A Convexity of the self-supervised loss function

To evaluate the convexity of the self-supervised loss function for event-based optical flow estimation from [56] and the adaptation that we propose in this work, we conducted an experiment with two partitions of 40k events from the ECD dataset [31]. In this experiment, for the selected partitions, we computed the value of Eq. 4 (with and without the scaling) for four sets of optical flow vectors given by: u Figure 1 highlights the main difference between the original and our adapted formulation. On the contrary, the scaling that we propose in Section 3.2 fixes this issue, and results in a convex loss function for any value of d. Numbers on top indicate the maximum per-axis pixel displacement for each column. Scaled L Original L (see Eq. 6) but without the reset mechanism.