Recursive estimation of time-varying motion and structure parameters

We present a computational framework for recovering both 1 st-order motion parameters (observer direction of translation and observer rotation), 2 nd-order motion parameters (observer rotational acceleration) and relative depth maps from time-varying optical ow. We recover translation speed and acceleration in units which are scaled relative to the distance to the object. Our assumption is that the observer rotational motion is no more than \second order"; in other words, observer motion is either constant or has at most constant acceleration. We examine the eeect of noise on the solution of the motion and structure parameters. This ensemble of unknowns comprises a solution to the classicaìstructure-and-motion from optic ow' problem. Our complete framework utilizes a method for interpreting the bilinear image velocity equation by solving simple systems of linear equations. Since our noise analysis yields uncertainty measures for each parameter, a Kalman lter is employed to incrementally integrate new measurements as they become available as each additional frame in the sequence is processed. We conclude by analyzing this reduction of uncertainty over time as the system converges to a stable solution for both synthetic and real image sequences.