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.

Error measurement in craniometrics: The comparative performance of four popular assessment methods using 2000 simulated cranial length datasets (g-op).

For measurements to be accurate and precise, measurement errors should be small. In the anthropometry and craniofacial identification literature, four methods are commonly used for assessing measurement error: Pearson's product moment correlation coefficient (r), intra-class correlation coefficients (ICC), statistical significance tests (often reported by P-values) and the technical error of measurement (TEM; also known as Dalberg's error/ratio). In this paper, the performance of all four of these statistics were evaluated using maximum cranial lengths (g-op) from Howells (n=2524), by duplicating the dataset and mathematically adding known degrees of error to the second set. This was repeated under a broad array of trials (2000 total) each with slightly different amounts of error simulation to comprehensively assess the four error metrics in terms of descriptive power and utility, using the same data for each of the four error assessment methods. Data simulations included the addition of random and systematic errors of different sizes with absolute differences ranging from 1 to 50mm (or in relative terms, 28% of the original measurement). Two sample sizes (n=25 and 2524 individuals) were explored and all analyses were conducted in R. P-values from Student's t-tests only showed significant differences (P<0.05) for the larger sample size when the error was systematic. Small samples, and/or any with random error, did not yield low or significant P-values (P<0.05). When raw differences were <4mm for 95% of the sample (n=2524), the ICC and r were high (>0.97) and remained so even after tripling the error, such that 95% of the sample possessed raw differences up to 12mm (r=0.8). In contrast, the TEM was low initially (<2mm or r-TEM<1%), and then increased (<4.5mm and 2.5%, TEM and r-TEM respectively). These data show that P-values, ICC and r values hold substantial limits for error description as they do not always flag error well. In contrast, TEM appears to covary with error more saliently and holds the advantage that changes are reported in the units of the original measurement. For these reasons, TEM is recommended in favour to P-values, ICC and r.