Estimation of the influence of second- and third-order moments on random sets reconstructions

Abstract To characterize a random image, we often limit ourselves to the use of two functions. The first one is the histogram, or grey-level distribution, the other is the covariance function which allows the study of the spatial grey level distribution. One evaluation of the relevance of these two functions to describe the morphology of images is presented. Especially, we show the importance of having recourse to the centered third-order moment, in addition to these two functions, to obtain a fine characterization of images. This study is done for binary random images generated from the same primary grains (Poisson polygons or discs) that are implanted in different ways. We simulate with the Gagalowicz's procedure some textures respecting the same second- or third-order moments. We study the resemblance, in term of the morphology described with erosion and dilation curves and with granulometry by opening and pseudo-granulometry by closing (with squares). The analysis of the results of these measurements is carried out with the help of correspondence analysis that allows a quantitative and qualitative approach of the differences of morphology.

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