Search results for "Euclidean geometry"
showing 10 items of 83 documents
L∞-variational problems associated to measurable Finsler structures
2016
Abstract We study L ∞ -variational problems associated to measurable Finsler structures in Euclidean spaces. We obtain existence and uniqueness results for the absolute minimizers.
LMI-based 2D-3D Registration: from Uncalibrated Images to Euclidean Scene
2015
International audience; This paper investigates the problem of registering a scanned scene, represented by 3D Euclidean point coordinates , and two or more uncalibrated cameras. An unknown subset of the scanned points have their image projections detected and matched across images. The proposed approach assumes the cameras only known in some arbitrary projective frame and no calibration or autocalibration is required. The devised solution is based on a Linear Matrix Inequality (LMI) framework that allows simultaneously estimating the projective transformation relating the cameras to the scene and establishing 2D-3D correspondences without triangulating image points. The proposed LMI framewo…
Real-time biomechanical modeling of the liver using Machine Learning models trained on Finite Element Method simulations
2020
[EN] The development of accurate real-time models of the biomechanical behavior of different organs and tissues still poses a challenge in the field of biomechanical engineering. In the case of the liver, specifically, such a model would constitute a great leap forward in the implementation of complex applications such as surgical simulators, computed-assisted surgery or guided tumor irradiation. In this work, a relatively novel approach for developing such a model is presented. It consists in the use of a machine learning algorithm, which provides real-time inference, trained on tens of thousands of simulations of the biomechanical behavior of the liver carried out by the finite element me…
Genesi geometrica delle volte centriche
1996
Un'analisi completa degli organismi voltati comporta lo studio delle molteplici componenti necessarie alla loro definizione: configurazione geometrica, sistema costruttivo, area storico-geografica di appartenenza, interpretazioni Stilistiche. L’obiettivo di questo studio è indirizzato all' analisi delle volte continue su pianta centrica definibili attraverso le leggi della geometria euclidea. L’indagine si pone all'interno dei confini relativi alla loro configurazione geometrica e il criterio adottato, svincolato da classificazioni di carattere tipologico o stilistico, propone l'identificazione di famiglie geometriche in base alla figura del poligono di base dell'impianto. Si può identifica…
MR imaging of the heart in patients after myocardial infarction: effect of increasing intersection gap on measurements of left ventricular volume, ej…
1999
International audience; Abstract: PURPOSE: To determine the extent to which the number of planes imaged at magnetic resonance (MR) imaging could be reduced without modifying the volume and thickness of the left ventricle. MATERIALS AND METHODS: Sixty-one patients were examined after a myocardial infarction. The whole left ventricle was imaged by using 5-mm contiguous breath-hold cine MR short-axis sections with no gap (SA(ng)) (two-dimensional fast low-angle shot sequence, 9/4.8 [repetition time msec/echo time msec]). The effect of omitting in two (short-axis sections with 5-mm gap [SA(5mm)]) or two sections in three(short-axis sections with 10-mm gap [SA(10mm)]) was studied. RESULTS: In th…
Products of snowflaked Euclidean lines are not minimal for looking down
2017
We show that products of snowflaked Euclidean lines are not minimal for looking down. This question was raised in Fractured fractals and broken dreams, Problem 11.17, by David and Semmes. The proof uses arguments developed by Le Donne, Li and Rajala to prove that the Heisenberg group is not minimal for looking down. By a method of shortcuts, we define a new distance $d$ such that the product of snowflaked Euclidean lines looks down on $(\mathbb R^N,d)$, but not vice versa.
Inductive synthesis of dot expressions
2005
We consider the problem of the synthesis of algorithms by sample computations. We introduce a formal language, namely, the so-called dot expressions, which is based on a formalization of the intuitive notion of ellipsis (‘...’). Whilst formally the dot expressions are simply a language describing sets of words, on the other hand, it can be considered as a programming language supporting quite a wide class of programs. Equivalence and asymptotical equivalence of dot expressions are defined and proved to be decidable. A formal example of a dot expression is defined in the way that, actually, it represents a sample computation of the program presented by the given dot expression. A system of s…
Pieri’s 1900 Point-and-Motion Memoir
2021
This chapter contains an English translation of Mario Pieri’s 1900a memoir, On Elementary Geometry as a Hypothetical Deductive System: Monograph on Point and on Motion.1 By elementary geometry, Pieri meant Euclidean geometry as taught then in elementary courses, except for the theorems dependent on the Euclidean parallel axiom.
Quasisymmetric structures on surfaces
2009
We show that a locally Ahlfors 2-regular and locally linearly locally contractible metric surtace is locally quasisymmetrically equivalent to tne disk. We also discuss an application of this result to the problem of characterizing surfaces embedded in some Euclidean spaces that are locally bi-Lipschitz equivalent to a ball in the plane.
A tour of the theory of absolutely minimizing functions
2004
A detailed analysis of the class of absolutely minimizing functions in Euclidean spaces and the relationship to the infinity Laplace equation