Abstract

Obtaining accurate experimental data from Lagrangian tracking and tomographic velocimetry requires an accurate camera calibration consistent over multiple views. Established calibration procedures are often challenging to implement when the length scale of the measurement volume exceeds that of a typical laboratory experiment. Here, we combine tools developed in computer vision and non-linear camera mappings used in experimental fluid mechanics, to successfully calibrate a four-camera setup that is imaging inside a large tank of dimensions sim 10 times 25 times 6 ; mathrm {m}^3. The calibration procedure uses a planar checkerboard that is arbitrarily positioned at unknown locations and orientations. The method can be applied to any number of cameras. The parameters of the calibration yields direct estimates of the positions and orientations of the four cameras as well as the focal lengths of the lenses. These parameters are used to assess the quality of the calibration. The calibration allows us to perform accurate and consistent linear ray-tracing, which we use to triangulate and track fish inside the large tank. An open-source implementation of the calibration in Matlab is available.Graphic abstract

Highlights

  • New studies in biophysics and fluid mechanics require the quantitative imaging of large-scale field experiments

  • We combine the pinhole camera model (Tsai 1987) with non-linear polynomial camera mappings used in experimental fluid mechanics (Soloff et al 1997) to perform a multiple camera calibration over a large-scale measurement volume inside the tank of the aquarium located in the Rotterdam zoo

  • Our method is of particular interest to large-scale fields experiments, when spatial access to the measurement volume is limited and laboratory equipment to precisely position the target cannot be installed

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Summary

Introduction

New studies in biophysics and fluid mechanics require the quantitative imaging of large-scale field experiments. We combine the pinhole camera model (Tsai 1987) with non-linear polynomial camera mappings used in experimental fluid mechanics (Soloff et al 1997) to perform a multiple camera calibration over a large-scale measurement volume inside the tank of the aquarium located in the Rotterdam zoo. We apply the planar checkerboard calibration technique by Zhang (2000), see Zhang (1998, 1999), Sturm and Maybank (1999), Menudet et al (2008) and Bouguet (2015) This approach eliminates the need to accurately position the calibration target, as required in conventional calibration procedures. By sequentially acquiring multiple calibration images while freely moving the calibration target, we achieve a camera calibration that spans over length scales much larger than the calibration target itself This approach yields an accurate calibration over the measurement volume with a characteristic length scale on the order of several tens of meters. The method is versatile and can be implemented in field experiments over large length scales and for measurement volumes that are challenging to access experimentally

Camera setup and calibration procedure
Image processing
Distortion correction
Page 4 of 12
Single‐camera calibration
Multiple‐camera calibration
Assessment of the calibration method
Intrinsic and extrinsic camera parameters
Page 6 of 12
Convergence and robustness
Spatial accuracy of the camera calibration
Application to field experiments
Conclusion
Compliance with ethical standards
Page 10 of 12
A: Optical distortion across an interface
B: Relative camera positioning from calibrated views
D: Magnification of the distortion map
E: Point triangulation and skewness
Findings
Page 12 of 12
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