Related papers: A Numerical Framework for Efficient Motion Estimat…
A high-order accurate implicit-mesh discontinuous Galerkin framework for wave propagation in single-phase and bi-phase solids is presented. The framework belongs to the embedded-boundary techniques and its novelty regards the spatial…
We present a novel discontinuous Galerkin finite element method for numerical simulations of the rotating thermal shallow water equations in complex geometries using curvilinear meshes, with arbitrary accuracy. We derive an entropy…
A proof of convergence is given for semi- and full discretizations of mean curvature flow of closed two-dimensional surfaces. The numerical method proposed and studied here combines evolving finite elements, whose nodes determine the…
Computing the epipolar geometry between cameras with very different viewpoints is often problematic as matching points are hard to find. In these cases, it has been proposed to use information from dynamic objects in the scene for…
Spectral methods, thanks to the high accuracy and the possibility of using fast algorithms, represent an effective way to approximate collisional kinetic equations in kinetic theory. On the other hand, the loss of some local invariants can…
We present a simple method for measuring cosmological bulk flows from large redshift surveys, based on the apparent dimming or brightening of galaxies due to their peculiar motion. It is aimed at estimating bulk flows of cosmological…
This work introduces a novel discontinuity-tracking framework for resolving discontinuous solutions of conservation laws with high-order numerical discretizations that support inter-element solution discontinuities, such as discontinuous…
We introduce variational approximations for curve evolutions in two-dimensional Riemannian manifolds that are conformally flat, i.e.\ conformally equivalent to the Euclidean space. Examples include the hyperbolic plane, the hyperbolic disk,…
A third-order moving mesh cell-centered scheme without the remapping of physical variables is developed for the numerical solution of one-dimensional elastic-plastic flows with the Mie-Gr\"{u}neisen equation of state, the Wilkins…
In this work, we propose a local multiscale model reduction approach for the time-domain scalar wave equation in a heterogenous media. A fine mesh is used to capture the heterogeneities of the coefficient field, and the equation is solved…
Optical flow is the pattern of apparent motion of objects in a scene. The computation of optical flow is a critical component in numerous computer vision tasks such as object detection, visual object tracking, and activity recognition.…
Thanks to its capability of acquiring full-view frames at multiple kilohertz, ultrafast ultrasound imaging unlocked the analysis of rapidly changing physical phenomena in the human body, with pioneering applications such as ultrasensitive…
This paper introduces a set of numerical methods for Riemannian shape analysis of 3D surfaces within the setting of invariant (elastic) second-order Sobolev metrics. More specifically, we address the computation of geodesics and geodesic…
We describe the development of a tracking device, mounted on an epi-fluorescent inverted microscope, suited to obtain time resolved 3D Lagrangian tracks of fluorescent passive or active micro-objects in micro-fluidic devices. The system is…
Unlike a traditional gyroscope, a visual gyroscope estimates camera rotation through images. The integration of omnidirectional cameras, offering a larger field of view compared to traditional RGB cameras, has proven to yield more accurate…
In this paper, we study numerical methods for the solution of partial differential equations on evolving surfaces. The evolving hypersurface in $\Bbb{R}^d$ defines a $d$-dimensional space-time manifold in the space-time continuum…
A numerical method based on the hybridizable discontinuous Galerkin method in space and backward Euler in time is formulated and analyzed for solving the miscible displacement problem. Under low regularity assumptions, convergence is…
Cardiac motion estimation is an important diagnostic tool to detect heart diseases and it has been explored with modalities such as MRI and conventional ultrasound (US) sequences. US cardiac motion estimation still presents challenges…
Discontinuous Galerkin methods are developed for solving the Vlasov-Maxwell system, methods that are designed to be systematically as accurate as one wants with provable conservation of mass and possibly total energy. Such properties in…
This article describes the implementation of the joint motion estimation and image reconstruction framework presented by Burger, Dirks and Sch\"onlieb and extends this framework to large-scale motion between consecutive image frames. The…