Neural construction of 3D medial axis from the binocular fusion of 2D MAs

The perceptual constancy of shape, including view invariance, is an amazing property of the visual system. Cortical representation by the medial axis (MA) is an attractive candidate for maintaining the constancy of a wide range of arbitrary shapes. Recent physiological studies have reported that neurons in the primary visual cortex (V1) show a response to two-dimensional (2D) MAs, and those in the inferior temporal cortex (IT) are selective to three-dimensional (3D) MAs. However, little is known about the neural mechanisms underlying the transformation of 2D to 3D MAs. As a first step toward investigating the cortical mechanism, we have proposed as a hypothesis that a pair of monocular 2D MAs is fused to generate a 3D MA. We examined the computational plausibility of the hypothesis; specifically, whether an energy-based fusion model is capable of generating 3D MAs. We generated blob-like, physiologically plausible 2D MAs, and used a standard energy model to detect the disparity between a pair of 2D MAs. The model successfully generated 3D MAs for a variety of objects that included typical shape characteristics. A reconstruction test showed that the computed 3D MAs captured the essential structure of the objects with reasonable accuracy and view invariance. These results indicate that the fusion of monocular blob-like 2D MAs is capable of generating a reasonable 3D MA within the framework of the energy model.