Next-generation osteometric sorting: Using 3D shape, elliptical Fourier analysis, and Hausdorff distance to optimize osteological pair-matching.

Determining which bilateral bones belong to the same person based on shape and size similarity is called pair-matching and it is instrumental for sorting commingled skeletons. To date, pair-matching has popularly been accomplished by visual inspection and/or linear caliper measurements; however, attention is turning increasingly to computational analysis. In this paper, we investigate a fast three-dimensional (3D) computerized shape-analysis method for whole-bone pair-matching using a test sample of 14 individuals (23 femora, 26 humeri, and 26 tibiae). Specifically, the method aims to find bilateral pairs using, as the shape signature criterion, a single 3D outline that snakes around each bone's perimeter as described by a 3D elliptical Fourier analysis function. This permits substantial 3D-point-cloud data reduction, that is, to 0.02% of the starting c.500,000 point cloud or just 100 points, while preserving key 3D shape information. The mean Hausdorff distance (Hd) was applied to measure the distance between each mirrored right-side outline to every left-side outline in pairwise fashion (132, 168 and 169 comparisons, respectively). Both thresholds and lowest Hd were investigated as pair-match criteria, with the lowest Hd producing the best performance results for searches jointly utilizing right-left and left-right directions for comparison: true positive rates of 1.00 (10/10), 1.00 (12/12), and 0.92 (11/12) for the femora, humeri, and tibiae, respectively. The computational time to calculate 469 pairwise 3D comparisons on a single stock-standard Intel Core™ i7-4650U CPU @ 1.70 GHz was 5 s. This short data processing time makes the method viable for real-world application.