TDE-3: an improved prior for optical flow computation in spiking neural networks

Motion detection is a primary task required for robotic systems to perceive and navigate in their environment. Proposed in the literature bioinspired neuromorphic Time-Difference Encoder (TDE-2) combines event-based sensors and processors with spiking neural networks to provide real-time and energy-efficient motion detection through extracting temporal correlations between two points in space. However, on the algorithmic level, this design leads to a loss of direction-selectivity of individual TDEs in textured environments. In the present work, we propose an augmented 3-point TDE (TDE-3) with additional inhibitory input that makes TDE-3 direction-selectivity robust in textured environments. We developed a procedure to train the new TDE-3 using backpropagation through time and surrogate gradients to linearly map input velocities into an output spike count or an Inter-Spike Interval (ISI). Using synthetic data, we compared training and inference with spike count and ISI with respect to changes in stimuli dynamic range, spatial frequency, and level of noise. ISI turns out to be more robust toward variation in spatial frequency, whereas the spike count is a more reliable training signal in the presence of noise. We conducted an in-depth quantitative investigation of optical flow coding with TDE and compared TDE-2 vs. TDE-3 in terms of energy efficiency and coding precision. The results show that at the network level, both detectors show similar precision (20° angular error, 88% correlation with the truth of the ground). However, due to the more robust direction selectivity of individual TDEs, the TDE-3 based network spikes less and is hence more energy efficient. Reported precision is on par with model-based methods but the spike-based processing of the TDEs provides allows more energy-efficient inference with neuromorphic hardware. Additionally, we also employed TDE-2 and TDE-3 to estimate ego-motion and showed results competitive with those achieved by neural networks with 1.5 × 10⁵ parameters.