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Radon Cumulative Distribution Transform Subspace Modeling for Image Classification

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Abstract

We present a new supervised image classification method applicable to a broad class of image deformation models. The method makes use of the previously described Radon Cumulative Distribution Transform (R-CDT) for image data, whose mathematical properties are exploited to express the image data in a form that is more suitable for machine learning. While certain operations such as translation, scaling, and higher-order transformations are challenging to model in native image space, we show the R-CDT can capture some of these variations and thus render the associated image classification problems easier to solve. The method—utilizing a nearest-subspace algorithm in the R-CDT space—is simple to implement, non-iterative, has no hyper-parameters to tune, is computationally efficient, label efficient, and provides competitive accuracies to state-of-the-art neural networks for many types of classification problems. In addition to the test accuracy performances, we show improvements (with respect to neural network-based methods) in terms of computational efficiency (it can be implemented without the use of GPUs), number of training samples needed for training, as well as out-of-distribution generalization. The Python code for reproducing our results is available at Shifat-E-Rabbi et al. (Python code implementing the Radon cumulative distribution transform subspace model for image classification. https://github.com/rohdelab/rcdt_ns_classifier).

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Notes

  1. We are using a slightly different definition of the CDT than in [31]. The properties of the CDT outlined here hold in both definitions.

  2. Rigorously speaking, if \(\widehat{\mathbb {V}}^{(p)}\) is a closed subspace, then \(d^2( \widehat{s},\widehat{\mathbb {V}}^{(p)})>0\) if and only if \(\widehat{s}\notin \widehat{\mathbb {V}}^{(p)} \). In practice, \(\widehat{\mathbb {V}}^{(p)}\) will be a finite dimensional space and hence, the closedness condition is satisfied.

  3. The same grid is chosen for all images. m, n are positive integers.

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Author information

Author notes

  1. Xuwang Yin and Abu Hasnat Mohammad Rubaiyat have contributed equally to this work.

Authors and Affiliations

  1. Department of Biomedical Engineering, University of Virginia, Charlottesville, VA, 22908, USA

    Mohammad Shifat-E-Rabbi & Shiying Li

  2. Department of Electrical and Computer Engineering, University of Virginia, Charlottesville, VA, 22904, USA

    Xuwang Yin & Abu Hasnat Mohammad Rubaiyat

  3. Department of Computer Science, Vanderbilt University, Nashville, TN, 37212, USA

    Soheil Kolouri

  4. Department of Mathematics, Vanderbilt University, Nashville, TN, 37212, USA

    Akram Aldroubi

  5. U.S. Naval Research Laboratory, Washington, DC, 20375, USA

    Jonathan M. Nichols

  6. Department of Biomedical Engineering, University of Virginia, Charlottesville, VA, 22908, USA

    Gustavo K. Rohde

  7. Department of Electrical and Computer Engineering, University of Virginia, Charlottesville, VA, 22908, USA

    Gustavo K. Rohde

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  1. Mohammad Shifat-E-Rabbi
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Correspondence to Mohammad Shifat-E-Rabbi.

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This work was supported in part by NIH Grants GM130825, GM090033.

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Shifat-E-Rabbi, M., Yin, X., Rubaiyat, A.H.M. et al. Radon Cumulative Distribution Transform Subspace Modeling for Image Classification. J Math Imaging Vis 63, 1185–1203 (2021). https://doi.org/10.1007/s10851-021-01052-0

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