Three-dimensional Voronoï imaging methods for the measurement of near-wall particulate flows

Abstract

A set of stereoscopic imaging techniques is proposed for the measurement of rapidly flowing dispersions of opaque particles observed near a transparent wall. The methods exploit projective geometry and the Voronoı diagram. They rely on purely geometrical principles to reconstruct 3D particle positions, concentrations, and velocities. The methods are able to handle position and motion ambiguities, as well as particle-occlusion effects, difficulties that are common in the case of dense dispersions of many identical particles. Fluidization cell experiments allow validation of the concentration estimates. A mature debris-flow experimental run is then chosen to test the particle-tracking algorithm. The Voronoı ¨stereo methods are found to perform well in both cases, and to present significant advantages over monocular imaging measurements.

Stereoscopic and velocimetric reconstructions of the free surface topography of antidune flows

“…Conversely, a point having image coordinates (X (V) , Y (V) ) under viewpoint V belongs to a 3D ray defined by parametric equation ð3a; bÞ A least squares camera calibration procedure is needed to obtain matrix A (V) and vector b (V) for each viewpoint, as explained in more detail in Spinewine et al (2003). In the present experiments, each of the viewpoints V=L, R and T is calibrated using some 200 points of known world and image coordinates.…”

Enhanced upswing in immersed collisions of tethered spheres

“…The centroids of the screw heads mounted on both sides of each sphere are extracted from synchronized images ͑resolution 778ϫ 1032 pixels͒ acquired at frame rate 20 Hz. Their three-dimensional positions are then determined by ray intersection 9 followed by a distortion correction, yielding a spatial accuracy of 0.6 mm. Excursions left and right of the plane of swing due to lateral sway do not exceed 4 mm.…”

An adaptive discretization of shallow‐water equations based on discontinuous Galerkin methods

“…The experiments were performed at the Civil Engineering Department of the Università e catholique de Louvain (Belgium), on the set-up sketched in Figure 11 The friction coe cient n of (9) was chosen as n = 0:01. Two types of ow measurements were performed: Water level and velocity at 5 gauging points, and ÿeld data using a Vorono imaging technique [26,27]. This latter technique, initially developed for dense granular ow measurements, was used to obtain the experimental pictures that are compared to the computations in some of the following ÿgures.…”