Geometric Morphometrics operations in Python
Welcome to Morphops!
Morphops implements common operations and algorithms for Geometric Morphometrics, in Python 3.
Some high-level operations in the current version are
- Centering, rescaling data:
- Rigid Rotation, Ordinary and Generalized Procrustes alignment:
- Thin-plate spline warping:
- Reading from and writing to *.dta files:
pip install morphops
import morphops as mops # Create 3 landmark sets, each having 5 landmarks in 2 dimensions. A = [[0,0],[2,0],[2,2],[1,3],[0,2]] B = [[0.1,-0.1],[2,0],[2.3,1.8],[1,3],[0.4,2]] C = [[-0.1,-0.1],[2.1,0],[2,1.8],[0.9,3.1],[-0.4,2.1]] # Perform Generalized Procrustes alignment to align A, B, C. res = mops.gpa([A, B, C]) # res['aligned'] contains the aligned A, B, C. res['mean'] is their mean. # Create a Thin-plate Spline warp from A to B and warp C. warped_C = mops.tps_warp(A, B, C) # warped_C contains the image of the pts in C under the TPS warp.
What is Geometric Morphometrics?
Geometric Morphometrics is a statistical toolkit for quantifying and studying shapes of forms that are represented by homologous landmark sets.
“Shape” has a specific notion here. For a given landmark set, its shape refers to the spatial information that survives after discarding its absolute position, scale and rotation. So two landmark sets have the same shape if they can be brought in perfect alignment by only changing their positions, scales and rotations.
Common Operations and Algorithms in Studies
Geometric Morphometrics is often used when pursuing statistical questions involving the morphology of biological forms, like do corvid species that frequently probe have longer bills and more to-the-side orbits than corvid species that frequently peck. It helps inform the Data Collection, Preprocessing and Analysis steps of such statistical studies with sound theoretical or practical justifications.
The most prevalent form of Data Collection involves picking homologous landmarks on each form. For curving forms with few homologous points but well-understood homologous regions, there is a notion of semilandmarks which can “slide” to minimize equidistant sampling artifacts.
A common file format for saving landmarks for a set of specimens is the *.dta format used by the IDAV Landmark Editor software.
As discussed before, a central idea in Geometric Morphometrics is extracting the “shapes” of the landmark sets. One way to achieve this is to use the Generalized Procrustes Alignment algorithm or GPA. GPA aligns all the landmark sets by modifying their locations, orientations and sizes so as to minimize their collective interlandmark distances.
After this step, the aligned shapes all lie in a high-dimensional non-linear manifold. For example, if the orignal landmark sets were a set of triangles, the aligned shapes lie on a sphere. Moreover, for naturally arising datasets, the shapes likely lie very close to each other and are distributed around a mean shape. This usually makes it permissible to project all the shapes into the tangent space at the mean shape, and this way the final shape vectors lie in a linear space.
With the shapes lying in a high-dimensional linear space after preprocessing, they can now be submitted to various commonly used statistical procedures like Principal Components Analysis and various kinds of regression for further analysis.
(This file was autogenerated from README_for_docs.rst by running `make README_for_gh html` in the docs directory)
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