Robust Filtering based on Complex Cell Networks from the Visual Cortex

We propose a novel approach for filtering that is inspired by Complex Cell Networks (CCN) in the primary visual cortex of mammals; our aim is to emulate the robustness of the biological system, showing graceful degradation in face of gross deterioration of the input. Instead of relying on energy minimization as in frequency-based filter design, or on Bayes’ theorem as in statistical filtering, our formulation is founded on three principles that have been observed in real neural responses: 1) winner-take-all, where perceptual ambiguity is solved by focusing on the strongest signal; 2) persistence, where information is fused across time to lessen the impact of noise, outliers, and temporary cancellations in the input data; and 3) boundedness, where the responses in the filter are bounded to be non-negative and below a maximum value. In neuroscience, the typical goal is to find models that match and explain measurements from a biological system. In this paper, we take an engineering approach, where we encode the three properties above as mathematical constraints, and find filter parameters that guarantee convergence of the filter (for constant, bounded inputs), optimize bounds on the convergence rate, and improve sparsity of the filter kernel; overall, the filter is obtained from the solution to a Linear Program (LP). As a proof-of-concept, we integrated the proposed filter architecture with a neural network to estimate the vehicle speed solely based on camera images in extremely noisy environments.