Refraction corrected calibration for aquatic locomotion research: application of Snell's law improves spatial accuracy.

Images of underwater objects are distorted by refraction at the water-glass-air interfaces and these distortions can lead to substantial errors when reconstructing the objects' position and shape. So far, aquatic locomotion studies have minimized refraction in their experimental setups and used the direct linear transform algorithm (DLT) to reconstruct position information, which does not model refraction explicitly. Here we present a refraction corrected ray-tracing algorithm (RCRT) that reconstructs position information using Snell's law. We validated this reconstruction by calculating 3D reconstruction error-the difference between actual and reconstructed position of a marker. We found that reconstruction error is small (typically less than 1%). Compared with the DLT algorithm, the RCRT has overall lower reconstruction errors, especially outside the calibration volume, and errors are essentially insensitive to camera position and orientation and the number and position of the calibration points. To demonstrate the effectiveness of the RCRT, we tracked an anatomical marker on a seahorse recorded with four cameras to reconstruct the swimming trajectory for six different camera configurations. The RCRT algorithm is accurate and robust and it allows cameras to be oriented at large angles of incidence and facilitates the development of accurate tracking algorithms to quantify aquatic manoeuvers.

Model-based RSA of a femoral hip stem using surface and geometrical shape models.

Roentgen stereophotogrammetry (RSA) is a highly accurate three-dimensional measuring technique for assessing micromotion of orthopaedic implants. A drawback is that markers have to be attached to the implant. Model-based techniques have been developed to prevent using special marked implants. We compared two model-based RSA methods with standard marker-based RSA techniques. The first model-based RSA method used surface models, and the second method used elementary geometrical shape (EGS) models. We used a commercially available stem to perform experiments with a phantom as well as reanalysis of patient RSA radiographs. The data from the phantom experiment indicated the accuracy and precision of the elementary geometrical shape model-based RSA method is equal to marker-based RSA. For model-based RSA using surface models, the accuracy is equal to the accuracy of marker-based RSA, but its precision is worse. We found no difference in accuracy and precision between the two model-based RSA techniques in clinical data. For this particular hip stem, EGS model-based RSA is a good alternative for marker-based RSA.