Search results for "Geodesic"

Central catadioptric image processing with geodesic metric

2011

International audience; Because of the distortions produced by the insertion of a mirror, catadioptric images cannot be processed similarly to classical perspective images. Now, although the equivalence between such images and spherical images is well known, the use of spherical harmonic analysis often leads to image processing methods which are more difficult to implement. In this paper, we propose to define catadioptric image processing from the geodesic metric on the unitary sphere. We show that this definition allows to adapt very simply classical image processing methods. We focus more particularly on image gradient estimation, interest point detection, and matching. More generally, th…

Curve Extraction by Geodesics Fusion: Application to Polymer Reptation Analysis

2016

© Springer International Publishing Switzerland 2016. In the molecular field, researchers analyze dynamics of polymers by microscopy: several measurements such as length and curvature are performed in their studies. To achieve correct analysis they need to extract the curve representing as good as possible the observed polymer shape which is a grayscale thick curve with noise and blur. We propose, in this paper, a method to extract such a curve. A polymer chain moves in a snake-like fashion (Reptation): it can self-intersect and form several complex geometries. To efficiently extract the different geometries, we generate the curve by computing a piecewise centerline browsing the shape by ge…

Verification of Radiative Transfer Schemes for the EHT

2020

Authors: Gold, Roman; Broderick, Avery E.; Younsi, Ziri; Fromm, Christian M.; Gammie, Charles F.; Mościbrodzka, Monika; Pu, Hung-Yi; Bronzwaer, Thomas; Davelaar, Jordy; Dexter, Jason; Ball, David; Chan, Chi-kwan; Kawashima, Tomohisa; Mizuno, Yosuke; Ripperda, Bart; Akiyama, Kazunori; Alberdi, Antxon; Alef, Walter; Asada, Keiichi; Azulay, Rebecca Baczko, Anne-Kathrin; Baloković, Mislav; Barrett, John; Bintley, Dan; Blackburn, Lindy; Boland, Wilfred; Bouman, Katherine L.; Bower, Geoffrey C.; Bremer, Michael; Brinkerink, Christiaan D.; Brissenden, Roger; Britzen, Silke; Broguiere, Dominique; Byun, Do-Young; Carlstrom, John E.; Chael, Andrew; Chatterjee, Koushik; Chatterjee, Shami; Chen, Ming-T…

Fixed Points for Multivalued Convex Contractions on Nadler Sense Types in a Geodesic Metric Space

2019

In 1969, based on the concept of the Hausdorff metric, Nadler Jr. introduced the notion of multivalued contractions. He demonstrated that, in a complete metric space, a multivalued contraction possesses a fixed point. Later on, Nadler&rsquo

Abel transforms with low regularity with applications to X-ray tomography on spherically symmetric manifolds

2017

We study ray transforms on spherically symmetric manifolds with a piecewise $C^{1,1}$ metric. Assuming the Herglotz condition, the X-ray transform is injective on the space of $L^2$ functions on such manifolds. We also prove injectivity results for broken ray transforms (with and without periodicity) on such manifolds with a $C^{1,1}$ metric. To make these problems tractable in low regularity, we introduce and study a class of generalized Abel transforms and study their properties. This low regularity setting is relevant for geophysical applications.

QUANTIZATION OPERATORS ON QUADRICS

2008

Our Friend and Mathematician Karl Strambach

2020

This paper is dedicated to Karl Strambach on the occasion of his 80th birthday. Here we want to describe our work with Prof. Karl Strambach.

Bruhat–Tits Trees and Modular Groups

2019

In this chapter, we give background information and preliminary results on the main link between the geometry and the algebra used for our arithmetic applications: the (discrete-time) geodesic ow on quotients of Bruhat{Tits trees by arithmetic lattices.

Generalized John disks

2014

Abstract We establish the basic properties of the class of generalized simply connected John domains.

Old and New on the Quasihyperbolic Metric

1998

Let D be a proper subdomain of \( {\mathbb{R}^d}\). Following Gehring and Palka [GP] we define the quasihyperbolic distance between a pair x 1, x 2 of points in D as the infimum of \( {\smallint _\gamma }\frac{{ds}}{{D\left( {x,\partial D} \right)}}\) over all rectifiable curves γ joining x 1, x 2 in D. We denote the quasihyperbolic distance between x 1, x 2 by k D (x 1, x 2). As pointed out by Gehring and Osgood [GO], x 1 and x 2 can be joined by a quasihyperbolic geodesic; also see [Mr]. The quasihyperbolic metric is comparable to the usual hyperbolic metric in a simply connected plane domain by the Koebe distortion theorem. For a multiply connected plane domain D these two metrics are co…