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Mapping Material Distribution in a Heterogeneous Sand Tank by Image Analysis

^a Rock-Water Interaction Group, Institute of Geological Sciences, Univ. of Bern, Baltzerstrasse 1-3, CH-3012 Bern, Switzerland, and Paul Scherrer Institut, CH-5232 Villigen, Switzerland
^b Univ. of Padova, Dep. IMAGE, Padova, Italy

View larger version (8K): [in a new window]   Fig. 1. Shapes of filters (filter windows) used in the classification procedure: (a) Window for the adaptive, layer shaped filter to smooth the gray values and estimate local coefficients of variation in Step B; (b) window for the adaptive, layer shaped filter to smooth the classified sand pattern in Step K; (c) structuring element centered at x for the closing operations in Step E.

View larger version (136K): [in a new window]   Fig. 2. Features (coefficient of variation, median of gray values) of calibration samples for various degrees of preprocessing. For (a) to (c) the features were extracted from a five by five square filter window, for (d) from the layer shaped window shown in Fig. 1a. (a) Uncorrected image; (b) image corrected for inhomogeneous illumination by flat fielding with a gray cardboard; (c) image (b) corrected also for inhomogeneous reflection by bootstrap method; (d) same as image (c), but the features were evaluated for the layer shaped filter window of Fig. 1a. The large symbols indicate means and the horizontal and vertical bars standard deviations; the contour lines encompass about 75, 50, and 25% of the data of each sand. The standard deviations and contour lines are drawn in white for coarse and in black for the other sands.

View larger version (123K): [in a new window]   Fig. 3. (a) Uncorrected reflection image of the sand tank; (b) estimated material map; (c) designed filling pattern. Coarse sand is indicated as dark gray, fine sand as white, and very fine sand as medium gray. Areas not classified in (b), or with no sand or a mixture of all sands in (c), are black. The white frames show the inner sections that were analyzed for averages. Note the slight horizontal stretching and vertical offset of the realized as compared to the designed pattern.

View larger version (37K): [in a new window]   Fig. 4. Comparison of horizontal average profiles of estimated and designed sand fractions for (a) coarse, (b) fine, and (c) very fine sand.

View larger version (31K): [in a new window]   Fig. 5. Comparison of vertical average profiles of estimated and designed sand fractions for (a) coarse, (b) fine, and (c) very fine sand.