Algebraic Topology for Data-Driven Artifact Removal Post-Video Stabilization of Indoor Videos Captured by Mobile Robots: Theory, Algorithm and Experiments

Video stabilization is the process of removing unwanted shaky motion from a video sequence. Often, it can be observed that the frames in the video obtained after stabilization (stabilized video) have some unknown unintended artifacts associated with it, resulting in degradation of its quality. This poses a challenge in inferring visual information from a stabilized video. In this work, we present a novel data-driven approach to enhance the quality of stabilized video by gaining insights into the indoor part of the natural image manifold using homological algebra. The enhancement is achieved by projecting the stabilized video frames onto an approximated thickened triangulated version of the manifold underlying an indoor image dataset, which we refer to as the indoor image manifold. This manifold can be thought of as an open subset of the natural image manifold, which is the part over which the indoor images are dense. The manifold is reconstructed using the lower bounds on the rank of Homology groups of the indoor image manifold. The lower bounds are derived using the functorial properties of classical singular homology. Our approach has been found to increase video stabilization quality assessment (VSQA) scores for certain classes of indoor stabilized videos from datasets.