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We propose to align distributional data from the perspective of Wasserstein means. We raise the problem of regularizing Wasserstein means and propose several terms tailored to tackle different problems. Our formulation is based on the…
Deep neural networks have shown exceptional learning capability and generalizability in the source domain when massive labeled data is provided. However, the well-trained models often fail in the target domain due to the domain shift.…
The Wasserstein distance has become increasingly important in machine learning and deep learning. Despite its popularity, the Wasserstein distance is hard to approximate because of the curse of dimensionality. A recently proposed approach…
While many Machine Learning methods were developed or transposed on Riemannian manifolds to tackle data with known non Euclidean geometry, Optimal Transport (OT) methods on such spaces have not received much attention. The main OT tool on…
The distance transform (DT) and its many variations are ubiquitous tools for image processing and analysis. In many imaging scenarios, the images of interest are corrupted by noise. This has a strong negative impact on the accuracy of the…
This paper introduces DRANet-SWD as a novel complete pipeline for disentangling content and style representations of images for unsupervised domain adaptation (UDA). The approach builds upon DRANet by incorporating the sliced Wasserstein…
We introduce a new class of distances between nonnegative Radon measures in Euclidean spaces. They are modeled on the dynamical characterization of the Kantorovich-Rubinstein-Wasserstein distances proposed by Benamou-Brenier and provide a…
Deep convolutional neural networks (CNNs) are the backbone of state-of-art semantic image segmentation systems. Recent work has shown that complementing CNNs with fully-connected conditional random fields (CRFs) can significantly enhance…
Moment methods to reconstruct images from their Radon transforms are both natural and useful. They can be used to suppress noise or other spurious effects and can lead to highly efficient reconstructions from relatively few projections. We…
Optimal transport has recently proved to be a useful tool in various machine learning applications needing comparisons of probability measures. Among these, applications of distributionally robust optimization naturally involve Wasserstein…
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…
Many applications in machine learning involve data represented as probability distributions. The emergence of such data requires radically novel techniques to design tractable gradient flows on probability distributions over this type of…
A relatively new set of transport-based transforms (CDT, R-CDT, LOT) have shown their strength and great potential in various image and data processing tasks such as parametric signal estimation, classification, cancer detection among many…
We propose a new unsupervised anomaly detection method based on the sliced-Wasserstein distance for training data selection in machine learning approaches. Our filtering technique is interesting for decision-making pipelines deploying…
Explicit calculations in dimension one show for Schur stable autoregressive processes with standard Gaussian noise that the ergodic convergence in the Wasserstein-$2$ distance is essentially given by the sum of the mean, which decays…
We define a modified Wasserstein distance for distribution clustering which inherits many of the properties of the Wasserstein distance but which can be estimated easily and computed quickly. The modified distance is the sum of two terms.…
This paper proposes a spatial-Radon domain CT image reconstruction model based on data-driven tight frames (SRD-DDTF). The proposed SRD-DDTF model combines the idea of joint image and Radon domain inpainting model of \cite{Dong2013X} and…
Depth estimation remains central to autonomous driving, and radar-camera fusion offers robustness in adverse conditions by providing complementary geometric cues. In this paper, we present XD-RCDepth, a lightweight architecture that reduces…
We introduce Deep Set Linearized Optimal Transport, an algorithm designed for the efficient simultaneous embedding of point clouds into an $L^2-$space. This embedding preserves specific low-dimensional structures within the Wasserstein…
Image moments are weighted sums over pixel values in a given image and are used in object detection and localization. Raw image moments are derived directly from the image and are fundamental in deriving moment invariants quantities. The…