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.
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…
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…
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…
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 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…
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…