Towards Equivariant Optical Flow Estimation with Deep Learning

Methods for Optical Flow (OF) estimation based on Deep Learning have considerably improved traditional approaches in challenging and realistic conditions. However, data-driven approaches can inherently be biased, leading to unexpected under-performance in real application scenarios. In this paper, we first observe that the OF estimation accuracy varies with motion direction, and name this phenomenon 'OF sign imbalance'. The sign imbalance cannot be assessed by means of the endpoint-error (EPE), the typical training and evaluation metric for Deep Optical Flow estimators. This paper tackles this issue by proposing a new metric to assess the sign imbalance, which is compared to the endpoint-error. We provide an extensive evaluation of the sign imbalance for the state-of-the-art optical flow estimators. Based on the evaluation, we propose two strategies to mitigate the phenomenon, i) by constraining the model estimations during inference, and, ii) by constraining the loss function during training. Testing and training code is available at: www.github.com/stsavian/equivariant_of_estimation.