Dynamic Reconstruction of Complex Planar Objects on Irregular Isothetic Grids

International audienceThe vectorization of discrete regular images has been widely developed in many image processing and synthesis applications, where images are considered as a regular static data. Regardless of final application, we have proposed in [14] a reconstruction algorithm of planar graphical elements on irregular isothetic grids. In this paper, we present a dynamic version of this algorithm to control the reconstruction. Indeed, we handle local refinements to update efficiently our complete shape representation. We also illustrate an application of our contribution for interactive approximation of implicit curves by lines, controlling the topology of the reconstruction

Unsupervised Polygonal Reconstruction of Noisy Contours by a Discrete Irregular Approach

International audienceIn this paper, we present an original algorithm to build a polygonal reconstruction of noisy digital contours. For this purpose, we first improve an algorithm devoted to the vectorization of discrete irregular isothetic objects. Afterwards we propose to use it to define a reconstruction process of noisy digital contours. More precisely, we use a local noise detector, introduced by Kerautret and Lachaud in IWCIA 2009, that builds a multi-scale representation of the digital contour, which is composed of pixels of various size depending of the local amount of noise. Finally, we compare our approach with previous works, by con- sidering the Hausdorff distance and the error on tangent orientations of the computed line segments to the original perfect contour. Thanks to both synthetic and real noisy objects, we show that our approach has interesting performance, and could be applied in document analysis systems

Courbure discrète : théorie et applications

International audienceThe present volume contains the proceedings of the 2013 Meeting on discrete curvature, held at CIRM, Luminy, France. The aim of this meeting was to bring together researchers from various backgrounds, ranging from mathematics to computer science, with a focus on both theory and applications. With 27 invited talks and 8 posters, the conference attracted 70 researchers from all over the world. The challenge of finding a common ground on the topic of discrete curvature was met with success, and these proceedings are a testimony of this wor

Collection of abstracts of the 24th European Workshop on Computational Geometry

International audienceThe 24th European Workshop on Computational Geomety (EuroCG'08) was held at INRIA Nancy - Grand Est & LORIA on March 18-20, 2008. The present collection of abstracts contains the 63 scientific contributions as well as three invited talks presented at the workshop

Topological and Geometrical Reconstruction of Complex Objects on Irregular Isothetic Grids

Abstract. In this paper, we address the problem of vectorization of binary images on irregular isothetic grids. The representation of graphical elements by lines is common in document analysis, where images are digitized on (sometimes very-large scale) regular grids. Regardless of final application, we propose to first describe the topology of an irregular two-dimensional object with its associated Reeb graph, and we recode it with simple irregular discrete arcs. The second phase of our algorithm consists of a polygonal reconstruction of this object, with discrete lines through the elementary arcs computed in the previous stage. We also illustrate the robustness of our method, and discuss applications and improvements.

30 años (1977-2007): Centro de Investigaciones Ópticas (CIOp)

La edición de este libro fue financiada en parte por la Comisión de Investigaciones Científicas de la Provincia de Buenos Aires

LIPIcs, Volume 274, ESA 2023, Complete Volume

LIPIcs, Volume 274, ESA 2023, Complete Volum

Géométrie discrète sur grilles irrégulières isothétiques

The systems that perform the acquisition of two or three (2-D or 3-D) dimensional images usually provide data structured on a regular grid, also called discrete data. Those discrete objects are now efficiently handled: for measure extraction or visualization, discrete geometry defines geometrical and mathematical tools for many applications.In this PhD thesis, our goal is to adapt algorithms developped in discrete geometry to irregular isothetic grids. This generic grid model allows to represent the image structures based on pixels or voxels with variable position and size (or cells): anisotropic grids, commonly used in medical imagery, hierarchical decompositions like quadtree/octree, the compression methods like the run length encoding, etc. We propose to extend two methodologies, widely studied for discrete shape analysis, to this representation: the reconstruction of complex binary objects and distance transformation. To process the topological and geometrical reconstruction of irregular objetcs, we build the irregular discrete Reeb graph, that sums up the shape of the input object. Then, we compute and exact polygonal structure. Those two representations can be quickely updated, when a cell of the object is refined, or when several cells are grouped together. We propose two applications of our system: the distinction of ambiguous characters in a software for licence plate recognition, and planar implicit curve approximation. The distance transformation of a regular image may be computed with many algorithms, their common point is generally that they build the discrete Voronoi diagram. In this PhD thesis, we study the computation of this decomposition on irregular isothetic grids and we propose an optimal and linear algorithm (in respect to the number of cells in the grid) in 2-D. We have also developed two algorithms extensible to ndimensions, which complexity (time et space) principally depends on the irregularity of the input grid.Les systèmes d’acquisition de données image en deux ou trois dimensions (2-D ou 3-D) fournissent généralement des données organisées sur une grille régulière, appelées données discrètes. Que ce soit pour la visualisation ou l’extraction de mesures, la géométrie discrète définit les outils mathématiques et géométriques pour de nombreuses applications.Dans cette thèse, nous nous intéressons à l’adaptation des algorithmes de la géométrie discrète aux grilles irrégulières isothétiques. Ce modèle de grille permet de représenter de manière générique les structurations d’images en pixels ou voxels de taille et de position variable (ou cellules) : les grilles anisotropes, très répandues en imagerie médicale, les décompositions hiérarchiques telles que quadtree/octree, les techniques de compression comme le run length encoding, etc. Nous proposons d’étendre deux méthodologies largement étudiées pour analyser les formes discrètes à cette représentation : la reconstructiond’objets binaires complexes et la transformée en distance. Pour réaliser la reconstruction topologique et géométrique d’objets irréguliers, nous construisons le graphe de Reeb discret irrégulier, qui résume la forme de l’objet traité. Ensuite, nous calculons une structure polygonale exacte. Ces deux représentations peuvent être rapidement mises à jour, lors du raffinement d’une cellule de l’objet, ou quand plusieurs cellules sont groupées ensemble. Nous proposons deux applications de ce système : la distinction de caractères ambigus dans un outil de reconnaissance de plaques minéralogiques, et l’approximation de courbes implicites planaires.La transformée en distance d’une image régulière peut être calculée par de nombreux algorithmes, dont le point commun est généralement le calcul d’un diagramme de Voronoï discret. Dans cette thèse, nous étudions le calcul de cette décomposition sur grilles irrégulières isothétiques, et nous proposons un algorithme optimal linéaire (en le nombre de cellules de la grille) en 2-D. Nous avons également développé deux techniques extensibles à ndimensions, dont la complexité (temps et espace) dépend principalement de l’irrégularité de la grille traitée