Robust shape-from-image-focus by 3-D multivariate statistical analyses

Shape-from-focus (SFF) methods involve recovering the topography of an observed object surface by axially maximising (along the optical axis) the sharpness information from a focus measurement throughout a sequence of numerous images acquired by optical sectioning with a limited depth-of-field imaging system. Nevertheless, some noisy data necessarily introduced by imaging equipments during the acquisition provides incorrect information of sharpness and strongly damages the reconstruction process. This paper introduces a new SFF method which, unlike traditional approaches, works in three dimensions throughout the image sequence. It thus simultaneously exploits all axial cues, that allows it to offer a high noise robustness. Comparisons to classical methods and experimental results on both simulated data and real optical microscopy acquisitions clearly demonstrate the efficiency of the proposed method.