Analyse locale de surface avec la base des Wavejets : définition de nouveaux invariants intégraux et application à l'amplification de détails géométriques

Surface analysis is a challenging research topic, which has gathered a lot of interest over the last few decades. When surface data is given as a set of points, which are the typical output of 3D laser scanners, the lack of structure makes it even more challenging. In this thesis, we tackle surface analysis by introducing a new function basis: the Wavejets. This basis allows to decompose locally the surface into a radial polynomial component and an angular frequency component. Stability properties with regards to a bad normal direction are demonstrated. By linking Wavejets coefficients to a high order differential tensor, we also define high order principal directions on the surface. Furthermore, locally splitting surfaces with respect to frequencies leads us to define new integral invariants, permitting to locally describe the surface. Such descriptors are quite robust since they result from an integration process. Finally, we develop an application of these new integral invariants for geometric detail amplification, either based on point position or on normal direction modification, creating in this case the illusion of a surface changeL'analyse de surface est un domaine de recherche difficile, qui a été un sujet de recherche très actif ces dernières décennies. Quand une surface est représentée par un ensemble de points, typiquement issus de scanners laser 3D, le manque de structure entre ces points rend leur traitement compliqué. Dans cette thèse, on propose une méthode d'analyse de surface en introduisant une nouvelle base de fonctions: les Wavejets. Cette base permet de décomposer localement une surface radialement en polynômes et angulairement en fréquences. Des propriétés de stabilité en fonction d'une mauvaise direction de normal sont démontrées. En liant les coefficients des Wavejets a des tenseurs différentiels à hauts ordres, on définit aussi des directions principales à haut ordre sur la surface. De plus, séparer localement les surfaces fréquentiellement nous amène à la définition de nouveaux invariants intégraux, permettant de décrire localement la surface. De tels descripteurs sont assez robutes car ils sont calculés par intégration. Enfin, Nous proposons une application à ces invariants intégraux pour l'amplification de détails géométriques, soit en changeant la position des points de la surface, soit en changeant la direction des normales, créant dans ce dernier cas l'illusion d'un changement de géometrie sur la surfac

Analyse locale de surface avec la base des Wavejets : définition de nouveaux invariants intégraux et application à l'amplification de détails géométriques

Surface analysis is a challenging research topic, which has gathered a lot of interest over the last few decades. When surface data is given as a set of points, which are the typical output of 3D laser scanners, the lack of structure makes it even more challenging. In this thesis, we tackle surface analysis by introducing a new function basis: the Wavejets. This basis allows to decompose locally the surface into a radial polynomial component and an angular frequency component. Stability properties with regards to a bad normal direction are demonstrated. By linking Wavejets coefficients to a high order differential tensor, we also define high order principal directions on the surface. Furthermore, locally splitting surfaces with respect to frequencies leads us to define new integral invariants, permitting to locally describe the surface. Such descriptors are quite robust since they result from an integration process. Finally, we develop an application of these new integral invariants for geometric detail amplification, either based on point position or on normal direction modification, creating in this case the illusion of a surface changeL'analyse de surface est un domaine de recherche difficile, qui a été un sujet de recherche très actif ces dernières décennies. Quand une surface est représentée par un ensemble de points, typiquement issus de scanners laser 3D, le manque de structure entre ces points rend leur traitement compliqué. Dans cette thèse, on propose une méthode d'analyse de surface en introduisant une nouvelle base de fonctions: les Wavejets. Cette base permet de décomposer localement une surface radialement en polynômes et angulairement en fréquences. Des propriétés de stabilité en fonction d'une mauvaise direction de normal sont démontrées. En liant les coefficients des Wavejets a des tenseurs différentiels à hauts ordres, on définit aussi des directions principales à haut ordre sur la surface. De plus, séparer localement les surfaces fréquentiellement nous amène à la définition de nouveaux invariants intégraux, permettant de décrire localement la surface. De tels descripteurs sont assez robutes car ils sont calculés par intégration. Enfin, Nous proposons une application à ces invariants intégraux pour l'amplification de détails géométriques, soit en changeant la position des points de la surface, soit en changeant la direction des normales, créant dans ce dernier cas l'illusion d'un changement de géometrie sur la surfac

Surface derivatives computation using Fourier Transform

National audienceWe present a method for computing high order derivatives on a smooth surface S at a point p by analyzing the vibrations of the surface along circles in the tangent plane, centered at p. By computing the Discrete Fourier Transform of the deviation of S from the tangent plane restricted to those circles, a linear relation between the Fourier coefficients and the derivatives can be expressed. Thus, given a smooth scalar field defined on the surface, all its derivatives at p can be computed simultaneously. The originality of this method is that no direct derivation process is applied to the data. Instead, integration is performed through the Discrete Fourier Transform, and the result is expressed as a one dimensional polynomial. We derive two applications of our framework namely normal correction and curvature estimation which we demonstrate on synthetic and real data

Wavejets: A Local Frequency Framework for Shape Details Amplification

International audienceDetail enhancement is a well-studied area of 3D rendering and image processing, which has few equivalents for 3D shape processing. To enhance details, one needs an efficient analysis tool to express the local surface dynamics. We introduce Wavejets, a new function basis for locally decomposing a shape expressed over the local tangent plane, by considering both angular oscillations of the surface around each point and a radial polynomial. We link the Wavejets coefficients to surface derivatives and give theoretical guarantees for their precision and stability with respect to an approximate tangent plane. The coefficients can be used for shape details amplification, to enhance, invert or distort them, by operating either on the surface point positions or on the normals. From a practical point of view, we derive an efficient way of estimating Wavejets on point sets and demonstrate experimentally the amplification results with respect to noise or basis truncation

Arbitrary order principal directions and how to compute them

Curvature principal directions on geometric surfaces are a ubiquitous concept of Geometry Processing techniques. However they only account for order 2 differential quantities, oblivious of higher order differential behaviors. In this paper, we extend the concept of principal directions to higher orders for surfaces in R 3 by considering symmetric differential tensors. We further show how they can be explicitly approximated on point set surfaces and that they convey valuable geometric information, that can help the analysis of 3D surfaces

Arbitrary order principal directions and how to compute them

Curvature principal directions on geometric surfaces are a ubiquitous concept of Geometry Processing techniques. However they only account for order 2 differential quantities, oblivious of higher order differential behaviors. In this paper, we extend the concept of principal directions to higher orders for surfaces in R 3 by considering symmetric differential tensors. We further show how they can be explicitly approximated on point set surfaces and that they convey valuable geometric information, that can help the analysis of 3D surfaces

Arbitrary order principal directions and how to compute them

Curvature principal directions on geometric surfaces are a ubiquitous concept of Geometry Processing techniques. However they only account for order 2 differential quantities, oblivious of higher order differential behaviors. In this paper, we extend the concept of principal directions to higher orders for surfaces in R 3 by considering symmetric differential tensors. We further show how they can be explicitly approximated on point set surfaces and that they convey valuable geometric information, that can help the analysis of 3D surfaces