Periodic motion is quite common in our everyday experience, and some of the most frequent and interesting examples arise from natural human motions such as walking and running. It has been recognized as an important cue in the literature by researchers interested in various areas, such as activity recognition and gait analysis, among others. However, since monocular systems are far more commonplace than multi-camera observations, existing techniques for analyzing periodicities are largely image-based. This typically implies a lack of view-invariance, since the same motion can have a drastically different appearance in the image if viewed from a different angle.
One way to address this is to first infer the characteristics of the motion in 3D, and then any subsequent analysis is performed in world coordinates, independent of the viewing angle from which the motion was originally imaged. In this thesis, we explore the idea of reconstructing periodic motions in 3D from a single camera, given only their appearances in image coordinates, along with the known physical constraints of periodicity. It is shown that such reconstructions are both possible to obtain and accurate in realistic settings, and that they contain useful information. Two different formulations of this reconstruction problem are presented, as well as theoretical results which guarantee solvability under different conditions. It is shown that natural human motions can be effectively reconstructed, allowing them to be analyzed in 3D world coordinates, and opening the door to a variety of applications.