Multiscale integral invariant for motion trajectory matching and recognition

Motion trajectory obtained from visual tracking provides an important clue to help understand motion content. This paper presents a multiscale integral invariant for motion trajectory representation which can be input to a classifier performing motion retrieve, action and gesture recognition. A meaningful integral invariant for motion trajectory under group transformations is first defined on progression of the Frenet-Serret frame with dynamic integral domain that is defined and bounded by the ball kernel function. The corresponding estimation approach is then investigated based on blurred segment of noise discrete curve. Accordingly we develop a multiscale representation of the proposed integral invariant in terms of varying scale radius of ball kernel function, by which the features of motion trajectory can be perceived at multiscale levels in coarse-to-fine manner. Through the experiments, we examine the robustness and effectiveness of our proposed representation being able to capture the motion cues in trajectory matching and gesture recognition. This multiscale integral invariant also benefits the shape representation and matching in both planar and 3D objects recognition.