Estimating the distribution of 3D generalized cylinders angles from an image

Abstract

The use of 3D imaging techniques is a choice approach for the study of the inner structure of materials. However, for large industrial applications, the stereological analysis of 2D snapshots of material sections is still necessary for obvious time and cost reasons. We present a novel method to analyze the 3D layout of cylindrical structures from a single 2D section. In particular we propose to estimate the distribution of cutting angles i.e. angles between the cylinders axis and the normal to the image plane. Contrary to existing approaches, the knowledge of the cylinder cross section shape is not a prerequisite. The only required input is the statistical distribution of the cylinder cross section area. Our approach is based on the minimization of a least squares criterion under linear constraints. It is evaluated on synthetic data and applied to microscopy images of fibrous composites. Our experimental study focuses on the capabilities and limitations of the approach.