Abstract
The calibration of a multi-camera system for volumetric measurements is a basic requirement of reliable 3D measurements and object tracking. In order to refine the precision of the mapping functions, a new, tomographic reconstruction-based approach is presented. The method is suitable for Volumetric Particle Image Velocimetry (PIV), where small particles, drops or bubbles are illuminated and precise 3D position tracking or velocimetry is applied. The technique is based on the 2D cross-correlation of original images of particles with regions from a back projection of a tomographic reconstruction of the particles. The off-set of the peaks in the correlation maps represent disparities, which are used to correct the mapping functions for each sensor plane in an iterative procedure. For validation and practical applicability of the method, a sensitivity analysis has been performed using a synthetic data set followed by the application of the technique on Tomo-PIV measurements of a jet-flow. The results show that initial large disparities could be corrected to an average of below 0.1 pixels during the refinement steps, which drastically improves reconstruction quality and improves measurement accuracy and reliability.
Highlights
Volumetric measurement based on distributed multi-camera systems requires a proper calibration.Typical methods to calibrate the system include the estimation of the parameters of the lenses and image sensor positions in the form of a mapping matrix, which is based on the parametric description of the imaging in the form of a pinhole camera model where the parameters were gained from imaging a calibration target
This study presents a new approach to enhance or refine an initial multi-camera calibration based on particle images
The initial total volume, represented as a voxel-based grid, is generated from the parameters of an initial classical calibration procedure. This volume is subdivided into smaller cuboids (Interrogation Volumes interrogation volumes (IVs)) for each of which a back-projection into the camera planes is calculated
Summary
Volumetric measurement based on distributed multi-camera systems requires a proper calibration. Disparities are calculated based on their distance away from the theoretical crossing of the epipolar lines in the image plane and those are used to correct the initial calibrations. The projection of a particle from the world coordinate system into the image plane is described mathematically for each camera via its mapping functions—see the equations given in Appendix B. The proposed method aims to correct the disparities in the image planes (and the mapping functions) such that the LOSs intersect again and the spherical character of the particles is fully restored. Gray solid lines show the LOSs for perfect initial calibration, which cross in the true particle world camera. Gray solid lines show the LOSs for perfect initial calibration, which cross in the true particle coordinate in the center of gravity. The mismatch correction can be done by left correcting only left camera or all cameras simultaneously
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