State-Space Optical Flow

| Optical ow estimators of motion in image sequences are sometimes found using varia-tional frameworks, which produce partial diierential equations as the estimators. In this paper, we show that certain state-space formulations, solved by linear smoothing theory, lead to these same solutions. The advantages of viewing these problems in this way include explicit stochastic motion models, a priori error measures, and alternate ways to choose regularization parameters. In this paper, we cast the algorithm of Horn and Schunk and that of Gennert and Negahdaripour and the newer DIV-CURL spline formulations in this fashion, with care taken to form well-posed models. Finally, we demonstrate one important use of these models, which is the simulation of the motion elds for which the algorithms are optimal.