Cinematic L1 Video Stabilization with a Log-Homography Model
authors Arwen Bradley, Jason Klivington, Joseph Triscari, Rudolph van der Merwe
We present a method for stabilizing handheld video that simulates the camera motions cinematographers achieve with equipment like tripods, dollies, and Steadicams. We formulate a constrained convex optimization problem minimizing the ℓ1-norm of the first three derivatives of the stabilized motion. Our approach extends the work of Grundmann et al.  by solving with full homographies (rather than affinities) in order to correct perspective, preserving linearity by working in log-homography space. We also construct crop constraints that preserve field-of-view; model the problem as a quadratic (rather than linear) program to allow for an ℓ2 term encouraging fidelity to the original trajectory; and add constraints and objectives to reduce distortion. Furthermore, we propose new methods for handling salient objects via both inclusion constraints and centering objectives. Finally, we describe a windowing strategy to approximate the solution in linear time and bounded memory. Our method is computationally efficient, running at 300fps on an iPhone XS, and yields high-quality results, as we demonstrate with a collection of stabilized videos, quantitative and qualitative comparisons to  and other methods, and an ablation study.
In spite of the success of deep learning, we know relatively little about the many possible solutions to which a trained network can converge. Networks generally converge to some local minima—a region in space where the loss function increases in every direction—of their loss function during training. Our research explores why local minima outperforms others when a trained network is evaluated on a held-out test set.