A landmark-free method for quantifying biological shape variation

• Main Authors: Joshi, Shantanu H., Prieto-Marquez, Albert, Parker, William C.
• Format: Article in Journal/Newspaper
• Language: English
• Published: 2011
• Subjects: biology; evolution; geodesic; geometry; morphometrics; GLOBOROTALIA-TRUNCATULINOIDES; GEOMETRIC MORPHOMETRICS; EIGENSHAPE ANALYSIS; PLANKTONIC-FORAMINIFERA; FUNCTIONAL-MORPHOLOGY; PHYLOGENETIC SIGNALS; FOURIER DESCRIPTORS; OCEAN; PLEISTOCENE; Planktonic foraminifera
• Online Access: https://hdl.handle.net/1983/0b28f44b-1bbb-4fa5-8e03-d175563db92c; https://research-information.bris.ac.uk/en/publications/0b28f44b-1bbb-4fa5-8e03-d175563db92c; https://doi.org/10.1111/j.10958312.2011.01704.x

We implement a landmark-free method for the quantification of shape variation in evolutionary biology. The method is referred to as 'geodesic distance analysis' (GDA). It represents shapes as continuous boundaries that are invariant to translation, rotation and uniform scaling. Boundaries are represented as functions in an infinite-dimensional nonlinear space. The arc length of the curve is used as a parameter to model the shape. The angle between the tangent vector to the curve and the positive x axis is defined as a function of the arc length. In this way, shapes are compared and represented using their angle functions. Shape differences are calculated by finding geodesics (or shortest paths) between shapes of curves on the shape space. GDA offers an environment for the performance of shape statistics that are intrinsic to the space of planar continuous curves. The method becomes especially appropriate when the objects of study are continuous curves for which landmarks cannot be identified with certainty. We present applications of this method to the analysis of organismal morphology. (C) 2011 The Linnean Society of London, Biological Journal of the Linnean Society, 2011, 104, 217-233.