D13 3D kinematic analysis

Topic

The three-dimensional movement of an insect's wing during flight can be reconstructed without touching the insect by simultaneously combining footage from several calibrated high-speed cameras; this is the function of 3D kinematic analysis, which reconstructs the wing's motion based on the individual views captured by each camera.

The Direct Linear Transformation technique addresses the limitation wherein a single camera can only project the wing's 3D motion onto a 2D image plane, thereby losing information regarding the wing's depth relative to the camera; consequently, at least two distinct views of the same wing movement—captured from different angles—are required to recover this lost depth data and reconstruct the full three-dimensional motion.

Before these camera views can be combined, each camera must be calibrated using a checkerboard pattern with precisely known geometry; this process allows for the determination of both intrinsic parameters (such as focal length, principal point, and specific optical distortions) and extrinsic parameters (the camera's exact position and orientation relative to the others).

The quality of each camera's calibration is validated using the reprojection error; when this error remains below half a pixel, the calibration is sufficiently precise to ensure that the 3D reconstruction of the wing's motion has an uncertainty of less than one millimeter.

Once the cameras are calibrated in this manner, markers placed directly on the insect's wing—whether passive markers (points painted with reflective ink) or active ones (tiny miniature lights)—enable the tracking of Euler angles in every captured frame, thereby describing the wing's exact orientation at any given moment. The angles resulting from this tracking—the stroke, elevation, and wing rotation angles—are not an end in themselves; rather, they serve as the primary input required by unsteady aerodynamics and wing-beat mechanics models to calculate, based on this three-dimensionally reconstructed wing motion, the forces and torques generated by that movement during insect flight.

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