The Radon cumulative distribution transform and its application to image classification
This addresses the limitation of linear transforms in image classification, offering a potential improvement for computer vision tasks, though it appears incremental as it builds on existing transforms.
The authors tackled the problem of simplifying image class representation for classification by introducing a nonlinear, invertible transform combining the Radon transform and the 1D Cumulative Distribution Transform, showing it can often render problems linearly separable in transform space.
Invertible image representation methods (transforms) are routinely employed as low-level image processing operations based on which feature extraction and recognition algorithms are developed. Most transforms in current use (e.g. Fourier, Wavelet, etc.) are linear transforms, and, by themselves, are unable to substantially simplify the representation of image classes for classification. Here we describe a nonlinear, invertible, low-level image processing transform based on combining the well known Radon transform for image data, and the 1D Cumulative Distribution Transform proposed earlier. We describe a few of the properties of this new transform, and with both theoretical and experimental results show that it can often render certain problems linearly separable in transform space.