# Reconstruction of 3D objects using a functional representation

Created by W.Langdon from gp-bibliography.bib Revision:1.7776

@PhdThesis{fayolle:tel-00476678,
• author = "Pierre-Alain Fayolle",
• title = "Reconstruction of {3D} objects using a functional representation",
• title_fr = "Reconstruction 3D d'objets par une representation fonctionnelle",
• school = "Universite d'Orleans",
• year = "2007",
• month = Dec,
• keywords = "genetic algorithms, genetic programming, STGP, SARDF, 3D modeling, optimization, point-set modeling, Modelisation d'objets 3D, optimisation, nuage de points",
• hal_id = "tel-00476678",
• hal_version = "v1",
• URL = "https://tel.archives-ouvertes.fr/tel-00476678/file/These_francaise.pdf",
• URL = "https://tel.archives-ouvertes.fr/tel-00476678",
• size = "112 pages",
• abstract = "This dissertation focuses on modeling volumetric objects with distance-based scalar fields. The Euclidean distance from a given point in space to a set of points representing the boundary of a solid, corresponds to the shortest distance (defined using the Euclidean norm) between this given point and any other points of the set. Representing a solid by the distance to its boundary is a concise yet powerful method for defining and manipulating solids. Within that domain, we have restricted our attention to the constructive modeling of solids and how to implement set-theoretic operations by functions with certain properties such as: good approximation of the Euclidean distance and smoothness (differentiability) of the resulting function (a property useful for many applications). Constructions of the set-theoretic operations: union, intersection and difference have been introduced and discussed. These functions can then be applied to primitives, defined by the distance to the primitive's boundary, in order to recursively construct complex solids, whose defining function corresponds to an approximation of the distance to the resulting solid's boundary. These functions are a type of R-Function, obtained by modifying the contour lines of the min/max functions (traditionally used to model set operations with implicit surfaces). We call these functions SARDF for Signed Approximation Real Distance Functions. The SARDF framework, made by these operations and primitives defined by the Euclidean distance function, is used for heterogeneous material modeling, where the distance to the shape boundary and material features is used to parametrise the material distribution inside the solid. This framework is implemented as an extension of the HyperFun Java applet and the HyperFun interpreter. Modeling objects in a constructive way, i.e. by recursively applying set-theoretic operations to primitives is a well-known and powerful paradigm in solid modeling. Combined with the functional expression of the final solid and the Euclidean distance property, it provides a powerful tool for solid modeling and applications. The construction of objects following this constructive paradigm may however be tedious and sometimes repetitive. We have considered several approaches to automate this construction. The notion of template model was introduced for this automation purpose, and several algorithms were proposed for optimizing a template model to discrete point-sets (obtained for example with a laser scanner) on or near the surface of a solid. The idea of using template models comes from the observation that most of the solids can be clustered in classes. For example, several vases can have a common shape that can be abstracted by a template model. Parameters governing the shape of the vases can be extracted and then optimized using a combination of meta-heuristics such as Simulated Annealing or Genetic Algorithm and direct methods such as Levenberg-Marquardt or Newton type methods. Defining the template models using the SARDF framework is preferable as it gives better results with the optimization algorithms. Automation of the creation of a constructive model that can further be used as a template model is also considered by using two different approaches. The first approach consists in using genetic programming to create constructive models from a discrete set of points. The second approach creates a constructive model from a segmented point-set and a list of primitives. A genetic algorithm is used to find the best constructive expression involving the primitives fitted to the segmented point-set and operations from a set of possible operations. Both approaches have been implemented and their results discussed.",
• resume = "NOUS nous sommes essentiellement interesses a la modelisation d'objets volume-triques par des champs de distance scalaire. La distance Euclidienne d'un point aun ensemble de points representant la frontiere d'un solide, correspond a la plus petite distance (definie a partir de la norme Euclidienne) entre ce point et n'importe quel point de l'ensemble. La representation du solide par la distance a la surface du solideest une methode concise mais relativement puissante pour definir et manipuler des solides. Dans ce cadre, nous nous sommes interesses a la modelisation constructive desolides, et a la facon d'implementer les operations ensemblistes par des fonctions afinde garantir une bonne approximation de la distance ainsi que certaines proprietes de differentiabilite, necessaire pour plusieurs classes d'operations ou applications sur les solides. Nous avons construit differents types de fonctions implementant les principales operations ensemblistes (union, intersection, difference). Ces fonctions peuvent etre ensuite appliquees a des primitives, definies par la distance a la surface de la primitive, afin de construire recursivement des solides complexes, definies eux-memes par une approximation a la distance du solide. Ces fonctions correspondent en fait a une certaine classe de R-fonctions, obtenues en lissant les points critiques des fonctions min/max (qui sont elles memes des R-fonctions). Ces fonctions sont appelees Signed Approximate Real Distance Functions (SARDF).

Le cadre SARDF, constitue des fonctions decrites ci-dessuset de primitives definiespar la fonction distance, a ete utilise pour la modelisation heterogene de solides. La distance, ou son approximation, a la surface du solide ou desmateriaux internesest utilisee comme un parametre pour modeliser la distribution des materiaux a l'interieur du solide. Le cadre SARDF a principalement ete implemente comme une extension de l'interpreteur d'HyperFun et a l'interieur del'applet Java d'HyperFun. La modelisation constructive de solides possede de nombreux avantages qui en font un outil puissant pour la modelisation de solides. Neanmoins, la definition constructive de solides peut etre fastidieuse et repetitive. Nous avons etudie differents aspects pour l'automatiser.

Dans un premier temps, nous avons introduit la notion de modeles template, et propose differents algorithmes pour optimiser la forme d'untemplate a differentes instances correspondant a des nuages de points, sur ou aux alentours de la surface du solide. L'idee des templates vient de l'observation que les solides traditionnelle-ment modelises par ordinateur peuvent etre regroupes en differentes classes possedant des caracteristiques communes. Par exemple, differents vases peuvent avoir une forme commune. Cette forme generale est modelisee une seule fois, et differents parametresgouvernant les caracteristiques de la forme sont extraits. Ces parametres sont ensuite optimises a l'aide d'une combinaison de meta-heuristique comme le recuit simule oules algorithmes genetiques avec des methodes directes du type Newton ou Levenberg-Marquardt. L'utilisation du cadre SARDF pour BibTeX entry too long. Truncated

Genetic Programming entries for Pierre-Alain Fayolle

Citations