PyTransKit

Python Transport Based Signal Processing Toolkit

Website and documentation: https://pytranskit.readthedocs.io/

Introduction video

This python package provides signal/image representation software methods (i.e. mathematical transforms) based on the idea of matching signals & images to a reference by pixel displacement operations that are physically related to the concept of transport phenomena. You can think of and use the transforms described below just as one would with the Fourier or Wavelet Transforms. By solving signal/image analysis in transport transform (e.g. Wasserstein embedding) space, one can dramatically simplify and linearize statistical regression problems, enabling the straight forward (e.g. closed form) solution of signal/image detection, estimation, and classification problems with increased accuracy using few training samples, with mathematical understanding and interpretability, better generalization properties, and computationally efficiently.

Installation

The library could be installed through pip

pip install pytranskit

Alternately, you could clone/download the repository and add the pytranskit directory to your Python path

import sys
sys.path.append('path/to/pytranskit')

from pytranskit.optrans.continuous.cdt import CDT

Introduction video

Low Level Functions

CDT, SCDT

• Cumulative Distribution Transform (CDT) [1] [notebook] [nbviewer]
  • Videos: CDT, Code
• Signed Cumulative Distribution Transform (SCDT) [6] tutorial [notebook] [nbviewer]
• SCDT tutorial with domain adaptation [notebook] [nbviewer]

R-CDT

• Radon-CDT tutorial [notebook] [nbviewer]
• 3D Radon-CDT tutorial [notebook][nbviewer]

RSCDT

• RSCDT tutorial : Forward and Inverse Transform [10][notebook]
• RSCDT based nearest subspace method for image classification [10]. [notebook]

CLOT

• Continuous Linear Optimal Transport Transform (CLOT) tutorial [notebook] [nbviewer]

Classification Examples

• CDT Nearest Subspace (CDT-NS) classifier for 1D data [notebook] [nbviewer]
• SCDT Nearest Subspace (SCDT-NS) classifier for 1D data [8] [notebook] [nbviewer]
• SCDT Nearest Local Subspace (SCDT-NLS) classifier for 1D data [9] [notebook] [nbviewer]
• Radon-CDT Nearest Subspace (RCDT-NS) classifier for 2D data [4] [notebook] [nbviewer]
• 3D Radon-CDT Nearest Subspace (3D-RCDT-NS) classifier for 3D data [notebook] [nbviewer]
• Discrete Radon-CDT Nearest Subspace classifier for illumination-invariant Face Recognition [notebook]
• RSCDT based nearest subspace method for image classification [10]. [notebook]

Estimation Examples

• Time delay estimation using CDT [5] [notebook] [nbviewer]
• Time delay and linear dispersion estimation using CDT [5] [notebook] [nbviewer]
• PDE system identification using the SCDT [11] [notebook] [nbviewer]

Transport-based Morphometry

• Transport-based Morphometry to detect and visualize cell phenotype differences [7] [notebook] [nbviewer]

References

1. The cumulative distribution transform and linear pattern classification, Applied and Computational Harmonic Analysis, November 2018
2. The Radon Cumulative Distribution Transform and Its Application to Image Classification, IEEE Transactions on Image Processing, December 2015
3. A continuous linear optimal transport approach for pattern analysis in image datasets, Pattern Recognition, March 2016
4. Radon cumulative distribution transform subspace modeling for image classification, Journal of Mathematical Imaging and Vision, 2021
5. Parametric Signal Estimation Using the Cumulative Distribution Transform, IEEE Transactions on Signal Processing, May 2020
6. The Signed Cumulative Distribution Transform for 1-D Signal Analysis and Classification, ArXiv 2021
7. Detecting and visualizing cell phenotype differences from microscopy images using transport-based morphometry, PNAS 2014
8. Nearest Subspace Search in the Signed Cumulative Distribution Transform Space for 1D Signal Classification, IEEE International Conference on Acoustics, Speech and Signal Processing, May 2022
9. End-to-End Signal Classification in Signed Cumulative Distribution Transform Space, arXiv 2022
10. The Radon Signed Cumulative Distribution Transform and its applications in classification of Signed Images, arXiv 2023.
11. System Identification Using the Signed Cumulative Distribution Transform In Structural Health Monitoring Applications, arXiv 2023

Resources

External website http://imagedatascience.com/transport/

Video [tutorials]

Authors

• Abu Hasnat Mohammad Rubaiyat
• Mohammad Shifat E Rabbi
• Liam Cattell
• Xuwang Yin
• Shiying Li
• Yan Zhuang
• Gustavo K. Rohde
• Soheil Kolouri
• Serim Park