaces of 3D shape. However, how the cortex translates a pair of 2D retinal images into 3D shape has not been clarified. In the present study, we investigated the problem of 3D shape representation in the cortices with the specific focus on the translation of 2D to 3D shape representation. Based on the neurophysiological evidence, we propose that a pair of 2D-MA that encodes 2D surfaces in V1 is fused to generate a 3D-MA that represents 3D shape in higher cortex. In order to investigate this hypothesis, we developed a computational model and analyzed its behavior. The model computes 2D-MAs from a pair of stereo images, detects the disparities of the 2D-MAs using an energy model that mimics V1 complex cells, and computes 3D-MA from the disparities between the 2D-MAs. Our model reconstructed successfully 3D shape from a number of objects including natural objects and those with complex structures. The results support our hypothesis that a pair of 2D-MA is computed independently in V1, and then 3D-MA that represent 3D shape is computed from the fusion of the 2D-MAs

Medial Axis for the Cortical Representation of 3D Shape