Size and shape estimation of 3-D convex objects from their 2-D projections: application to crystallization processes
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Updated: May 17, 2026

Assessing Two-dimensional Crystallization Trials of Small Membrane Proteins for Structural Biology Studies by Electron Crystallography
Published on: October 29, 2010
B Presles1, J Debayle, J-C Pinoli
1École Nationale Supérieure des Mines de Saint-Étienne, CIS-SPIN-LPMG/CNRS, 158 cours Fauriel, 42023 Saint-Étienne cedex 2, France.
Abstract:
The aim of this paper is to present a new projective stereological method that enables to estimate the size and the shape of a three-dimensional convex object from measurements only made on its two-dimensional projections. To do so, some geometrical and morphometrical measurements on the projected shadows of the three-dimensional convex object are done and the value of the three-dimensional convex object size and shape parameters are retrieved using the maximum likelihood estimation method. The proposed method is then applied to estimate three-dimensional particle size distributions during crystallization processes.
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