Comparing and combining sliding semilandmarks and weighted spherical harmonics for shape analysis

Quantifying morphological variation is critical for conducting anatomical research. Three-dimensional geometric morphometric (3D GM) landmark analyses quantify shape using homologous Cartesian coordinates (landmarks). Setting up a high-density landmark set and placing it on all specimens, however, can be a time-consuming task. Weighted spherical harmonics (SPHARM) provides an alternative method for analyzing the shape of such objects. Here we compare sliding semilandmark and SPHARM analyses of the calcaneus of Gorilla gorilla gorilla (n = 20), Pan troglodytes troglodytes (n = 20), and Homo sapiens (n = 20) to determine whether the SPHARM and sliding semilandmark analyses capture comparable levels of shape variation. We also compare both the sliding semilandmark and SPHARM analyses to a novel combination of the two methods, here termed SPHARM-sliding. In SPHARM-sliding, the vertices of the surface models produced from the SPHARM analysis (that are the same in number and relative location) are used as the starting landmark positions for a sliding semilandmark analysis. Calcaneal shape variation quantified by all three analyses was summarized using separate principal components analyses. Results were compared using the root mean square (RMS) and maximum distance between surface models of species averages scaled (up) to centroid size created from each analysis. The average RMS was 0.23 mm between sliding semilandmark and SPHARM average surface models, 0.19 mm between SPHARM and SPHARM sliding average surface models, and 0.22 mm between sliding semilandmark and SPHARM sliding average surface models. Although results indicate that all three analyses are comparable methods for 3D shape analysis, there are advantages and disadvantages to each. While the SPHARM analysis is less time-intensive, it is unable to capture the same level of detail around the sharp edges of articular facets on average surface models as the sliding semilandmark analysis. The SPHARM analysis also does not allow for individual articular facets to be analyzed in isolation. SPHARM-sliding, however, captures the same level of detail as the sliding semilandmark analysis, and (as in the sliding semilandmark analysis) allows for the evaluation of individual portions of bone. SPHARM is a comparable method to a 3D GM analysis for small, irregularly shaped bones, such as the calcaneus, and SPHARM-sliding allows for an expedited set up process for a sliding semilandmark analysis.