`Dynamism of a Dog on a Leash' or Behavior Classiÿcation by Eigen-Decomposition of Periodic Motions

Following Futurism, we show how periodic motions can be represented by a small number of eigen-shapes that capture the whole dynamic mechanism of periodic motions. Spectral decomposition of a silhouette of an object in motion serves as a basis for behavior classiÿcation by principle component analysis. The boundary contour of the walking dog, for example, is ÿrst computed eÆciently and accurately. After normalization, the implicit representation of a sequence of silhouette contours given by their corresponding binary images, is used for generating eigen-shapes for the given motion. Singular value decomposition produces these eigen-shapes that are then used to analyze the sequence. We show examples of object as well as behavior classiÿcation based on the eigen-decomposition of the binary silhouette sequence.