Capturing human activity by a curve

One of the main challenges of human behavior analysis is the high dimensionality of the representation space. In shape representation, however, a specific human behavior may naturally be described by a 1D path which lies in shape space. According to Whitney Embedding Theorem, such a 1D manifold may be embedded in R3. Motivated by the potential of reducing the dimensionality of behavior representation, we construct an embedding to map the path of evolution of the silhouette in shape space to a representational curve in R3. In contrast to other behavioral embedding, where each point of the path in shape space is projected to lower dimension, we embed the homotopy function of the whole path to be a planar curve function. The proposed embedding utilizes sampling theory to provide computational efficiency and simple reconstruction from the embedding space. Upon validating such a representation, we proceed to model different activities by an AR model of the representative curve. Experiments are provided to illustrate our technique and to demonstrate its viability.