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In this paper, we consider a novel low-complexity real-time image-processing-based approach to the detection of neonatal clonic seizures. Our approach is based on the extraction, from a video of a newborn, of an average luminance signal representative of the body movements. Since clonic seizures are characterized by periodic movements of parts of the body (e.g., the limbs), by evaluating the periodicity of the extracted average luminance signal it is possible to detect the presence of a clonic seizure. The periodicity is investigated, through a hybrid autocorrelation-Yin estimation technique, on a per-window basis, where a time window is defined as a sequence of consecutive video frames. While processing is first carried out on a single window basis, we extend our approach to interlaced windows. The performance of the proposed detection algorithm is investigated, in terms of sensitivity and specificity, through receiver operating characteristic curves, considering video recordings of newborns affected by neonatal seizures.