D5 Photogrammetry and 3D kinematic reconstruction

Topic

High-speed photogrammetry is a technique that reconstructs the three-dimensional shape and kinematics of a fish's body using synchronized images captured by multiple high-speed cameras capable of recording between five hundred and ten thousand frames per second. Unlike the particle image velocimetry technique described earlier in this series—which measures fluid movement around the fish—high-speed photogrammetry measures the movement of the fish's solid body itself.

To reconstruct the three-dimensional shape of the fish's body, high-speed photogrammetry follows one of two approaches: either it detects control points on the fish's body—such as markers painted on the skin or recognizable anatomical landmarks—and triangulates them stereoscopically, much like triangulating the position of an entire fish during the 3D swimming tracking described earlier in this series; or it reconstructs the fish's full body silhouette based on the silhouettes projected by the body onto each camera's view.

In this second approach, each camera defines a visual cone: the region of space that, when projected onto that camera, falls within the silhouette of the fish's body observed in its image. The intersection of the visual cones from all cameras defines the visual volume of the fish's body—that is, the maximum possible volume consistent with all the silhouettes observed from the various cameras.

To obtain the complete kinematics of the fish's body, high-speed photogrammetry repeats this shape reconstruction for each successive frame and tracks the position of each point or body segment over time. The deformation of the fish's body surface during swimming—known as the kinematic wave—is quantified by fitting a deformable surface model to the point cloud generated by the reconstruction at each instant. Based on this three-dimensional body kinematics, calculations are made for the amplitude of the wave traveling along the fish's body at any given point and time, the speed at which that kinematic wave moves along the body, the Strouhal number, and other relevant propulsive parameters. When combined with the computational fluid dynamics described earlier in this series, high-speed photogrammetry provides the precise body-deformation boundary conditions required by the simulation to calculate the resulting hydrodynamic forces acting on the fish.

The advantage of reconstructing this body kinematics in three dimensions—rather than solely in the lateral plane—is that it reveals movements occurring outside that plane which a two-dimensional lateral analysis would underestimate or fail to detect entirely; this is particularly evident during turning maneuvers or when the fish swims within a disturbed flow. Thus, the very same high-speed photogrammetry—initially described as a technique capable of measuring the movement of the fish's solid body rather than just the surrounding fluid—ultimately reveals a richness of body movement that simpler two-dimensional tracking techniques overlook.

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