Geostatistical and morphological methods applied to three‐dimensional microscopy

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Abstract
Three‐dimensional (3‐D) images of osteocyte lacunae were examined on a confocal microscope. Both geostatistical and morphological processing techniques were used to improve and to analyse them. By a geostatistical approach, this study aims at improving 3‐D confocal images before any further image processing. Optimized linear filters, which take account of the second‐order statistics and the 3‐D structure of the data, allow for the removal of imperfections such as noise and/or blur due to the axial convolution, and interpolate voxels on a face‐centred cubic grid from an initial cubic grid. An application of this technique to 3‐D biological images is demonstrated. In a second step, a 3‐D binary image is digitized and cleaned with 3‐D morphological filters. The standard 3‐D measurements cannot be applied in this case, since all osteocytes cut the border of the field. For this reason a 3‐D Boolean model has been adjusted, from which it is possible to derive all useful information on the repartition and the morphology of the osteocytes.