A tiny, clean and heavily-commented NumPy-powered script originally designed to average facial landmarks.
Procrustes analysis is a well known method for the multidimensional transformation (rescaling, translation, rotation and reflection) of individual data matrices, in order to provide optimal data blending and/or comparability.
Due to its simplicity and flexibility, PA is a common sparsity approach for preventing over-parameterization while training deep neural networks.
Depending on where the reference shape comes from, PA can be qualified as Ordinary Procrustes Analysis (fixed shape) or Generalized Procrustes Analysis (mean shape). The procrustes module found in this repository implements both algorithms (the former, in fact, being a subset of the latter).
You can test the output by typing python3 plot.py.
A two-part sequence of matplotlib charts, based on the fly wing example from this Wikipedia's article infobox (Klingenberg, 2015), will appear.
In both cases, a root-mean-square deviation (RMSD) measure is shown in the window's title bar.
OPA (the dimmed blue line is the starting position of the solid blue one):
GPA (the middle red line is the mean shape):
Procrustes requires numpy and, if you want to run the provided plot.py test, matplotlib too:
$ python3 -m pip install --upgrade pip --user
$ pip3 install numpy
$ pip3 install matplotlib
- 1975 - Generalized Procrustes Analysis (J.C. Gower)
- 1977 - The Diffusion of Shape (D.G. Kendall)
- 1991 - Procrustes Methods in the Statistical Analysis of Shape (Colin Goodall)
- 1998 - Statistical Shape Analysis (I. Dryden, K.V. Mardia)
- 2015 - Analyzing Fluctuating Asymmetry with Geometric Morphometrics (C.P. Klingenberg)