Normalized Radon Cumulative Distribution Transforms for Invariance and Robustness in Optimal Transport Based Image Classification

2025-06-10

AI Summary

Few-shot image classification suffers from insufficient robustness against non-affine deformations and impulse noise, alongside uncertain class linear separability. Method: This paper proposes the normalized Radon Cumulative Distribution Transform (R-CDT), integrating Radon transform, cumulative distribution functions, and optimal transport theory. It introduces two novel normalization strategies: max-normalization—preserving strict linear separability under affine transformations—and mean-normalization—enhancing robustness to local non-affine deformations and impulse noise. Theoretical analysis establishes intrinsic connections between R-CDT and both Wasserstein-∞ and Wasserstein-2 distances. Results: Experiments demonstrate that R-CDT achieves high classification accuracy in few-shot settings and exhibits superior invariance and robustness under measurement distortions, notably in watermark recognition tasks.

Technology Category

• Computer Vision: Adversarial Attacks & Robustness
• Machine Learning: Multi-class/Multi-label Learning & Extreme Classification
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization

Application Category

• Web Mining and Content Analysis: Normalization, clustering, classification, and summarization of Web text
• Responsible Web: Measurement, analysis, and circumvention of Web censorship
• Security and Privacy: Large-scale security measurements

Abstract

The Radon cumulative distribution transform (R-CDT), is an easy-to-compute feature extractor that facilitates image classification tasks especially in the small data regime. It is closely related to the sliced Wasserstein distance and provably guaranties the linear separability of image classes that emerge from translations or scalings. In many real-world applications, like the recognition of watermarks in filigranology, however, the data is subject to general affine transformations originating from the measurement process. To overcome this issue, we recently introduced the so-called max-normalized R-CDT that only requires elementary operations and guaranties the separability under arbitrary affine transformations. The aim of this paper is to continue our study of the max-normalized R-CDT especially with respect to its robustness against non-affine image deformations. Our sensitivity analysis shows that its separability properties are stable provided the Wasserstein-infinity distance between the samples can be controlled. Since the Wasserstein-infinity distance only allows small local image deformations, we moreover introduce a mean-normalized version of the R-CDT. In this case, robustness relates to the Wasserstein-2 distance and also covers image deformations caused by impulsive noise for instance. Our theoretical results are supported by numerical experiments showing the effectiveness of our novel feature extractors as well as their robustness against local non-affine deformations and impulsive noise.

Problem

• Enhancing image classification robustness under affine transformations
• Improving separability against non-affine image deformations
• Developing normalized R-CDT versions for noise resilience

Innovation

• Max-normalized R-CDT for affine invariance
• Mean-normalized R-CDT for noise robustness
• Wasserstein distance-based separability analysis