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This paper presents the development of regularized optical flow computation methods and an evaluation of their performance in the extraction of quantitative motion information from video recordings of neonatal seizures. A general formulation of optical flow computation is presented and a mathematical framework for the development of practical tools for computing optical flow is outlined. In addition, this paper proposes an alternative formulation of the optical flow problem that relies on a discrete approximation of a family of quadratic functionals. These regularized optical flow computation methods are used to extract motion strength signals from video recordings of neonatal seizures.