# A Model for Binocular Fusion

## Keywords

Binocular misalignment, position disparity, phase disparity, depth perception, misalignment energy

## Abstract

This study proposed a model for binocular fusion, which aims to minimize binocular misalignment. The model consists of an array of phase and position disparity detectors in each spatial-frequency channel that calculate position and phase disparity energies at each location. Binocular misalignment is defined as the offset of two eyes’ projections of a 3D target into a depth plane, and is evaluated using misalignment energy (MisaE). MisaE is calculated as a weighted summation of squared phase disparity energies with weights proportional to the absolute phase disparity. MisaE is always greater than 0, except on the depth plane of the 3D target, where it reaches its minimum value of 0. Binocular fusion is achieved by searching for a depth plane where the MisaE reaches the minimum. The readout of position disparity is driven by the MisaE gradient along position disparity space to reduce the MisaE until it reaches the minimum or falls below a threshold. Depth perception during this process is given by calculating the disparity energy, which combines both position and phase disparity energies. At a small stimulus disparity, the MisaE reaches the minimum, resulting in perfect fusion. However, at a large stimulus disparity, it may reach a local minimum that does not match the stimulus disparity, leading to ambiguous depth perception. Computational simulations of the proposed model using both random dot stereograms and a real stereo image show that the model works well to search for stimulus disparity at each location when the stimulus disparity varies smoothly in space.

A Model for Binocular Fusion

This study proposed a model for binocular fusion, which aims to minimize binocular misalignment. The model consists of an array of phase and position disparity detectors in each spatial-frequency channel that calculate position and phase disparity energies at each location. Binocular misalignment is defined as the offset of two eyes’ projections of a 3D target into a depth plane, and is evaluated using misalignment energy (MisaE). MisaE is calculated as a weighted summation of squared phase disparity energies with weights proportional to the absolute phase disparity. MisaE is always greater than 0, except on the depth plane of the 3D target, where it reaches its minimum value of 0. Binocular fusion is achieved by searching for a depth plane where the MisaE reaches the minimum. The readout of position disparity is driven by the MisaE gradient along position disparity space to reduce the MisaE until it reaches the minimum or falls below a threshold. Depth perception during this process is given by calculating the disparity energy, which combines both position and phase disparity energies. At a small stimulus disparity, the MisaE reaches the minimum, resulting in perfect fusion. However, at a large stimulus disparity, it may reach a local minimum that does not match the stimulus disparity, leading to ambiguous depth perception. Computational simulations of the proposed model using both random dot stereograms and a real stereo image show that the model works well to search for stimulus disparity at each location when the stimulus disparity varies smoothly in space.