A differential geometric approach to representing the human actions

This paper presents a novel representation for human actions which encodes the variations in the shape and motion of the performing actor. When an actor performs an action, at each time instant, the outer object boundary is projected to the image plane as a 2D contour. A sequence of such contours forms a 3D volume in the spatiotemporal space. The differential geometric analysis of the volume surface results in a set of action descriptors. These descriptors constitute the action sketch which is used to represent the human actions. The action sketch captures the changes in the shape and motion of the performing actor in an unified manner. Since the action sketch is obtained from the extrema of the differential geometric surface features, it is robust to viewpoint changes. We demonstrate the versatility of the action sketch in the context of action recognition, which is formulated as a view geometric similarity problem.