Topological Eulerian Synthesis of Slow Motion Periodic Videos

TL;DR

This paper introduces a novel topological and geometric approach to synthesize a single cycle of periodic motion from noisy, drifting, and occluded videos without tracking, using topological data analysis and spectral methods.

Contribution

It presents a tracking-free Eulerian method that leverages topological data analysis and spectral geometry to robustly reorder frames into a single motion cycle.

Findings

Robust to camera shake, noise, and occlusions.

Effective in synthesizing detailed single-cycle videos.

Applicable across various types of periodic motion.

Abstract

We consider the problem of taking a video that is comprised of multiple periods of repetitive motion, and reordering the frames of the video into a single period, producing a detailed, single cycle video of motion. This problem is challenging, as such videos often contain noise, drift due to camera motion and from cycle to cycle, and irrelevant background motion/occlusions, and these factors can confound the relevant periodic motion we seek in the video. To address these issues in a simple and efficient manner, we introduce a tracking free Eulerian approach for synthesizing a single cycle of motion. Our approach is geometric: we treat each frame as a point in high-dimensional Euclidean space, and analyze the sliding window embedding formed by this sequence of points, which yields samples along a topological loop regardless of the type of periodic motion. We combine tools from topological data analysis and spectral geometric analysis to estimate the phase of each window, and we exploit the sliding window structure to robustly reorder frames. We show quantitative results that highlight the robustness of our technique to camera shake, noise, and occlusions, and qualitative results of single-cycle motion synthesis across a variety of scenarios.