Technical note: A new method for measuring long bone curvature using 3D landmarks and semi-landmarks

Here we describe and evaluate a new method for quantifying long bone curvature using geometric morphometric and semi-landmark analysis of the human femur. The technique is compared with traditional ways of measuring subtense and point of maximum curvature using either coordinate calipers or projection onto graph paper. Of the traditional methods the graph paper method is more reliable than using coordinate calipers. Measurement error is consistently lower for measuring point of maximum curvature than for measuring subtense. The results warrant caution when comparing data collected by the different traditional methods. Landmark data collection proves reliable and has a low measurement error. However, measurement error increases with the number of semi-landmarks included in the analysis of curvature. Measurements of subtense can be estimated more reliably using 3D landmarks along the curve than using traditional techniques. We use equidistant semi-landmarks to quantify the curve because sliding the semi-landmarks masks the curvature signal. Principal components analysis of these equidistant semi-landmarks provides the added benefit of describing the shape of the curve. These results are promising for functional and forensic analysis of long bone curvature in modern human populations and in the fossil record.