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Adenoviruses (Ad) and other DNA viruses induce extensive reorganization of the cell nucleus and formation of nuclear Replication Compartments (RCs), where the viral genome is replicated and expressed. In this work an automatic algorithm designed for detection and segmentation of RCs using ellipses is presented. Unlike algorithms available in the literature, this approach is deterministic, automatic, and can adjust multiple RCs using ellipses. The proposed algorithm is non iterative, computationally efficient and is invariant to affine transformations. The method was validated over both synthetic images and more than 400 real images of Ad-infected cells at various timepoints of the viral replication cycle obtaining relevant information about the biogenesis of adenoviral RCs. 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