Search results for "Euclidean"

showing 10 items of 185 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.

010101 applied mathematicsPure mathematicsApplied Mathematics010102 general mathematicsEuclidean geometryMathematics::Metric GeometryUniqueness0101 mathematics01 natural sciencesAnalysisMathematicsNonlinear Analysis
researchProduct

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…

0209 industrial biotechnology3d registrationPixelbusiness.industry[INFO.INFO-RB] Computer Science [cs]/Robotics [cs.RO][ INFO.INFO-RB ] Computer Science [cs]/Robotics [cs.RO]Linear matrix inequalityComputingMethodologies_IMAGEPROCESSINGANDCOMPUTERVISIONImage registration[INFO.INFO-CV]Computer Science [cs]/Computer Vision and Pattern Recognition [cs.CV]02 engineering and technology[ INFO.INFO-CV ] Computer Science [cs]/Computer Vision and Pattern Recognition [cs.CV]020901 industrial engineering & automation[INFO.INFO-CV] Computer Science [cs]/Computer Vision and Pattern Recognition [cs.CV]Robustness (computer science)Projective frameComputer Science::Computer Vision and Pattern RecognitionEuclidean geometry0202 electrical engineering electronic engineering information engineering[INFO.INFO-RB]Computer Science [cs]/Robotics [cs.RO]020201 artificial intelligence & image processingComputer visionArtificial intelligencebusinessMathematics
researchProduct

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…

0209 industrial biotechnologyComputer scienceINGENIERIA MECANICA02 engineering and technologyMachine learningcomputer.software_genreField (computer science)020901 industrial engineering & automationArtificial IntelligenceEuclidean geometryMachine learning0202 electrical engineering electronic engineering information engineeringFinite element method Real timebusiness.industryWork (physics)General EngineeringCoherent point driftBiomechanical engineeringFinite element methodComputer Science ApplicationsRange (mathematics)Liver020201 artificial intelligence & image processingArtificial intelligenceBiomechanical modelingbusinesscomputer
researchProduct

Static and Dynamic Objects Analysis as a 3D Vector Field

2017

International audience; In the context of scene modelling, understanding, and landmark-based robot navigation, the knowledge of static scene parts and moving objects with their motion behaviours plays a vital role. We present a complete framework to detect and extract the moving objects to reconstruct a high quality static map. For a moving 3D camera setup, we propose a novel 3D Flow Field Analysis approach which accurately detects the moving objects using only 3D point cloud information. Further, we introduce a Sparse Flow Clustering approach to effectively and robustly group the motion flow vectors. Experiments show that the proposed Flow Field Analysis algorithm and Sparse Flow Clusterin…

0209 industrial biotechnologyComputer sciencebusiness.industry[INFO.INFO-RB] Computer Science [cs]/Robotics [cs.RO][ INFO.INFO-RB ] Computer Science [cs]/Robotics [cs.RO]ComputingMethodologies_IMAGEPROCESSINGANDCOMPUTERVISIONPoint cloud[INFO.INFO-CV]Computer Science [cs]/Computer Vision and Pattern Recognition [cs.CV]Context (language use)Motion detection02 engineering and technology[ INFO.INFO-CV ] Computer Science [cs]/Computer Vision and Pattern Recognition [cs.CV][INFO.INFO-CV] Computer Science [cs]/Computer Vision and Pattern Recognition [cs.CV]020901 industrial engineering & automationFlow (mathematics)Motion estimation0202 electrical engineering electronic engineering information engineering[INFO.INFO-RB]Computer Science [cs]/Robotics [cs.RO]020201 artificial intelligence & image processingSegmentationComputer visionArtificial intelligenceCluster analysisbusinessEuclidean vector2017 International Conference on 3D Vision (3DV)
researchProduct

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…

0209 industrial biotechnologyGeodesicComputingMethodologies_IMAGEPROCESSINGANDCOMPUTERVISIONImage processing02 engineering and technologyCatadioptric system020901 industrial engineering & automation0202 electrical engineering electronic engineering information engineering[INFO.INFO-RB]Computer Science [cs]/Robotics [cs.RO]Computer visionImage gradientFeature detection (computer vision)MathematicsCatadioptric imagebusiness.industry[ INFO.INFO-RB ] Computer Science [cs]/Robotics [cs.RO]Spherical imageimage processingInterest point detectionEuclidean distancespherical image * Corresponding author Tel : +33-385-731-128Computer Science::Computer Vision and Pattern RecognitionSignal ProcessingMetric (mathematics)020201 artificial intelligence & image processingComputer Vision and Pattern RecognitionArtificial intelligencebusiness
researchProduct

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…

A comprehensive analysis of vaulted bodies involves the study of the multiple components necessary for their definition: geometric configuration construction system historical-geographical area of belonging interpretations Stylistic. The objective of this study is directed to the 'analysis of continuous vaults on a centric plan definable through the laws of Euclidean geometry. The investigation arises within the boundaries related to their geometric configuration and the criterion adopted freed from typological or stylistic classifications proposes the identification of geometric families based on the figure of the basic polygon of the plant. An ordering process can be identified to explain the compositional process of curved-roofed central plants: that is the elaboration of a series of theoretical models developed according to an abacus referring to the basic geometries of the triangle square and pentagon is possible. It is not intended to impose a classification but to propose a study tool that thanks to a few simple compositional rules develops a very large number of configurationthe question remains as to why only a part has been used for the realization of vaulted covered centric buildings but this presumes considerations of a historical formal and constructive nature extraneous to this discussion.Settore ICAR/17 - Disegno
researchProduct

A finite element-based machine learning approach for modeling the mechanical behavior of the breast tissues under compression in real-time

2017

[EN] This work presents a data-driven method to simulate, in real-time, the biomechanical behavior of the breast tissues in some image-guided interventions such as biopsies or radiotherapy dose delivery as well as to speed up multimodal registration algorithms. Ten real breasts were used for this work. Their deformation due to the displacement of two compression plates was simulated off-line using the finite element (FE) method. Three machine learning models were trained with the data from those simulations. Then, they were used to predict in real-time the deformation of the breast tissues during the compression. The models were a decision tree and two tree-based ensemble methods (extremely…

AdultFinite element methodsMean squared errorComputer scienceQuantitative Biology::Tissues and OrgansINGENIERIA MECANICAFinite Element AnalysisPhysics::Medical PhysicsDecision treeBreast compressionHealth Informatics02 engineering and technologyMachine learningcomputer.software_genreModels Biological030218 nuclear medicine & medical imagingSet (abstract data type)03 medical and health sciencesImaging Three-Dimensional0302 clinical medicineMachine learning0202 electrical engineering electronic engineering information engineeringHumansBreastbusiness.industryModelingEnsemble learningFinite element methodComputer Science ApplicationsRandom forestEuclidean distanceTree (data structure)Female020201 artificial intelligence & image processingArtificial intelligenceBreast biomechanicsbusinesscomputerLENGUAJES Y SISTEMAS INFORMATICOS
researchProduct

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…

AdultMaleHeart Ventriclesvolume measurementinfarction[INFO.INFO-IM] Computer Science [cs]/Medical ImagingMyocardial InfarctionInfarctionheart030204 cardiovascular system & hematologyIntersection (Euclidean geometry)030218 nuclear medicine & medical imaging03 medical and health sciences0302 clinical medicinemedicine[INFO.INFO-IM]Computer Science [cs]/Medical ImagingHumansRadiology Nuclear Medicine and imagingMyocardial infarctionejection fractionAgedAged 80 and overvolumeEjection fractionmedicine.diagnostic_test[ INFO.INFO-IM ] Computer Science [cs]/Medical Imagingbusiness.industryventriclesMyocardiumMagnetic resonance imagingStroke VolumeStroke volumeMRMiddle Agedmedicine.diseaseMagnetic Resonance Imagingmedicine.anatomical_structureVentricleEnd-diastolic volumeFemalebusinessNuclear medicinemagnetic resonance (MR)cine studyRadiology
researchProduct

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.

Ahlfors-regularity26B05 (Primary) 28A80 (Secondary)01 natural sciences010104 statistics & probabilityFractalMathematics - Metric GeometryEuclidean geometryClassical Analysis and ODEs (math.CA)FOS: MathematicsHeisenberg groupMathematics::Metric GeometryBPI-spacesbpi-spacessecondary 28a800101 mathematicsbilipschitz piecesMathematicsDiscrete mathematicsQA299.6-433ahlfors-regularityApplied Mathematics010102 general mathematicsprimary 26b05Metric Geometry (math.MG)biLipschitz piecesMathematics - Classical Analysis and ODEsProduct (mathematics)Geometry and TopologyAnalysis
researchProduct

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…

AlgebraComputationObject languageEuclidean geometryFormal languageInductive reasoningEquivalence (formal languages)AlgorithmExpression (mathematics)DecidabilityMathematics
researchProduct