Periodic and Cyclic Motion Analysis

Steve Seitz, Chuck Dyer

Many real-life motions are periodic in some frame of reference. For instance, most human locomotory motions (e.g., walking running, skipping, shuffling) are periodic in a frame of reference that moves with the person. We have developed an approach for determining if an image sequence could have been produced by an object whose motion is periodic in some reference frame. Unlike all previous attempts to determine periodicity information, our approach allows the camera to move during filming. For more information on this work, click here.

Period Trace

This image shows the period trace (red lines) recovered from an image sequence of a phonograph turntable. Ramps correspond to moments in time where the turntable was momentarily slowed. The period trace is shown superimposed on the error surface from which it was recovered.

Real repeating motions tend not to be perfectly even, i.e., the period varies slightly from one cycle to the next, because of physically important changes in the scene. A generalization of period is defined for cyclic motions that makes periodic variation explicit. This representation, called the period trace, is compact and purely temporal, describing the evolution of an object or scene without reference to spatial quantities such as position or velocity. By delimiting cycles and identifying correspondences across cycles, the period trace provides a means of temporally parsing a cyclic motion. In addition, several purely temporal motion features can be derived, relating to the nature and location of irregularities. The period trace can also be used for medical image enhancement by compositing images from different cycles. Furthermore, the period trace can be reliably recovered from image sequences in a view-invariant fashion using a theory of affine invariance. For more information on this work, cick here.

Heart X-ray Image Enhancement

Top: two corresponding angiographic images determined from period trace. Bottom: composite of 5 such corresponding images. Note additional structure visible in composite but not apparent in single raw images.