Computation of 3D curvatures on a wet snow sample

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Abstract
The map of 3D curvatures of a porous medium characterizes most of its capillary properties. A model for directly computing curvatures from a three-dimensional image of the solid matrix of a porous medium is presented. A precise distance map of the object is built using the “chamfer” distance of discrete geometry. The set of local maxima of the distance map is used for quick location of the normal to each point P of the object's surface. The normal being known, principal radii of curvature are computed in 2D and lead to 3D curvature. This model was validated on geometric shapes of known curvature, then applied on a natural snow sample. The snow image was obtained from a serial cut (performed in cold laboratory) observed under specularly reflected light. Views of both fresh and sublimated sections were taken for each of the 64 section planes: this allowed easier distinction between snow and filling medium and made possible automatic contouring of section plane images. Curvature maps computed from pore and grain phases respectively were found to be in excellent agreement for each tested object shape, including the snow sample.