Related papers: Geodesic Warps by Conformal Mappings
This paper presents a generalization to image matching of the Hamiltonian approach for planar curve matching developed in the context of group of diffeomorphisms. We propose an efficient framework to deal with discontinuous images in any…
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…
This paper combines image metamorphosis with deep features. To this end, images are considered as maps into a high-dimensional feature space and a structure-sensitive, anisotropic flow regularization is incorporated in the metamorphosis…
We analyze a variational time discretization of geodesic calculus on finite- and certain classes of infinite-dimensional Riemannian manifolds. We investigate the fundamental properties of discrete geodesics, the associated discrete…
Continuous image morphing is a classical task in image processing. The metamorphosis model proposed by Trouv\'e, Younes and coworkers casts this problem in the frame of Riemannian geometry and geodesic paths between images. The associated…
We develop a new method for visualizing and refining the invariances of learned representations. Specifically, we test for a general form of invariance, linearization, in which the action of a transformation is confined to a low-dimensional…
Image retargeting, which resizes images to one with a prescribed aspect ratio by determining an optimal warping map, has gained substantial interest in imaging science. Despite significant advances, existing methods often fail to ensure…
This paper proposes a new framework and algorithms to address the problem of diffeomorphic registration on a general class of geometric objects that can be described as discrete distributions of local direction vectors. It builds on both…
Conformal mapping has been applied mostly to harmonic functions, i.e. solutions of Laplace's equation. In this paper, it is noted that some other equations are also conformally invariant and thus equally well suited for conformal mapping in…
Recent successes in deep learning based deformable image registration (DIR) methods have demonstrated that complex deformation can be learnt directly from data while reducing computation time when compared to traditional methods. However,…
Based on a local approximation of the Riemannian distance on a manifold by a computationally cheap dissimilarity measure, a time discrete geodesic calculus is developed, and applications to shape space are explored. The dissimilarity…
Morphing is the process of changing one figure into another. Some numerical methods of 3D surface morphing by deformable modeling and conformal mapping are shown in this study. It is well known that there exists a unique Riemann conformal…
Anatomical variabilities seen in longitudinal data or inter-subject data is usually described by the underlying deformation, captured by non-rigid registration of these images. Stationary Velocity Field (SVF) based non-rigid registration…
Non-rigid 3D mesh matching is a critical step in computer vision and computer graphics pipelines. We tackle matching meshes that contain topological artefacts which can break the assumption made by current approaches. While Functional Maps…
We present a framework for shape matching in computational anatomy allowing users control of the degree to which the matching is diffeomorphic. This control is given as a function defined over the image and parameterises the template…
We address the following problem: given two smooth densities on a manifold, find an optimal diffeomorphism that transforms one density into the other. Our framework builds on connections between the Fisher-Rao information metric on the…
In this paper we propose a novel method for image matching based on dense local features and tailored for visual geolocalization. Dense local features matching is robust against changes in illumination and occlusions, but not against…
This paper presents a novel method, named geodesic deformable networks (GDN), that for the first time enables the learning of geodesic flows of deformation fields derived from images. In particular, the capability of our proposed GDN being…
The paper surveys variational approaches for image reconstruction in dynamic inverse problems. Emphasis is on methods that rely on parametrised temporal models. These are here encoded as diffeomorphic deformations with time dependent…
We propose a novel optimization algorithm for continuous functions using geodesics and contours under conformal mapping.The algorithm can find multiple optima by first following a geodesic curve to a local optimum then traveling to the next…