Related papers: Geodesic Warps by Conformal Mappings

In this paper, we address the problem of building dense correspondences between human images under arbitrary camera viewpoints and body poses. Prior art either assumes small motion between frames or relies on local descriptors, which cannot…

This paper addresses the morphing of manifold-valued images based on the time discrete geodesic paths model of Berkels, Effland and Rumpf 2015. Although for our manifold-valued setting such an interpretation of the energy functional is not…

The availability of affordable and portable depth sensors has made scanning objects and people simpler than ever. However, dealing with occlusions and missing parts is still a significant challenge. The problem of reconstructing a (possibly…

This paper introduces the use of unbalanced optimal transport methods as a similarity measure for diffeomorphic matching of imaging data. The similarity measure is a key object in diffeomorphic registration methods that, together with the…

In the statistical analysis of shape a goal beyond the analysis of static shapes lies in the quantification of `same' deformation of different shapes. Typically, shape spaces are modelled as Riemannian manifolds on which parallel transport…

In this work, an evolutionary art project is presented where images are approximated by transparent, overlapping and geometric shapes of different types, e.g., polygons, circles, lines. Genotypes representing features and order of the…

Image segmentation is a fundamental task in computer vision aimed at delineating object boundaries within images. Traditional approaches, such as edge detection and variational methods, have been widely explored, while recent advances in…

We present a diffeomorphic image registration algorithm to learn spatial transformations between pairs of images to be registered using fully convolutional networks (FCNs) under a self-supervised learning setting. The network is trained to…

We prove conformal versions of the local decomposition theorems of de Rham and Hiepko of a Riemannian manifold as a Riemannian or a warped product of Riemannian manifolds. Namely, we give necessary and sufficient conditions for a Riemannian…

In this paper we introduce a new class of diffeomorphic smoothers based on general spline smoothing techniques and on the use of some tools that have been recently developed in the context of image warping to compute smooth diffeomorphisms.…

Deformable image registration is one of the fundamental tasks in medical imaging. Classical registration algorithms usually require a high computational cost for iterative optimizations. Although deep-learning-based methods have been…

Deformable shape modeling approaches that describe objects in terms of their medial axis geometry (e.g., m-reps [Pizer et al., 2003]) yield rich geometrical features that can be useful for analyzing the shape of sheet-like biological…

In medical image segmentation, particularly in UNet-like architectures, upsampling is primarily used to transform smaller feature maps into larger ones, enabling feature fusion between encoder and decoder features and supporting multi-scale…

Effective learning of asymmetric and local features in images and other data observed on multi-dimensional grids is a challenging objective critical for a wide range of image processing applications involving biomedical and natural images.…

In this paper, we present an adaptive gradient descent method for geodesically convex optimization on a Riemannian manifold with nonnegative sectional curvature. The method automatically adapts to the local geometry of the function and does…

We study the problem of registering images. The framework we use is metamorphosis and we construct a variational Eulerian space-time setting and pose the registration problem as an infinite-dimensional optimisation problem. The geodesic…

This paper addresses the solution of inverse problems in imaging given an additional reference image. We combine a modification of the discrete geodesic path model for image metamorphosis with a variational model,actually the $L^2$-$TV$…

A random-walk Metropolis sampler is geometrically ergodic if its equilibrium density is super-exponentially light and satisfies a curvature condition [Stochastic Process. Appl. 85 (2000) 341-361]. Many applications, including Bayesian…

The curvature regularities are well-known for providing strong priors in the continuity of edges, which have been applied to a wide range of applications in image processing and computer vision. However, these models are usually non-convex,…

The length of the geodesic between two data points along a Riemannian manifold, induced by a deep generative model, yields a principled measure of similarity. Current approaches are limited to low-dimensional latent spaces, due to the…