改进图像特征提取方法，提升小样本数据下的识别鲁棒性
Generalizations of the Normalized Radon Cumulative Distribution Transform for Limited Data Recognition
- 提出广义归一化方法，增强对仿射变换的适应性
- 在2D图像、3D形状和旋转矩阵上实现接近完美的分类准确率
- 适用于小样本、非欧空间场景，如水印识别等特殊任务
径向累积分布变换（R-CDT）利用一维Wasserstein流与Radon变换来表征图像中的显著特征，与切片Wasserstein距离密切相关，尤其适合小样本分类任务，如细纹学中的水印识别。由于测量过程可能引入仿射变换，本文提出一种两步归一化策略以实现R-CDT在任意仿射变换下的不变性。本工作旨在两方面：首先，提出一族广义归一化方法以提升应用灵活性；其次，通过广义Radon变换拓展至多维及非欧空间。理论证明新特征表示在特定变换下保持不变，并可在特征空间中线性可分。数值实验基于2D图像、3D形状和3D旋转矩阵，结果表明分类与聚类性能接近完美。
原文摘要 · Abstract (English)
The Radon cumulative distribution transform (R-CDT) exploits one-dimensional Wasserstein transport and the Radon transform to represent prominent features in images. It is closely related to the sliced Wasserstein distance and facilitates classification tasks, especially in the small data regime, like the recognition of watermarks in filigranology. Here, a typical issue is that the given data may be subject to affine transformations caused by the measuring process. To make the R-CDT invariant under arbitrary affine transformations, a two-step normalization of the R-CDT has been proposed in our earlier works. The aim of this paper is twofold. First, we propose a family of generalized normalizations to enhance flexibility for applications. Second, we study multi-dimensional and non-Euclidean settings by making use of generalized Radon transforms. We prove that our novel feature representations are invariant under certain transformations and allow for linear separation in feature space. Our theoretical results are supported by numerical experiments based on 2d images, 3d shapes and 3d rotation matrices, showing near perfect classification accuracies and clustering results.
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