Multi-Frame Optical Flow Estimation using Subspace Constraints

We show that the set of all ow elds in a se quence of frames imaging a rigid scene resides in a low dimensional linear subspace Based on this observa tion we develop a method for simultaneous estimation of optical ow across multiple frames which uses these subspace constraints The multi frame subspace con straints are strong constraints and replace commonly used heuristic constraints such as spatial or temporal smoothness The subspace constraints are geometri cally meaningful and are not violated at depth discon tinuities or when the camera motion changes abruptly Furthermore we show that the subspace constraints on ow elds apply for a variety of imaging models scene models and motion models Hence the presented ap proach for constrained multi frame ow estimation is general However our approach does not require prior knowledge of the underlying world or camera model Although linear subspace constraints have been used successfully in the past for recovering D information e g it has been assumed that D correspon dences are given However correspondence estimation is a fundamental problem in motion analysis In this paper we use multi frame subspace constraints to con strain the D correspondence estimation process itself and not for D recovery