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This paper presents a new method for tracking features in video. This method estimates the displacement of a feature between two successive frames by minimizing an error function defined in terms of the feature intensities at these frames. The minimization problem is made analytically tractable by approximating the error function using a second-order Taylor expansion. The displacement between two successive frames is computed in an iterative fashion using gradient descent. The improved reliability of the proposed method is illustrated by its application in the extraction of temporal motor activity signals from video recordings of neonatal seizures.