Level set-based image segmentation of

A three-dimensional level set-based image segmentation method is presented for a robust identification and accurate characterization of the different cell types defining complex wood micro-structures. The method can be applied to arbitrary wood species, and in this contribution is elaborated for oak. The evolution of the level set function and the corresponding boundary conditions are rigorously derived from a variational framework based on the Local Chan-Vese energy functional. The application of the level-set image segmentation approach enables to distinguish the cell wall material from the cell cavities. The cell material objects are subsequently segmented into axial cell objects and ray parenchyma cell objects that are oriented in the longitudinal and radial material directions of oak wood, respectively. This additional segmentation step facilitates the collection of statistical information on the inner cell dimensions and wall thickness of axial cells and ray parenchyma cells from images taken across principal material planes of the oak micro-structure. The performance and results of the image segmentation method are analyzed by using as input detailed micro-structural images of two representative oak samples containing a single growth ring, as obtained from X-ray micro-computed tomography experiments. The assessment of the robustness and convergence behaviour of the image segmentation method shows that the method converges very fast into a unique oak micro-structure that is independent of the initial configuration selected. The accuracy of the image segmentation result is shown through a comparison with the results obtained by two other image segmentation methods presented in the literature, and by visualizing and identifying small-scale morphological features within oak growth rings in great detail. The computational cost of the image segmentation method is evaluated by comparing its performance on CPU and GPU hardware. Additionally, a statistical analysis is carried out of the maximum and minimum inner cell diameters and the cell wall thickness of the various axial cells-fibers and axial parenchyma, earlywood vessels, latewood vessels-and ray parenchyma cells defining the micro-structure of the oak growth ring samples. The density histograms constructed for these geometrical parameters provide their statistical spread and most frequent value, which are quite similar for the two oak samples and are in good agreement with other experimental data reported in the literature. The oak micro-structures identified and characterized by the present image segmentation method may serve as input for dedicated finite element models that compute their mechanical/physical behaviour as a function of the geometrical and physical properties of the individual cells.