Search results for "Euclid"
showing 10 items of 190 documents
Lung CT Image Registration through Landmark-constrained Learning with Convolutional Neural Network
2020
Accurate registration of lung computed tomography (CT) image is a significant task in thorax image analysis. Recently deep learning-based medical image registration methods develop fast and achieve promising performance on accuracy and speed. However, most of them learned the deformation field through intensity similarity but ignored the importance of aligning anatomical landmarks (e.g., the branch points of airway and vessels). Accurate alignment of anatomical landmarks is essential for obtaining anatomically correct registration. In this work, we propose landmark constrained learning with a convolutional neural network (CNN) for lung CT registration. Experimental results of 40 lung 3D CT …
An overdetermined problem for the anisotropic capacity
2015
We consider an overdetermined problem for the Finsler Laplacian in the exterior of a convex domain in \({\mathbb {R}}^{N}\), establishing a symmetry result for the anisotropic capacitary potential. Our result extends the one of Reichel (Arch Ration Mech Anal 137(4):381–394, 1997), where the usual Newtonian capacity is considered, giving rise to an overdetermined problem for the standard Laplace equation. Here, we replace the usual Euclidean norm of the gradient with an arbitrary norm H. The resulting symmetry of the solution is that of the so-called Wulff shape (a ball in the dual norm \(H_0\)).
Continuity of the radon transform and its inverse on Euclidean space
1983
A Monge-Kantorovich mass transport problem for a discrete distance
2011
This paper is concerned with a Monge-Kantorovich mass transport problem in which in the transport cost we replace the Euclidean distance with a discrete distance. We fix the length of a step and the distance that measures the cost of the transport depends of the number of steps that is needed to transport the involved mass from its origin to its destination. For this problem we construct special Kantorovich potentials, and optimal transport plans via a nonlocal version of the PDE formulation given by Evans and Gangbo for the classical case with the Euclidean distance. We also study how these problems, when rescaling the step distance, approximate the classical problem. In particular we obta…
A New Iterative Estimation Procedure for the Localization of Passive Stationary Objects from Received RF Signals in Indoor Environments
2019
This paper deals with the localization of passive stationary objects from the received radio- frequency (RF) signals in 3-dimensional (3D) indoor environments. Each object located in the 3D indoor environment is modelled by a single point scatterer. The propagation space is equipped with a multiple-input multiple-output (MIMO) wireless communication system. The employed channel model is flexible and allows to have a line-of-sight (LOS) component as well as single- and double- bounce scattering components. Here, we present a new accurate iterative estimation technique for computing the optimal coordinates as well as the number of the main stationary objects (scatterers) in indoor areas. The …
A New Iterative Procedure for the Localization of a Moving Object/Person in Indoor Areas from Received RF Signals
2019
This paper presents a new iterative estimation method to localize a single moving object or person in non-stationary 3-dimensional (3D) indoor environments from received radiofrequency (RF) signals. The moving object/person is modelled by a moving single point scatterer. The indoor space is equipped with a multiple-input multiple-output (MIMO) communication system. This work starts by introducing a new geometrical channel model which considers the effects of the line-of-sight (LOS) component, the fixed objects located in a room, and the moving object (point scatterer). Then, we present an iterative estimation technique for computing the time-variant (TV) coordinates of the moving scatterer.…
On Randomness and Structure in Euclidean TSP Instances: A Study With Heuristic Methods
2021
Prediction of the quality of the result provided by a specific solving method is an important factor when choosing how to solve a given problem. The more accurate the prediction, the more appropriate the decision on what to choose when several solving applications are available. In this article, we study the impact of the structure of a Traveling Salesman Problem instance on the quality of the solution when using two representative heuristics: the population-based Ant Colony Optimization (ACO) and the local search Lin-Kernighan (LK) algorithm. The quality of the result for a solving method is measured by the computation accuracy, which is expressed using the percent error between its soluti…
On proper branched coverings and a question of Vuorinen
2022
We study global injectivity of proper branched coverings from the open Euclidean n$n$-ball onto an open subset of the Euclidean n$n$-space in the case where the branch set is compact. In particular, we show that such mappings are homeomorphisms when n=3$n=3$ or when the branch set is empty. This gives a positive answer to the corresponding cases of a question of Vuorinen. Peer reviewed
X-ray Tomography of One-forms with Partial Data
2021
If the integrals of a one-form over all lines meeting a small open set vanish and the form is closed in this set, then the one-form is exact in the whole Euclidean space. We obtain a unique continuation result for the normal operator of the X-ray transform of one-forms, and this leads to one of our two proofs of the partial data result. Our proofs apply to compactly supported covector-valued distributions.
Inverse problems for elliptic equations with power type nonlinearities
2021
We introduce a method for solving Calder\'on type inverse problems for semilinear equations with power type nonlinearities. The method is based on higher order linearizations, and it allows one to solve inverse problems for certain nonlinear equations in cases where the solution for a corresponding linear equation is not known. Assuming the knowledge of a nonlinear Dirichlet-to-Neumann map, we determine both a potential and a conformal manifold simultaneously in dimension $2$, and a potential on transversally anisotropic manifolds in dimensions $n \geq 3$. In the Euclidean case, we show that one can solve the Calder\'on problem for certain semilinear equations in a surprisingly simple way w…