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Multi-Frame Optical Flow Estimation Using Subspace Constraint

Michal Irani.

We show that the set of all flow-fields in a sequence of frames imaging a rigid scene resides in a low-dimensional linear subspace. Based on this observation, we develop a method for simultaneous estimation of optical-flow across multiple frames, which uses these subspace constraints. The multi-frame subspace constraints are strong constraints, and replace commonly used  heuristic constraints, such as spatial or temporal smoothness. The subspace constraints are geometrically meaningful, and are  not violated at depth discontinuities, or when the camera-motion changes abruptly. Furthermore, we show that the subspace constraints on flow-fields  apply for a variety of imaging models, scene models, and motion models. Hence, the presented approach for constrained multi-frame flow 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 3D information (e.g., [Tomasi&Kanade]), it has been assumed that 2D correspondences are given. However, correspondence estimation is a fundamental problem in motion analysis. In this paper, we use multi-frame subspace constraints to constrain  the 2D correspondence estimation process itself, and  not  for 3D recovery.