Christophe Fiorio - Academia.edu (original) (raw)

Papers by Christophe Fiorio

Research paper thumbnail of Flexible Terrain Erosion - A Fluid Simulation-Independent Approach Compatible with Multiple Representations

Research Square (Research Square), Apr 18, 2024

In this paper, we present a novel particlebased method for simulating erosion on various terrain ... more In this paper, we present a novel particlebased method for simulating erosion on various terrain representations, including height fields, voxel grids, material layers, and implicit terrains. Our approach breaks down erosion into two key processes-terrain alteration and material transport-allowing for flexibility in simulation. We utilize independent particles governed by basic particle physics principles, enabling efficient parallel computation. For increased precision, a vector field can adjust particle speed, adaptable for realistic fluid simulations or user-defined control. We address material alteration in 3D terrains with a set of equations applicable across diverse models, requiring only per-particle specifications for size, density, coefficient of restitution, and sediment capacity. Our modular algorithm is versatile for real-time and offline use, suitable for both 2.5D and 3D terrains.

Research paper thumbnail of Automatic Extraction of a Piecewise Symmetry Surface of a 3D Mesh: Application to Scoliosis

Lecture Notes in Computer Science, 2018

Symmetry analysis of the surface of anatomical structures offers good promise for diagnosis, foll... more Symmetry analysis of the surface of anatomical structures offers good promise for diagnosis, follow-up and therapy planning of pathologies causing abnormal deformities. This paper addresses the problem of detecting and modelling symmetry of bilateral structures, even in cases where the transformation between the two lateral parts is not a simple planar reflection but a symmetry with respect to a curved symmetry surface. We describe a new method to compute a piecewise curved symmetry surface for 3D objects. The algorithm is based on the computation of a 3D symmetry line, which defines strips by orthogonal slicing. A local symmetry plane is computed for each strip by an ICP-like method. The set of all local symmetry planes forms a piecewise symmetry surface. The method is first validated on parametric objects. Then, we show its potential as a non-invasive technique for the study of patients affected by scoliosis. Finally, our approach is generic enough that it could be extended to other medical applications such as facial dysplasia.

Research paper thumbnail of Dev IOS V.01: Conception - Presenter

Research paper thumbnail of The Star-Topology: a topology for image analysis

Discrete Geometry for Computer Imagery, 1995

Our previous works in image analysis dealing with image representations by means of adjacency or ... more Our previous works in image analysis dealing with image representations by means of adjacency or boundary graphs, led us to the need for a coherent representation model. In fact, classical approaches to this problem seem to be unsu cient o r e v en uncoherent for example they are unclear with the well-known connectivity paradox o r w i t h t h e b o r d e r description of regions. Di erent works like those of Kovalevsky, Herman and Malandain pointed out the advantages of cellular complex based topologies Kovalevsky89, Herman90, Malandain93]. But no one of them suggested a formalism that can be applied to any type of image. In this work we propose a topological representation for any type of image, colour or grey-level of whatever dimension. It is based on convex complexes, and looks closely at the elements realizing the connectivity within complexes and later within regions. Futhermore it remains coherent with pixel and voxel only based representations. An important feature is still maintaining a direct correspondance with the classical IR n topology. Finally, w e suggest a characterization of regions, their borders and boundaries which is useful as a basic tool for segmentation.

Research paper thumbnail of Discrete Geometry for Computer Imagery

Lecture Notes in Computer Science, 1997

Research paper thumbnail of Proceedings of the 7th International Workshop on Discrete Geometry for Computer Imagery

Research paper thumbnail of 画像対に及ぼす欠如マーカーを用いた祖先推定によるJPEG画像の系統発生【Powered by NICT】

IEEE Conference Proceedings, 2016

Research paper thumbnail of Phylogeny of JPEG images by ancestor estimation using missing markers on image pairs

2016 Sixth International Conference on Image Processing Theory, Tools and Applications (IPTA), 2016

Nowadays it is extremely easy to tamper with images and share them thanks to social media. Identi... more Nowadays it is extremely easy to tamper with images and share them thanks to social media. Identifying the transformation history is imperative to be able to trust these images. We address this problem by using image phylogeny trees, where the root is the image that has been less tampered with and as every generation is obtained from the transformation of its parents, the leaves are the most transformed images. Our method for image phylogeny trees reconstruction is based on a binary decision between two images using JPEG compression artifacts. Experimental results show that when there is no missing image data, the reconstruction is very accurate.

Research paper thumbnail of Processus de diffusion discret : opérateur laplacien appliqué à l'étude de surfaces

Http Www Theses Fr, Aug 30, 2012

Bibliographie Table des figures CHAPITRE La théorie, c'est quand on sait tout et que rien ne fonc... more Bibliographie Table des figures CHAPITRE La théorie, c'est quand on sait tout et que rien ne fonctionne. La pratique, c'est quand tout fonctionne et que personne ne sait pourquoi.

Research paper thumbnail of Discrete Geometry for Computer Imagery

Discrete Applied Mathematics, 2013

Discrete geometry plays an essential role in the fields of computer graphics, pattern recognition... more Discrete geometry plays an essential role in the fields of computer graphics, pattern recognition, shape modeling, computer vision, and image and document analysis. Although it encompasses some well-known and used concepts, new results regularly appear, and useful theorems and developments must still be proposed. Discrete geometry provides both a theoretical and a computational framework for the analysis of digital images. The sixteenth International Conference on Discrete Geometry for Computer Imagery (DGCI), was held in Nancy, France, on April 6-8, 2011. Seventy papers were submitted, from 22 different countries, confirming the international status of this main conference on the topic. Once reviewed, 40 papers were accepted for publication. This special issue corresponds to a call for papers announced during the 16th DGCI that was open to all the researchers in the field on discrete geometry. Among the nine contributions to this special issue, five are significantly revised and extended versions of the original papers presented at the 16th DGCI. The papers were accepted after two extra review cycles and they address topics relevant to the discrete applied mathematics community. DGCI 2011 was supported by the International Association for Pattern Recognition (IAPR), and is the main conference associated with the Technical Committee 18 on Discrete Geometry of the IAPR. We thank our sponsoring institutions for providing financial support, essential for a successful event. We also sincerely want to thank the authors who contributed to this special issue, and especially the anonymous referees for their useful reviews and for contributing to the improvement of the quality of the papers. Special thanks are given to Professor Endre Boros, the Editor-in-Chief of Discrete Applied Mathematics, for the opportunity he gave us to publish this special issue. We hope you will enjoy reading it.

Research paper thumbnail of Hyperspectral image segmentation: a strategy

Le Centre pour la Communication Scientifique Directe - HAL - Cirad, 2009

Cet article présente une stratégie de segmentation d'images hyperspectrales liant de façon symétr... more Cet article présente une stratégie de segmentation d'images hyperspectrales liant de façon symétrique et conjointe les aspects spectraux et spatiaux. Pour cela, nous proposons de construire des variables latentes permettant de définir un sous-espace représentant au mieux la topologie de l'image. Dans cet article, nous limiterons cette notion de topologieà la seule appartenance aux régions. Pour ce faire, nous utilisons d'une part les notions de l'analyse discriminante (variance intra, inter) et les propriétés des algorithmes de segmentation en région liéesà celles-ci. Le principe générique théorique est exposé puis décliné sous la forme d'un exemple d'implémentation optimisé utilisant un algorithme de segmentation en région type split and merge. Les résultats obtenus sur des images de synthèse et réelle sont exposés et commentés.

Research paper thumbnail of Scénarios pédagogiques numériques via l'utilisation de l'iPad par et pour les étudiants de Polytech Montpellier

Research paper thumbnail of REX:Innovation pédagogique via l'utilisation de tablettes numériques à Polytech Montpellier

L'ecole polytechnique universitaire de Montpellier est impliquee dans une demarche d'adop... more L'ecole polytechnique universitaire de Montpellier est impliquee dans une demarche d'adoption du numerique et d'innovation pedagogique. Dans cette logique, l'ecole equipe depuis janvier 2013 ses etudiants de tablette iPad personnelles pour developper de nouvelles methodes d'apprentissage et de pedagogie avec les outils numeriques actuels. Les enseignants de l'ecole travaillent a repenser les approches d'enseignements (principalement en presentiels) a l'aide des tablettes et formalisent plusieurs scenarios pedagogiques experimentes avec les etudiants. Par exemples : presentation simple & prises de note ; presentation interactive ; compte rendu de travaux pratiques ; QCM ; suivi de presence ; etc. Ces scenarios (non exclusifs) servent de cas d'utilisation de reference pour lesquels entre aide, formation, logistique, et budget peuvent etre planifies pour assurer le plus grand succes a l'operation.

Research paper thumbnail of Dev IOS V.01: Conception - Presenter

Research paper thumbnail of Hyperspectral images segmentation: a proposal

Manuscrit reçu le 31 janvier 2008 Résumé et mots clés Cet article présente une stratégie de segme... more Manuscrit reçu le 31 janvier 2008 Résumé et mots clés Cet article présente une stratégie de segmentation d'images hyperspectrales liant de façon symétrique et conjointe les aspects spectraux et spatiaux. Pour cela, nous proposons de construire des variables latentes permettant de définir un sous-espace représentant au mieux la topologie de l'image. Dans cet article, nous limiterons cette notion de topologie à la seule appartenance aux régions. Pour ce faire, nous utilisons d'une part les notions de l'analyse discriminante (variance intra, inter) et les propriétés des algorithmes de segmentation en région liées à celles-ci. Le principe générique théorique est exposé puis décliné sous la forme d'un exemple d'implémentation optimisé utilisant un algorithme de segmentation en région type split and merge. Les résultats obtenus sur une image de synthèse puis réelle sont exposés et commentés. Imagerie hyperspectrale, segmentation d'images, chimiométrie.

Research paper thumbnail of Representation: Definition and Optimal

HAL is a multi-disciplinary open access archive for the deposit and dissemination of sci-entific ... more HAL is a multi-disciplinary open access archive for the deposit and dissemination of sci-entific research documents, whether they are pub-lished or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et a ̀ la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Research paper thumbnail of Automatic extraction of the 3D symmetry line of back surface: application on scoliotic adolescents

2018 40th Annual International Conference of the IEEE Engineering in Medicine and Biology Society (EMBC), 2018

We propose a new method to extract automatically the symmetry line of the 3D back surface of pati... more We propose a new method to extract automatically the symmetry line of the 3D back surface of patients affected by scoliosis. Our method is based on the detection of local symmetry planes computed on thick layers of the back. Results have been obtained on a sample of 112 scoliotic adolescents and we compare the symmetry line obtained by our method with a reference line defined by clinicians. We also study the influence of the scoliosis severity and of the Body Mass Index on the results.

Research paper thumbnail of Modélisation, Analyse, Représentation des Images Numériques Approche combinatoire de l'imagerie. (Modeling, Analysis, Digital image representation Combinatorial approach of imagery)

Mes travaux de recherche sont bases sur une approche combinatoire et discrete de l’imagerie. Ma d... more Mes travaux de recherche sont bases sur une approche combinatoire et discrete de l’imagerie. Ma demarche est de proposer des definitions de modeles mathematiques fournissant une abstraction de la realite physique, cette abstraction permettant de definir des nouvelles techniques amenant des solutions originales a des problemes poses. Dans ce cadre, je me suis plus particulierement interesse a la definition d’un modele formel d’image, a la segmentation en regions par des techniques algorithmiques et statistiques, et a la structuration du resultat a l’aide d’une representation combinatoire.

Research paper thumbnail of Curvature Estimation for Discrete Curves Based on Auto-adaptive Masks of Convolution

Lecture Notes in Computer Science, 2010

We propose a method that we call auto-adaptive convolution which extends the classical notion of ... more We propose a method that we call auto-adaptive convolution which extends the classical notion of convolution in pictures analysis to function analysis on a discrete set. We define an averaging kernel which takes into account the local geometry of a discrete shape and adapts itself to the curvature. Its defining property is to be local and to follow a normal law on discrete lines of any slope. We used it together with classical differentiation masks to estimate first and second derivatives and give a curvature estimator of discrete functions. 2 Diffusion Processes Heat kernel or random walks have been widely used in image processing, for example lately by Sun, Ovsjanikov and Guibas [18] and Gebal, Baerentzen, Aanaes and Larsen [9] in shape analysis. It is indeed a very precious tool because two manifolds are isometric if and only if their heat kernels are the same (in the non degenerate case).

Research paper thumbnail of Border Map: A Topological Representation for nD Image Analysis

Lecture Notes in Computer Science, 1999

This article presents an algorithm computing a border map of an image that generalizes to the n d... more This article presents an algorithm computing a border map of an image that generalizes to the n dimension graph structures used in image analysis. Such a map represents simple and multiple adjacencies, inclusion of regions, as well as the frontier type between two adjacent regions. An algorithm computing a border map, linear to the number of elements of an image, is defined in 2D, then generalized in 3D and in nD.

Research paper thumbnail of Flexible Terrain Erosion - A Fluid Simulation-Independent Approach Compatible with Multiple Representations

Research Square (Research Square), Apr 18, 2024

In this paper, we present a novel particlebased method for simulating erosion on various terrain ... more In this paper, we present a novel particlebased method for simulating erosion on various terrain representations, including height fields, voxel grids, material layers, and implicit terrains. Our approach breaks down erosion into two key processes-terrain alteration and material transport-allowing for flexibility in simulation. We utilize independent particles governed by basic particle physics principles, enabling efficient parallel computation. For increased precision, a vector field can adjust particle speed, adaptable for realistic fluid simulations or user-defined control. We address material alteration in 3D terrains with a set of equations applicable across diverse models, requiring only per-particle specifications for size, density, coefficient of restitution, and sediment capacity. Our modular algorithm is versatile for real-time and offline use, suitable for both 2.5D and 3D terrains.

Research paper thumbnail of Automatic Extraction of a Piecewise Symmetry Surface of a 3D Mesh: Application to Scoliosis

Lecture Notes in Computer Science, 2018

Symmetry analysis of the surface of anatomical structures offers good promise for diagnosis, foll... more Symmetry analysis of the surface of anatomical structures offers good promise for diagnosis, follow-up and therapy planning of pathologies causing abnormal deformities. This paper addresses the problem of detecting and modelling symmetry of bilateral structures, even in cases where the transformation between the two lateral parts is not a simple planar reflection but a symmetry with respect to a curved symmetry surface. We describe a new method to compute a piecewise curved symmetry surface for 3D objects. The algorithm is based on the computation of a 3D symmetry line, which defines strips by orthogonal slicing. A local symmetry plane is computed for each strip by an ICP-like method. The set of all local symmetry planes forms a piecewise symmetry surface. The method is first validated on parametric objects. Then, we show its potential as a non-invasive technique for the study of patients affected by scoliosis. Finally, our approach is generic enough that it could be extended to other medical applications such as facial dysplasia.

Research paper thumbnail of Dev IOS V.01: Conception - Presenter

Research paper thumbnail of The Star-Topology: a topology for image analysis

Discrete Geometry for Computer Imagery, 1995

Our previous works in image analysis dealing with image representations by means of adjacency or ... more Our previous works in image analysis dealing with image representations by means of adjacency or boundary graphs, led us to the need for a coherent representation model. In fact, classical approaches to this problem seem to be unsu cient o r e v en uncoherent for example they are unclear with the well-known connectivity paradox o r w i t h t h e b o r d e r description of regions. Di erent works like those of Kovalevsky, Herman and Malandain pointed out the advantages of cellular complex based topologies Kovalevsky89, Herman90, Malandain93]. But no one of them suggested a formalism that can be applied to any type of image. In this work we propose a topological representation for any type of image, colour or grey-level of whatever dimension. It is based on convex complexes, and looks closely at the elements realizing the connectivity within complexes and later within regions. Futhermore it remains coherent with pixel and voxel only based representations. An important feature is still maintaining a direct correspondance with the classical IR n topology. Finally, w e suggest a characterization of regions, their borders and boundaries which is useful as a basic tool for segmentation.

Research paper thumbnail of Discrete Geometry for Computer Imagery

Lecture Notes in Computer Science, 1997

Research paper thumbnail of Proceedings of the 7th International Workshop on Discrete Geometry for Computer Imagery

Research paper thumbnail of 画像対に及ぼす欠如マーカーを用いた祖先推定によるJPEG画像の系統発生【Powered by NICT】

IEEE Conference Proceedings, 2016

Research paper thumbnail of Phylogeny of JPEG images by ancestor estimation using missing markers on image pairs

2016 Sixth International Conference on Image Processing Theory, Tools and Applications (IPTA), 2016

Nowadays it is extremely easy to tamper with images and share them thanks to social media. Identi... more Nowadays it is extremely easy to tamper with images and share them thanks to social media. Identifying the transformation history is imperative to be able to trust these images. We address this problem by using image phylogeny trees, where the root is the image that has been less tampered with and as every generation is obtained from the transformation of its parents, the leaves are the most transformed images. Our method for image phylogeny trees reconstruction is based on a binary decision between two images using JPEG compression artifacts. Experimental results show that when there is no missing image data, the reconstruction is very accurate.

Research paper thumbnail of Processus de diffusion discret : opérateur laplacien appliqué à l'étude de surfaces

Http Www Theses Fr, Aug 30, 2012

Bibliographie Table des figures CHAPITRE La théorie, c'est quand on sait tout et que rien ne fonc... more Bibliographie Table des figures CHAPITRE La théorie, c'est quand on sait tout et que rien ne fonctionne. La pratique, c'est quand tout fonctionne et que personne ne sait pourquoi.

Research paper thumbnail of Discrete Geometry for Computer Imagery

Discrete Applied Mathematics, 2013

Discrete geometry plays an essential role in the fields of computer graphics, pattern recognition... more Discrete geometry plays an essential role in the fields of computer graphics, pattern recognition, shape modeling, computer vision, and image and document analysis. Although it encompasses some well-known and used concepts, new results regularly appear, and useful theorems and developments must still be proposed. Discrete geometry provides both a theoretical and a computational framework for the analysis of digital images. The sixteenth International Conference on Discrete Geometry for Computer Imagery (DGCI), was held in Nancy, France, on April 6-8, 2011. Seventy papers were submitted, from 22 different countries, confirming the international status of this main conference on the topic. Once reviewed, 40 papers were accepted for publication. This special issue corresponds to a call for papers announced during the 16th DGCI that was open to all the researchers in the field on discrete geometry. Among the nine contributions to this special issue, five are significantly revised and extended versions of the original papers presented at the 16th DGCI. The papers were accepted after two extra review cycles and they address topics relevant to the discrete applied mathematics community. DGCI 2011 was supported by the International Association for Pattern Recognition (IAPR), and is the main conference associated with the Technical Committee 18 on Discrete Geometry of the IAPR. We thank our sponsoring institutions for providing financial support, essential for a successful event. We also sincerely want to thank the authors who contributed to this special issue, and especially the anonymous referees for their useful reviews and for contributing to the improvement of the quality of the papers. Special thanks are given to Professor Endre Boros, the Editor-in-Chief of Discrete Applied Mathematics, for the opportunity he gave us to publish this special issue. We hope you will enjoy reading it.

Research paper thumbnail of Hyperspectral image segmentation: a strategy

Le Centre pour la Communication Scientifique Directe - HAL - Cirad, 2009

Cet article présente une stratégie de segmentation d'images hyperspectrales liant de façon symétr... more Cet article présente une stratégie de segmentation d'images hyperspectrales liant de façon symétrique et conjointe les aspects spectraux et spatiaux. Pour cela, nous proposons de construire des variables latentes permettant de définir un sous-espace représentant au mieux la topologie de l'image. Dans cet article, nous limiterons cette notion de topologieà la seule appartenance aux régions. Pour ce faire, nous utilisons d'une part les notions de l'analyse discriminante (variance intra, inter) et les propriétés des algorithmes de segmentation en région liéesà celles-ci. Le principe générique théorique est exposé puis décliné sous la forme d'un exemple d'implémentation optimisé utilisant un algorithme de segmentation en région type split and merge. Les résultats obtenus sur des images de synthèse et réelle sont exposés et commentés.

Research paper thumbnail of Scénarios pédagogiques numériques via l'utilisation de l'iPad par et pour les étudiants de Polytech Montpellier

Research paper thumbnail of REX:Innovation pédagogique via l'utilisation de tablettes numériques à Polytech Montpellier

L'ecole polytechnique universitaire de Montpellier est impliquee dans une demarche d'adop... more L'ecole polytechnique universitaire de Montpellier est impliquee dans une demarche d'adoption du numerique et d'innovation pedagogique. Dans cette logique, l'ecole equipe depuis janvier 2013 ses etudiants de tablette iPad personnelles pour developper de nouvelles methodes d'apprentissage et de pedagogie avec les outils numeriques actuels. Les enseignants de l'ecole travaillent a repenser les approches d'enseignements (principalement en presentiels) a l'aide des tablettes et formalisent plusieurs scenarios pedagogiques experimentes avec les etudiants. Par exemples : presentation simple & prises de note ; presentation interactive ; compte rendu de travaux pratiques ; QCM ; suivi de presence ; etc. Ces scenarios (non exclusifs) servent de cas d'utilisation de reference pour lesquels entre aide, formation, logistique, et budget peuvent etre planifies pour assurer le plus grand succes a l'operation.

Research paper thumbnail of Dev IOS V.01: Conception - Presenter

Research paper thumbnail of Hyperspectral images segmentation: a proposal

Manuscrit reçu le 31 janvier 2008 Résumé et mots clés Cet article présente une stratégie de segme... more Manuscrit reçu le 31 janvier 2008 Résumé et mots clés Cet article présente une stratégie de segmentation d'images hyperspectrales liant de façon symétrique et conjointe les aspects spectraux et spatiaux. Pour cela, nous proposons de construire des variables latentes permettant de définir un sous-espace représentant au mieux la topologie de l'image. Dans cet article, nous limiterons cette notion de topologie à la seule appartenance aux régions. Pour ce faire, nous utilisons d'une part les notions de l'analyse discriminante (variance intra, inter) et les propriétés des algorithmes de segmentation en région liées à celles-ci. Le principe générique théorique est exposé puis décliné sous la forme d'un exemple d'implémentation optimisé utilisant un algorithme de segmentation en région type split and merge. Les résultats obtenus sur une image de synthèse puis réelle sont exposés et commentés. Imagerie hyperspectrale, segmentation d'images, chimiométrie.

Research paper thumbnail of Representation: Definition and Optimal

HAL is a multi-disciplinary open access archive for the deposit and dissemination of sci-entific ... more HAL is a multi-disciplinary open access archive for the deposit and dissemination of sci-entific research documents, whether they are pub-lished or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et a ̀ la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Research paper thumbnail of Automatic extraction of the 3D symmetry line of back surface: application on scoliotic adolescents

2018 40th Annual International Conference of the IEEE Engineering in Medicine and Biology Society (EMBC), 2018

We propose a new method to extract automatically the symmetry line of the 3D back surface of pati... more We propose a new method to extract automatically the symmetry line of the 3D back surface of patients affected by scoliosis. Our method is based on the detection of local symmetry planes computed on thick layers of the back. Results have been obtained on a sample of 112 scoliotic adolescents and we compare the symmetry line obtained by our method with a reference line defined by clinicians. We also study the influence of the scoliosis severity and of the Body Mass Index on the results.

Research paper thumbnail of Modélisation, Analyse, Représentation des Images Numériques Approche combinatoire de l'imagerie. (Modeling, Analysis, Digital image representation Combinatorial approach of imagery)

Mes travaux de recherche sont bases sur une approche combinatoire et discrete de l’imagerie. Ma d... more Mes travaux de recherche sont bases sur une approche combinatoire et discrete de l’imagerie. Ma demarche est de proposer des definitions de modeles mathematiques fournissant une abstraction de la realite physique, cette abstraction permettant de definir des nouvelles techniques amenant des solutions originales a des problemes poses. Dans ce cadre, je me suis plus particulierement interesse a la definition d’un modele formel d’image, a la segmentation en regions par des techniques algorithmiques et statistiques, et a la structuration du resultat a l’aide d’une representation combinatoire.

Research paper thumbnail of Curvature Estimation for Discrete Curves Based on Auto-adaptive Masks of Convolution

Lecture Notes in Computer Science, 2010

We propose a method that we call auto-adaptive convolution which extends the classical notion of ... more We propose a method that we call auto-adaptive convolution which extends the classical notion of convolution in pictures analysis to function analysis on a discrete set. We define an averaging kernel which takes into account the local geometry of a discrete shape and adapts itself to the curvature. Its defining property is to be local and to follow a normal law on discrete lines of any slope. We used it together with classical differentiation masks to estimate first and second derivatives and give a curvature estimator of discrete functions. 2 Diffusion Processes Heat kernel or random walks have been widely used in image processing, for example lately by Sun, Ovsjanikov and Guibas [18] and Gebal, Baerentzen, Aanaes and Larsen [9] in shape analysis. It is indeed a very precious tool because two manifolds are isometric if and only if their heat kernels are the same (in the non degenerate case).

Research paper thumbnail of Border Map: A Topological Representation for nD Image Analysis

Lecture Notes in Computer Science, 1999

This article presents an algorithm computing a border map of an image that generalizes to the n d... more This article presents an algorithm computing a border map of an image that generalizes to the n dimension graph structures used in image analysis. Such a map represents simple and multiple adjacencies, inclusion of regions, as well as the frontier type between two adjacent regions. An algorithm computing a border map, linear to the number of elements of an image, is defined in 2D, then generalized in 3D and in nD.