Shape recognition from shadows of 3-D convex geometrical objects

The aim of this article is to present a new projective stereological method which enables to estimate the size and the shape of a three-dimensional (3-D) convex geometrical object from measurements only made on some of its two-dimensional (2-D) projections. In order to do so, some geometrical and morphometrical measurements on the projected shadows of the 3-D convex object are done and the size and shape parameter values of the 3-D convex geometrical object are retrieved using the maximum likelihood estimation method. After several validation tests on synthetic 3-D convex objects, the proposed method is successfully applied to estimate the 3-D particle volume distribution during crystallization processes.