Related papers: Diffeomorphic density matching by optimal informat…

We consider the problem of selecting an optimal mask for an image manifold, i.e., choosing a subset of the pixels of the image that preserves the manifold's geometric structure present in the original data. Such masking implements a form of…

A central challenge in cellular signal processing is understanding how biochemical networks perform reliably despite molecular noise. Traditionally, mutual information has been widely used to quantify signaling fidelity, capturing how well…

In this paper the space of images is considered as a Riemannian manifold using the metamorphosis approach, where the underlying Riemannian metric simultaneously measures the cost of image transport and intensity variation. A robust and…

We consider the problem of computing dense correspondences between non-rigid shapes with potentially significant partiality. Existing formulations tackle this problem through heavy manifold optimization in the spectral domain, given…

We present a numerical method to solve the optimal transport problem with a quadratic cost when the source and target measures are periodic probability densities. This method is based on a numerical resolution of the corresponding…

We survey the role of symmetry in diffeomorphic registration of landmarks, curves, surfaces, images and higher-order data. The infinite dimensional problem of finding correspondences between objects can for a range of concrete data types be…

The emergence of generative AI and controllable diffusion has made image-to-image synthesis increasingly practical and efficient. However, when input images exhibit low entropy and sparse, the inherent characteristics of diffusion models…

Optimal transport is a powerful framework for the efficient allocation of resources between sources and targets. However, traditional models often struggle to scale effectively in the presence of large and heterogeneous populations. In this…

Deep learning based methods provide efficient solutions to medical image registration, including the challenging problem of diffeomorphic image registration. However, most methods register normal image pairs, facing difficulty handling…

This paper presents a novel mathematical framework for representing uncertainty in large deformation diffeomorphic image registration. The Bayesian posterior distribution over the deformations aligning a moving and a fixed image is…

Deformable image registration is able to achieve fast and accurate alignment between a pair of images and thus plays an important role in many medical image studies. The current deep learning (DL)-based image registration approaches…

We establish that solving an optimal transportation problem in which the source and target densities are defined on manifolds with different dimensions, is equivalent to solving a new nonlocal analog of the Monge-Amp\`ere equation,…

Many algorithms for surface registration risk producing significant errors if surfaces are significantly nonisometric. Manifold learning has been shown to be effective at improving registration quality, using information from an entire…

In this work, we study the dynamics of the logistic map based on a probabilistic characterization in terms of the invariant density. We analyze the relevant regimes of the dynamics (regular, oscillatory, onset chaotic and fully chaotic) in…

We propose a fast and scalable algorithm to project a given density on a set of structured measures defined over a compact 2D domain. The measures can be discrete or supported on curves for instance. The proposed principle and algorithm are…

We show that, on a $2$-dimensional compact manifold, the optimal transport map in the semi-discrete random matching problem is well-approximated in the $L^2$-norm by identity plus the gradient of the solution to the Poisson problem $-\Delta…

We present an information-theoretic approach to the registration of images with directional information, and especially for diffusion-Weighted Images (DWI), with explicit optimization over the directional scale. We call it Locally Orderless…

Optimal transport maps define a one-to-one correspondence between probability distributions, and as such have grown popular for machine learning applications. However, these maps are generally defined on empirical observations and cannot be…

We consider the problem of fusing an arbitrary number of multiband, i.e., panchromatic, multispectral, or hyperspectral, images belonging to the same scene. We use the well-known forward observation and linear mixture models with Gaussian…

We consider the problems of clustering, classification, and visualization of high-dimensional data when no straightforward Euclidean representation exists. Typically, these tasks are performed by first reducing the high-dimensional data to…