Comparing the coherent point drift algorithm to sliding semilandmark and weighted spherical harmonic whole‐bone three‐dimensional shape analyses

The ability to quantify 3D morphologies is critical for anatomical research; however, setting up high‐density landmark sets and positioning them on all specimens can represent a substantial challenge. The coherent point drift (CPD) algorithm, a technique for registering two point clouds based on the Gaussian mixture model, was recently used to investigate human variation; however, its performance has yet to be compared to other 3D shape analysis methods. Here we compare the results of a CPD analysis to a sliding semilandmark and weighted spherical harmonic (SPHARM) analysis of the same 60 human and African ape calcanei and a CPD analysis and SPHARM‐sliding analysis (a combination SPHARM and sliding semilandmark analysis) of 40 primate third manual proximal phalanges (mPP3s) to determine methodological comparability. Additionally, we run a CPD analysis on a small but wide‐ranging sample of primate ulnae to demonstrate its utility for proximodistally long and mediolaterally narrow long bones. All specimens were surface or micro‐CT scanned. All calcanei were subjected to a CPD analysis with 2000 semilandmarks, a sliding semilandmark analysis with 1007 semilandmarks, and a SPHARM analysis. All mPP3s underwent a CPD analysis with 2500 semilandmarks and a SPHARM‐sliding analysis with 2562 semilandmarks. For the ulna, a CPD analysis with 1252 semilandmarks was run. Shape variation for all analyses was summarized using (separate) principal component analyses (PCAs). Results of the respective analyses for the calcaneus and mPP3 were compared by calculating the maximum and root mean square distances (RMSD) between average taxon shape configurations (scaled based on centroid size) generated from each analysis. All three calcaneus analyses separate taxa along the first two PCs, with humans separating from African apes along PC1 and chimpanzees and gorillas separating across PC2. For the two mPP3 analyses, the three great ape taxa consistently separate along PC1, and Papio separates from the other taxa along PC2. The average RMSD between CPD and sliding semilandmark analyses for the calcaneus was 0.24 mm, and 0.21 mm between CPD and SPHARM analyses. For the mPP3, the average RMSD between CPD and SPHARM‐sliding was 0.14 mm. These results indicate that CPD is a comparable 3D shape analysis method to these other approaches. The CPD analysis was also able to place a semilandmark set on primate ulnae ranging from gorillas to tarsiers and capture morphological variations including shaft curvature, relative olecranon process length, and overall robusticity. CPD analyses are less time intensive than sliding semilandmark analyses; however, the sliding semilandmark analysis was better able to capture variation surrounding the borders of the articular facets (although differences were relatively minor), suggesting that these analyses may be better suited when the researcher is interested in a specific anatomical feature. CPD did capture edges better than SPHARM analyses; however, this is likely not an issue for small, relatively round bones such as carpals and most tarsals. In sum, CPD produces similar results to sliding semilandmark, SPHARM, and SPHARM‐sliding approaches and has benefits for analyses of long bones with complex morphologies or among taxa that exhibit large amounts of morphological variation.