A generalized preimage for the digital analytical hyperplane recognition

International audienceA new digital hyperplane recognition method is presented. This algorithm allows the recognition of digital analytical hyperplanes, such as Naive, Standard and Supercover ones. The principle is to incrementally compute in a dual space the generalized preimage of the ball set corresponding to a given hypervoxel set according to the chosen digitization model. Each point in this preimage corresponds to a Euclidean hyperplane the digitization of which contains all given hypervoxels. An advantage of the generalized preimage is that it does not depend on the hypervoxel locations. Moreover, the proposed recognition algorithm does not require the hypervoxels to be connected or ordered in any way

Architecture d'un modeleur géométrique à base topologique d'objets discrets et méthodes de reconstruction en dimensions 2 et 3

Dans cette thèse nous nous intéressons àla question suivante: comment obtenir un objet continu à partir d'un objet discret? Dans un premier temps, nous nous intéressons au problème de la reconnaissance de primitives discrètes, en proposant une notion de préimage généralisée. Cette préimage est un objet géométrique qui fournit l'ensemble des hyperplans discrets contenant les points discrets considérés. Nous en déduisons un nouvel algorithme incrémental de reconnaissance d'hyperplans discrets et de reconstruction inversibles en dimensions 2 et 3. Dans un deuxième temps, nous avons abordé la modélisation d'objets discrets sous la forme d'un outil de modélisation géométrique àbase topologique permettant la manipulation d'objets tant sous forme continue que discrète. Les différentes représentations d'un même objet géométrique coexistent à l'intérieur d'une unique structure hiérarchique. Chaque niveau de la structure ainsi que les opérations internes sont décrites.Digital geometry provides tools to manipulate digital data such as digital images. Especially, relations between discrete and Euclidiean objects are of interest. For instance, we try to answer the following questions : How to obtain digital objects from Euclidean ones, and in the same way, how to obtain Euclidean objects from digital ones ? In this thesis, we study these two problems. First, we are interested in the digital hyperplane recognition problem which consists in determining if a digital point set belongs to a same digital hyperplane. In order to solve this problem, we propose the definition of a generalized preimage, defined in a parameter space, which provides the set of digital hyperplanes that contain all given digital points. We deduce a new incremental digital hyperplane recognition algorithm. We propose two digital objects invertible reconstruction methods in dimensions 2 and 3. In the second part of this work, we present the kernel of a modeling software that handles geometric objects represented in continuous and digital forms. Different representations of a same object coexist in an unique hierarchical structure. Each level of this structure as well as construction operations are detailed.POITIERS-BU Sciences (861942102) / SudocSudocFranceF

Invertible Polygonalization of 3D Planar Digital Curves and Application to Volume Data Reconstruction

In this paper, we describe a new algorithm to compute in linear time a 3D planar polygonal curve from a planar digital curve, that is a curve which belongs to a digital plane. Based on this algorithm, we propose a new method for converting the boundary of digital volumetric objects into polygonal meshes which aims at providing a topologically consistent and invertible reconstruction, i.e. the digitization of the ob- tained object is equal to the original digital data. Indeed, we do not want any information to be added or lost. In order to limit the number of generated polygonal faces, our approach is based on the use of digital geometry tools which allow the reconstruction of large pieces of planes