Related papers: Generalizations of the Normalized Radon Cumulative…
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…
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…
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…
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,…
We present a new method for face recognition from digital images acquired under varying illumination conditions. The method is based on mathematical modeling of local gradient distributions using the Radon Cumulative Distribution Transform…
Deep convolutional neural networks (CNNs) are broadly considered to be state-of-the-art generic end-to-end image classification systems. However, they are known to underperform when training data are limited and thus require data…
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…
The Radon transform is a fundamental tool for analyzing data in tomographic imaging, optimal transport, crystallography, and geometric analysis. Numerical computations require an accurate discretization. To deal with voxelized images and…
There exist growing interests in intelligent systems for numerous medical imaging, image processing, and computer vision applications, such as face recognition, medical diagnosis, character recognition, and self-driving cars, among others.…
While statistical modeling of distributional data has gained increased attention, the case of multivariate distributions has been somewhat neglected despite its relevance in various applications. This is because the Wasserstein distance,…
Difference features obtained by comparing the images of two periods play an indispensable role in the change detection (CD) task. However, a pair of bi-temporal images can exhibit diverse changes, which may cause various difference…
Let $\mathcal R$ denote the generalized Radon transform (GRT), which integrates over a family of $N$-dimensional smooth submanifolds $\mathcal S_{\tilde y}\subset\mathcal U$, $1\le N\le n-1$, where an open set $\mathcal U\subset\mathbb R^n$…
Tomographic investigations are a central tool in medical applications, allowing doctors to image the interior of patients. The corresponding measurement process is commonly modeled by the Radon transform. In practice, the solution of the…
Discriminating data classes emanating from sensors is an important problem with many applications in science and technology. We describe a new transform for pattern identification that interprets patterns as probability density functions,…
The generalized spherical Radon transform associates the mean values over spherical tori to a function $f$ defined on $\mathbb{S}^3 \subset \mathbb{H}$, where the elements of $\mathbb{S}^3$ are considered as quaternions representing…
Reconstructing an image from its Radon transform is a fundamental computed tomography (CT) task arising in applications such as X-ray scans. In many practical scenarios, a full 180-degree scan is not feasible, or there is a desire to reduce…
The crossing properties of the matrix elements of non-local operators, parameterized by Generalized Parton Distribution, are considered. They are especially simple in terms of the Double Distributions which are common for the various…
We consider the generalized Radon transform (defined in terms of smooth weight functions) on hyperplanes in $\mathbb{R}^n$. We analyze general filtered backprojection type reconstruction methods for limited data with filters given by…
This paper extends the Radon transform, a classical image processing tool for fast tomography and denoising, to the quantum computing platform. A new kind of periodic discrete Radon transform (PDRT), called quantum Radon transform (QRT), is…
We introduce the Wasserstein Transform (WT), a general unsupervised framework for updating distance structures on given data sets with the purpose of enhancing features and denoising. Our framework represents each data point by a…