A unified model for binocular fusion and depth perception

We describe a new unified model to explain both binocular fusion and depth perception, over a broad range of depths. At each location, the model consists of an array of paired spatial frequency filters, with different relative horizontal shifts (position disparity) and interocular phase disparities of 0, 90, +/- 180, or -90 degrees. The paired filters with different spatial profiles (non-zero phase disparity) compute interocular misalignment and provide phase-disparity energy (binocular fusion energy) to drive selection of the appropriate filters along the position disparity space until the misalignment is eliminated and sensory fusion is achieved locally. The paired filters with identical spatial profiles (0 phase disparity) compute the position-disparity energy. After sensory fusion, the combination of position and possible residual phase disparity energies is calculated for binocular depth perception. Binocular fusion occurs at multiple scales following a coarse-to-fine process. At a given location, the apparent depth is the weighted sum of fusion shifts combined with residual phase disparity in all spatial-frequency channels, and the weights depend on stimulus spatial frequency and stimulus contrast. To test the theory, we measured disparity minimum and maximum thresholds (Dmin and Dmax) at three spatial frequencies and with different intraocular contrast levels. The stimuli were Random-Gabor-Patch (RGP) stereograms consisting of Gabor patches with random positions and phases, but with a fixed spatial frequency. The two eyes viewed identical arrays of patches except that one eye's array could be shifted horizontally and could differ in contrast. Our experiments and modeling reveal two contrast normalization mechanisms: (1) Energy Normalization (EN): Binocular energy is normalized with monocular energy after the site of binocular combination. This predicts constant Dmin thresholds when varying stimulus contrast in the two eyes; (2) DSKL model Interocular interactions: Monocular contrasts are normalized before the binocular combination site through interocular contrast gain-control and gain-enhancement mechanisms. This predicts contrast dependent Dmax thresholds. We tested a range of models and found that a model consisting of a second-order pathway with DSKL interocular interactions and a first-order pathway with EN at each spatial-frequency band can account for both the Dmin and Dmax data very well. Simulations show that the model makes reasonable predictions of suprathreshold depth perception.