The Radon Signed Cumulative Distribution Transform and its applications in classification of Signed Images

Here we describe a new image representation technique based on the mathematics of transport and optimal transport. The method relies on the combination of the well-known Radon transform for images and a recent signal representation method called the Signed Cumulative Distribution Transform. The newly proposed method generalizes previous transport-related image representation methods to arbitrary functions (images), and thus can be used in more applications. We describe the new transform, and some of its mathematical properties and demonstrate its ability to partition image classes with real and simulated data. In comparison to existing transport transform methods, as well as deep learning-based classification methods, the new transform more accurately represents the information content of signed images, and thus can be used to obtain higher classification accuracies. The implementation of the proposed method in Python language is integrated as a part of the software package PyTransKit, available on Github.

[1]  Gustavo K. Rohde,et al.  End-to-End Signal Classification in Signed Cumulative Distribution Transform Space , 2022, ArXiv.

[2]  Gustavo K. Rohde,et al.  Local Sliced-Wasserstein Feature Sets for Illumination-invariant Face Recognition , 2022, ArXiv.

[3]  Gustavo K. Rohde,et al.  Invariance encoding in sliced-Wasserstein space for image classification with limited training data , 2022, Pattern Recognit..

[4]  Akram Aldroubi,et al.  The Signed Cumulative Distribution Transform for 1-D Signal Analysis and Classification , 2021, Foundations of Data Science.

[5]  A. Aldroubi,et al.  Partitioning signal classes using transport transforms for data analysis and machine learning , 2020, Sampling Theory, Signal Processing, and Data Analysis.

[6]  Youssef Ghanou,et al.  2D geometric shapes dataset – for machine learning and pattern recognition , 2020, Data in brief.

[7]  Gustavo K. Rohde,et al.  Parametric Signal Estimation Using the Cumulative Distribution Transform , 2020, IEEE Transactions on Signal Processing.

[8]  A. Aldroubi,et al.  Radon Cumulative Distribution Transform Subspace Modeling for Image Classification , 2020, Journal of Mathematical Imaging and Vision.

[9]  E-mail Address , 2020, Definitions.

[10]  Carlos David Braga Borges,et al.  Static Hand Gesture Recognition Based on Convolutional Neural Networks , 2019, J. Electr. Comput. Eng..

[11]  Xiangyu Zhang,et al.  ShuffleNet V2: Practical Guidelines for Efficient CNN Architecture Design , 2018, ECCV.

[12]  Gustavo K. Rohde,et al.  Reconstructing high-resolution cardiac MR movies from under-sampled frames , 2017, 2017 51st Asilomar Conference on Signals, Systems, and Computers.

[13]  Gustavo K. Rohde,et al.  Optimal Mass Transport: Signal processing and machine-learning applications , 2017, IEEE Signal Processing Magazine.

[14]  Kilian Q. Weinberger,et al.  Densely Connected Convolutional Networks , 2016, 2017 IEEE Conference on Computer Vision and Pattern Recognition (CVPR).

[15]  Gustavo K. Rohde,et al.  A continuous linear optimal transport approach for pattern analysis in image datasets , 2016, Pattern Recognit..

[16]  Jian Sun,et al.  Deep Residual Learning for Image Recognition , 2015, 2016 IEEE Conference on Computer Vision and Pattern Recognition (CVPR).

[17]  Gustavo K. Rohde,et al.  The Radon Cumulative Distribution Transform and Its Application to Image Classification , 2015, IEEE Transactions on Image Processing.

[18]  Gustavo K. Rohde,et al.  The Cumulative Distribution Transform and Linear Pattern Classification , 2015, Applied and Computational Harmonic Analysis.

[19]  B. Koh,et al.  Wavelet energy-based visualization and classification of high-dimensional signal for bearing fault detection , 2015, Knowledge and Information Systems.

[20]  Gustavo K. Rohde,et al.  Transport-based single frame super resolution of very low resolution face images , 2015, 2015 IEEE Conference on Computer Vision and Pattern Recognition (CVPR).

[21]  Andrew Zisserman,et al.  Very Deep Convolutional Networks for Large-Scale Image Recognition , 2014, ICLR.

[22]  Nicholas Hamilton,et al.  Quantification and its Applications in Fluorescent Microscopy Imaging , 2009, Traffic.

[23]  C. Villani.  Topics in Optimal Transportation , 2003 .

[24]  Mitra Basu,et al.  Gaussian-based edge-detection methods - a survey , 2002, IEEE Trans. Syst. Man Cybern. Part C.

[25]  Ronald N. Bracewell,et al.  The Fourier Transform and Its Applications , 1966 .

[26]  Paul Strauss,et al.  Magnetic Resonance Imaging Physical Principles And Sequence Design , 2016 .

[27]  Wilhelm Burger,et al.  Digital Image Processing - An Algorithmic Introduction using Java , 2008, Texts in Computer Science.

[28]  L. Rifford.  Introduction to Optimal Transport , 2014 .

[29]  Gustavo K. Rohde,et al.  A Linear Optimal Transportation Framework for Quantifying and Visualizing Variations in Sets of Images , 2012, International Journal of Computer Vision.

[30]  E. T. Quinto,et al.  An Introduction to X-ray tomography and Radon Transforms , 2006 .

[31]  Yoshua Bengio,et al.  Gradient-based learning applied to document recognition , 1998, Proc. IEEE.

[32]  F. Natterer.  The Mathematics of Computerized Tomography , 1986 .

[33]  J. Radon.  On the determination of functions from their integral values along certain manifolds , 1986, IEEE Transactions on Medical Imaging.