Department of Mathematics
 Search | Help | Login | pdf version | printable version

Math @ Duke



Publications [#330010] of Sayan Mukherjee

Papers Published

  1. Gao, T; Yapuncich, GS; Daubechies, I; Mukherjee, S; Boyer, DM, Development and Assessment of Fully Automated and Globally Transitive Geometric Morphometric Methods, With Application to a Biological Comparative Dataset With High Interspecific Variation., The Anatomical Record : Advances in Integrative Anatomy and Evolutionary Biology (October, 2017) [doi]
    (last updated on 2017/12/08)

    Automated geometric morphometric methods are promising tools for shape analysis in comparative biology, improving researchers' abilities to quantify variation extensively (by permitting more specimens to be analyzed) and intensively (by characterizing shapes with greater fidelity). Although use of these methods has increased, published automated methods have some notable limitations: pairwise correspondences are frequently inaccurate and pairwise mappings are not globally consistent (i.e., they lack transitivity across the full sample). Here, we reassess the accuracy of published automated methods-cPDist (Boyer et al. Proc Nat Acad Sci 108 (2011) 18221-18226) and auto3Dgm (Boyer et al.: Anat Rec 298 (2015a) 249-276)-and evaluate several modifications to these methods. We show that a substantial percentage of alignments and pairwise maps between specimens of dissimilar geometries were inaccurate in the study of Boyer et al. (Proc Nat Acad Sci 108 (2011) 18221-18226), despite a taxonomically partitioned variance structure of continuous Procrustes distances. We show these inaccuracies are remedied using a globally informed methodology within a collection of shapes, rather than relying on pairwise comparisons (c.f. Boyer et al.: Anat Rec 298 (2015a) 249-276). Unfortunately, while global information generally enhances maps between dissimilar objects, it can degrade the quality of correspondences between similar objects due to the accumulation of numerical error. We explore a number of approaches to mitigate this degradation, quantify their performance, and compare the generated pairwise maps (and the shape space characterized by these maps) to a "ground truth" obtained from landmarks manually collected by geometric morphometricians. Novel methods both improve the quality of the pairwise correspondences relative to cPDist and achieve a taxonomic distinctiveness comparable to auto3Dgm. Anat Rec, 2017. © 2017 Wiley Periodicals, Inc.
ph: 919.660.2800
fax: 919.660.2821

Mathematics Department
Duke University, Box 90320
Durham, NC 27708-0320