Geostatistical and morphological methods applied to three‐dimensional microscopy

Abstract

SUMMARYThree‐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.

Stereology and 3d Microscopy: Useful Alternatives or Competitors in the Quantitative Analysis of Microstructures?

“…As the 3D coordinates are available, all the classical measuring techniques and parameters are readily accessible. 2D image analysis procedures were adopted for 3D analysis (see, for example Decker, Jeulin and Tovena, 1998, Conan et al, 1992, Gratin 1993or Delarue and Jeulin, 2003. It is anticipated that, with special software packages becoming available, parameters offered by mathematical morphology will be applied in 3D more frequently, yielding much more relevant information as that obtained by the usual 2D point processing procedures.…”

Practical limits of the deconvolution of images by kriging

“…However there is little discussion of their efficiency and their limitations, as will be presented in the next part of this paper using simulated images. [2], electron microprobe analysis [3], optical confocal microscopy [4][5][6].…”

“…We limit our discussion to 1-D convolution functions for the sake of simplicity as explained in the practical study presented in [4][5][6]. In practice the following weighting (or "convolution") functions (see Fig.…”

“…In order to make an objective comparison of the methods, the same data sets would have to be processed, such as the simulations used in this paper, so as to estimate the improvement of the SNR ratio. (6). Restoration of the image from the system of weights and calculation of the quality of the deconvolution from the SNR coefficients.…”

“…Once this is done, the next problem is to convolve the image by the appropriate convolution function p. Here this weighting function is derived from the sinc function as in references [4][5][6].…”