2.7. Aligning/registering the surfaces

Each reconstructed surface required cropping of extraneous surface detail, such as the surface of the floor, the handler’s arm or the head or limb of the horse. As the surface was located in different regions of the volume and at different orientations across trials, we placed all of the data within a new coordinate system based around the orientation of the horse: with one axis aligned parallel with the horse’s spinal column, another approximately parallel with gravity and the third orthogonal to the plane formed by those vectors, with the origin placed at the caudal spine marker. This coarse initial alignment allowed us to empirically identify a volume relative to that coordinate system that contained only the region of interest and lacked extraneous features that could affect fine-scale alignment. This coarse alignment and cropping of the surface enabled fine-scale alignment or registration using an ‘iterative-closest-point’ algorithm (pcregistericp.m in Mathworks 2022a; The Mathworks, Inc., Natick, USA), which minimized the disparity among surfaces by accounting for small rotations and translations that might exist in the coarse alignment. If we had not cropped extraneous surfaces, such as the floor, they would have biased and misaligned the surfaces of the horse.

After aligning the surfaces at each instant, we interpolated the ‘vertical’ elevation and depression over a 1 cm × 1 cm grid at each point along all of the surfaces. This was necessary as any surface was described at arbitrary locations and was, in effect, just a dense cloud of points, which would not have allowed for quantitative comparisons across surfaces, such as computing mean vertical movement. Once the surfaces were interpolated onto a common grid, we computed the mean surface elevation at each instant and the standard error of the means (s.e.m.) across the surface. Here, s.e. captured behavioural deviation from the mean, as well as errors in identifying the exact same instances in time, aligning or registering the surfaces and measurement error.

Finally, we described how surface elevation changed over the stride relative to the stride average. For walk, the stride-average surface is the average of eight instances evenly spaced in time. For trot, as the eight instances in time were unevenly spaced, we weighted the contribution of each surface by the duration between temporally adjacent instances in the stride to reconstruct the comparable stride-average surface.