3D Reconstruction of Periodic Motion from a Single View

Periodicity has been recognized as an important cue for tasks like activity recognition and gait analysis. However, most existing techniques analyze periodic motions only in image coordinates, making them very dependent on the viewing angle. In this paper we show that it is possible to reconstruct a periodic trajectory in 3D given only its appearance in image coordinates from a single camera view. We draw a strong analogy between this problem and that of reconstructing an object from multiple views, which allows us to rely on well-known theoretical results from the multi-view geometry domain and obtain significant guarantees regarding the solvability of the estimation problem. We present two different formulations of the problem, along with techniques for performing the reconstruction in both cases, and an algorithm for estimating the period of motion from its image-coordinate trajectory. Experimental results demonstrate the feasibility of the proposed techniques.