Solving da vinci stereopsis with depth-edge-selective v2 cells

As a consequence of binocular projection of three-dimensional space onto our retinas, monocular regions exist around depth boundaries between occluding surfaces and their background. Da Vinci stereopsis refers to the process by which our visual system is able to determine the location and ocularity (the eye of origin) of monocular regions, and to assign them ecologically correct depths, despite an absence of binocular correspondence (Nakayama and Shimojo, 1990). Most existing models of da Vinci stereopsis rely on detectors each only responding to a single disparity, and are thus not physiologically plausible. Additionally, the models usually include monocular cells perhaps because of the argument that monocular cells are needed to determine the ocularity of monocular regions (Nakayama and Shimojo, 1990). However, monocular regions are binocularly defined (seen by one eye AND not by the other), and may be best identified by binocular cells. Recent evidence indicates that some V2 cells are selective for depth boundaries (von der Heydt et al., 2000). I therefore examined whether these binocular V2 cells could solve da Vinci stereopsis. I propose a new model for da Vinci stereopsis based on a coarse-to-fine disparity-energy computation in V1 and disparity-boundary-selective units in V2. Unlike previous work, our model contains only binocular cells, relies on distributed representations of disparity, and has a simple V1-to-V2 feedforward structure. In the model, V1 cells are standard disparity energy units. A V2 cell then sums excitatory inputs from several specific V1 cells to create a bipartite V2 receptive field (RF) with differing disparity preferences in its left and right subregions. Each V2 cell is selective for a particular disparity combination and a population of V2 cells represents all possible disparity combinations within a certain disparity range at each image position. Since monocular regions are usually perceived at the depth of the background, I also assume that a V2 cell's response represents the farther one of its two preferred disparities. My simulations demonstrate, with random dot stereograms, that the V2 stage of our model is able to determine the location and the eye-of-origin of monocularly occuluded regions and improve disparity map computation. By locating the peak response of the population of V2 cells for a given image point, the model can reliably determine whether the point is in a binocular or monocular region, and its ocularity if the point is monocular. Furthermore, the V2 stage of the model improves the disparity computation in the V1 stage by assigning background disparity to the monocular regions. I also examine two related issues. First, I show that the coarse-to-fine V1 model for conventional stereopsis explains double matching in Panum's limiting case. This provides computational support to the notion that the perceived depth of a monocular bar next to a binocular rectangle may not be da Vinci stereopsis per se (Gillam et al. 2003). Second, I demonstrate that some stimuli previously deemed invalid have simple, valid geometric interpretations. My work suggests that studies of da Vinci stereopsis should focus on stimuli more general than the bar-and-rectangle type and that no monocular cells are required to solve da Vinci stereopsis. Finally, I propose that disparity-boundary-selective V2 cells may provide a simple physiological mechanism for da Vinci stereopsis.