Robust 3-D reconstruction of surfaces from image focus by local cross-sectional multivariate statistical analyses: Application to human ex vivo corneal endotheliums

The considered problem of 3-D reconstruction consists in computationally and passively recovering both topography and texture of a scene surface observed by optical sectioning with a limited depth-of-field imaging system (typically a conventional optical microscope). Throughout a sequence of registered 2-D images, the concepts of shape-from-focus and extended-depth-of-field involve recovering both topography (depth map) and texture image of the surface by researching in-focus information, respectively. Toward that aim, traditional approaches generally follow a 2-D sectional way and thereby fail to deal with noisy and disturbed acquisitions, quite frequent in transmitted light observations and of interest in this paper. Such examples are the acquisitions of human ex vivo corneal endotheliums from the medical issue addressed in this paper, which are mainly damaged by cellular fragments in the sample immersion medium and by emphasized contrast reversals. To achieve with such noisy and disturbed acquisitions, a new focus analysis is introduced that originally adopts a 3-D strategy throughout the image sequence. This method exploits simultaneously all available cross-sectional cues that effectively strengthens the robustness. More precisely, it locally performs multivariate statistical analyses over cross-sectional spatial windows so as to find sectional in-focus positions. Comparisons to state-of-the-art methods on both synthetic data and real acquisitions from the deal-with medical issue demonstrate the efficiency and the robustness of the proposed approach.

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► An image sequence of the surface is acquired by optical sectioning.
► A new robust 3-D focus measurement is proposed.
► Both topography and textural information is recovered.
► Comparisons to classical methods are performed.
► The surfaces of human corneal endotheliums are reconstructed.