Multi-camera orientation tracking method for anisotropic particles in particle-laden flows

TL;DR

This work presents a silhouette-based, quaternion-guided orientation tracking method for anisotropic particles imaged with multiple high-speed cameras. By constructing a library of synthetic projections from known orientations and optimizing against experimental silhouettes with Nelder–Mead, the method yields 3D position and orientation while correcting the center of mass projection. The approach supports flexible camera configurations and simultaneous tracking of multiple particle types, with rigorous robustness analysis across noise, image size, and camera setup, validated on chiral particles, tetrads, and oloids in both quiescent and turbulent flows. The results demonstrate accurate orientation estimation (mean errors on the order of $0.1^{\circ}$ under favorable imaging) and broad applicability to Lagrangian studies of complex particle dynamics in fluids.

Abstract

A method for particle orientation tracking is developed and demonstrated specifically for anisotropic particles. Using (high-speed) multi-camera recordings of anisotropic particles from different viewpoints, we reconstruct the 3D location and orientation of these particles using their known shape. This paper describes an algorithm which tracks the location and orientation of multiple anisotropic particles over time, enabling detailed investigations of location, orientation, and rotation statistics. The robustness and error of this method is quantified, and we explore the effects of noise, image size, the number of used cameras, and the camera arrangement by applying the algorithm to synthetic images. We showcase several use-cases of this method in several experiments (in both quiescent and turbulent fluids), demonstrating the effectiveness and broad applicability of the described tracking method. The proposed method is shown to work for widely different particle shapes, successfully tracks multiple particles simultaneously, and the method can distinguish between different types of particles.

Figures (22)

• Figure 1: a) A photo of several 3D printed anisotropic particles tracked using the described method. From left to right, back to front: tetrad, oloid left-handed chiral particle, right-handed chiral particle. b) Synthetic 3D images of the used particles. From left to right: tetrad, left-handed chiral particle, right-handed chiral particle, oloid (not to scale). c) 3D sketch of the oloid geometry. The convex hull ('shrink-wrapping') of the two perpendicular disks gives the oloid surface. The grey lines span from one disk to the other, indicating the oloid surface.
• Figure 2: Illustrated workflow of the orientation tracking algorithm, describing the order of steps taken in the determination of the particle orientation.
• Figure 3: Top view illustration of cameras viewing a particle using camera rays (particle not to scale) inside a Taylor-Couette geometry. Note that the calibration accounts for diffraction at the air-outer cylinder, and outer cylinder-water interfaces.
• Figure 4: a) A 3D representation of the cameras viewing a chiral particle. The cameras are set up as in the Taylor--Couette geometry described in section \ref{['sec:Application']}. The curved black surface represents the inner cylinder of the Taylor--Couette. Graphic not to scale. b) The particle as viewed by the four cameras in 3D (shown in the top row), and its projections (shown in the bottom row).
• Figure 5: Basic steps of the tracking algorithm. The left figure shows the complete raw image for one of the cameras. The top-right figure shows an extracted particle from the raw image. The middle-right figure shows the binarised particle. The bottom-right figure shows a projection of the optimised orientation of this particle.