Related papers: Hamiltonian approach to geodesic image matching
We introduce a comprehensive benchmark for local features and robust estimation algorithms, focusing on the downstream task -- the accuracy of the reconstructed camera pose -- as our primary metric. Our pipeline's modular structure allows…
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…
Homographies are among the most prevalent transformations occurring in geometric computer vision and projective geometry, and homography estimation is consequently a crucial step in a wide assortment of computer vision tasks. When working…
We propose an original method for vectorizing an image or zooming it at an arbitrary scale. The core of our method relies on the resolution of a geometric variational model and therefore offers theoretic guarantees. More precisely, it…
Metamorphosis is a method for diffeomorphic matching of shapes, with many potential applications for anatomical shape comparison in medical imagery, a problem which is central to the field of computational anatomy. An important tool for the…
Explicit and semi-explicit geometric integration schemes for dissipative perturbations of Hamiltonian systems are analyzed. The dissipation is characterized by a small parameter $\epsilon$, and the schemes under study preserve the…
Hamiltonian Monodromy is the simplest topological obstruction to the existence of global action-angle coordinates in a completely integrable system. We show that this property can be studied in a neighborhood of a focus-focus singularity by…
In this paper, we address several interconnected problems in the theory of harmonic maps between Riemannian manifolds. First, we present necessary background and establish one of the main results of the paper: a criterion characterizing…
This paper discusses the mathematical framework for designing methods of large deformation matching (LDM) for image registration in computational anatomy. After reviewing the geometrical framework of LDM image registration methods, a…
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 this work we propose to combine the advantages of learningbased and combinatorial formalisms for 3D shape matching. While learningbased methods lead to state-of-the-art matching performance, they do not ensure geometric consistency, so…
In this work, we present a consistent Hamiltonian analysis of cosmological perturbations at all orders. To make the procedure transparent, we consider a simple model and resolve the `gauge-fixing' issues and extend the analysis to scalar…
We present a general formalism for the Hamiltonian description of perturbation theory around any spatially homogeneous spacetime. We employ and refine the Dirac method for constrained systems, which is very well-suited to cosmological…
Despite advances in feature representation, leveraging geometric relations is crucial for establishing reliable visual correspondences under large variations of images. In this work we introduce a Hough transform perspective on…
This paper proposes a local search algorithm for a specific combinatorial optimisation problem in graph theory: the Hamiltonian Completion Problem (HCP) on undirected graphs. In this problem, the objective is to add as few edges as possible…
A variational model for learning convolutional image atoms from corrupted and/or incomplete data is introduced and analyzed both in function space and numerically. Building on lifting and relaxation strategies, the proposed approach is…
Matching deformable objects using their shapes is an important problem in computer vision since shape is perhaps the most distinguishable characteristic of an object. The problem is difficult due to many factors such as intra-class…
This paper proposes a variational framework for multi-objective level set topology optimization. The approach interprets the level set function as a generalized coordinate of a fictitious material and derives its equation of motion from…
Modern camera pipelines apply extensive on-device processing, such as exposure adjustment, white balance, and color correction, which, while beneficial individually, often introduce photometric inconsistencies across views. These appearance…
We consider solutions of the $2\times 2$ matrix Hamiltonian of physical systems within the context of the asymptotic iteration method. Our technique is based on transformation of the associated Hamiltonian in the form of the first order…