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Reconstruction 3D d'objets par une representation fonctionnelle

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 parameterize 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.
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Contributor : Pierre-Alain Fayolle Connect in order to contact the contributor
Submitted on : Tuesday, April 27, 2010 - 3:00:05 AM
Last modification on : Saturday, June 25, 2022 - 10:11:22 AM
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  • HAL Id : tel-00476678, version 1


Pierre-Alain Fayolle. Reconstruction 3D d'objets par une representation fonctionnelle. Interface homme-machine [cs.HC]. Université d'Orléans, 2007. Français. ⟨tel-00476678⟩



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