Estimating the shape of a moving contour

Most tracking problems in computer vision can be conceptualized as nonlinear estimation problems, with the gray level of each pixel being an observation. We introduce a coordinate system and represent the curve using its horizontal and vertical components, expressed as functions of time and arc length. We introduce continuum models for the evolution of the coordinates and noisy observation models that allow us to formulate and solve a realistic class of estimation problems. One interesting question brought into focus by this work is that of determining how to optimize the use of spatial correlation along the curve, and temporal correlation in the evolution of the curve, so as to reduce the effects of the observation noise