Differential equations for phase-based stereo-vision

In this work, the phase-difference-based technique for disparity estimation in stereo vision is formulated in terms of variational calculus. Non-local operations such as image convolutions with Gabor-like filters are replaced by solutions of systems of coupled differential equations (DE), whose degree depends on the smoothness of the convolution kernel. The variational formulation of the whole disparity-estimation problem allows the introduction of new computational features: (1) a regularization scheme that reduces irregularities in the computed disparity field; and (2) a coupling between the filter parameters and the system output in order to optimize DE system performance. In the perspective of analog computation on discrete lattice networks, this work indicates the possibility of performing a complex and global filtering operation by means of local operators.