Planar morphometrics using Teichmüller maps
Inspired by the question of quantifying wing shape,
we propose a computational approach for analysing
planar shapes. We first establish a correspondence
between the boundaries of two planar shapes with
boundary landmarks using geometric functional data
analysis and then compute a landmark-matching
curvature-guided Teichmüller mapping with uniform
quasi-conformal distortion in the bulk. This allows
us to analyse the pair-wise difference between the
planar shapes and construct a similarity matrix on
which we deploy methods from network analysis
to cluster shapes. We deploy our method to study
a variety of Drosophila wings across species to
highlight the phenotypic variation between them,
and Lepidoptera wings over time to study the
developmental progression of wings. Our approach
of combining complex analysis, computation and
statistics to quantify, compare and classify planar
shapes may be usefully deployed in other biological
and physical systems.
Prof. L. Mahadevan