TY - JOUR
UR - https://doi.org/10.7287/peerj.preprints.27270v1
DO - 10.7287/peerj.preprints.27270v1
TI - Alpha shapes: Determining 3D shape complexity across morphologically diverse structures
AU - Gardiner,James D
AU - Behnsen,Julia
AU - Brassey,Charlotte A
DA - 2018/10/10
PY - 2018
KW - shape complexity
KW - alpha shapes
KW - baculum
KW - morphometrics
AB -
Background. Following recent advances in bioimaging, high-resolution 3D models of biological structures are now generated rapidly and at low-cost. To utilise this data to address evolutionary and ecological questions, an array of tools has been developed to conduct 3D shape analysis and quantify topographic complexity. Here we focus particularly on shape techniques applied to irregular-shaped objects lacking clear homologous landmarks, and propose the new ‘alpha-shapes’ method for quantifying 3D shape complexity.
Methods. We apply alpha-shapes to quantify shape complexity in the mammalian baculum as an example of a morphologically disparate structure. Micro- computed-tomography (μCT) scans of bacula were conducted. Bacula were binarised and converted into point clouds. Following application of a scaling factor to account for absolute differences in size, a suite of alpha-shapes was fitted to each specimen. An alpha shape is a formed from a subcomplex of the Delaunay triangulation of a given set of points, and ranges in refinement from a very coarse mesh (approximating convex hulls) to a very fine fit. ‘Optimal’ alpha was defined as the degree of refinement necessary in order for alpha-shape volume to equal CT voxel volume, and was taken as a metric of overall shape ‘complexity’.
Results Our results show that alpha-shapes can be used to quantify interspecific variation in shape ‘complexity’ within biological structures of disparate geometry. The ‘stepped’ nature of alpha curves is informative with regards to the contribution of specific morphological features to overall shape ‘complexity’. Alpha-shapes agrees with other measures of topographic complexity (dissection index, Dirichlet normal energy) in identifying ursid bacula as having low shape complexity. However, alpha-shapes estimates mustelid bacula as possessing the highest topographic complexity, contrasting with other shape metrics. 3D fractal dimension is found to be an inappropriate metric of complexity when applied to bacula.
Conclusions. The alpha-shapes methodology can be used to calculate ‘optimal’ alpha refinement as a proxy for shape ‘complexity’ without identifying landmarks. The implementation of alpha-shapes is straightforward, and is automated to process large datasets quickly. Beyond genital shape, we consider the alpha-shapes technique to hold considerable promise for new applications across evolutionary, ecological and palaeoecological disciplines.
VL - 6
SP - e27270v1
T2 - PeerJ Preprints
JO - PeerJ Preprints
J2 - PeerJ Preprints
SN - 2167-9843
ER -