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Inverse Geometry: from the Raw Point Cloud to the 3D Surface: Theory And Inverse geometry : from the raw point cloud to the 3d surface : theory and algorithms Julie Digne To cite this version: Julie Digne. Inverse geometry : from the raw point cloud to the 3d surface : theory and algorithms. General Mathematics [math.GM]. École normale supérieure de Cachan - ENS Cachan, 2010. English. NNT : 2010DENS0038. tel-00610432 HAL Id: tel-00610432 https://tel.archives-ouvertes.fr/tel-00610432 Submitted on 22 Jul 2011 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. École Normale Supérieure de Cachan Thèse Présentée par Julie DIGNE pour l’obtention du titre de Docteur de l’École Normale Supérieure de Cachan Spécialité : Mathématiques Appliquées Géométrie inverse: du nuage de points brut à la surface D Théorie et Algorithmes Inverse Geometry: from the Raw Point Cloud to the D Surface Theory and Algorithms Directeur de thèse: Jean-Michel Morel soutenue le Novembre à l’ENS Cachan tel-00557589, version 1 - 19 Jan 2011 Jury : Président : Yves Meyer - CMLA - ENS Cachan Rapporteurs : Pierre Alliez - INRIA Sophia Antipolis Ron Kimmel - Technion Guillermo Sapiro - University of Minnesota Directeur : Jean-Michel Morel - CMLA - ENS Cachan Examinateurs : Tamy Boubekeur - Telecom ParisTech Frédéric Chazal - INRIA Saclay Claire Lartigue - LURPA - ENS Cachan Invité : Jacques Blanc-Talon - DGA tel-00557589, version 1 - 19 Jan 2011 Remerciements Trois ans de travail sont résumés dans les pages qui vont suivre. Cela semble presque trop peu (les lecteurs me contrediront sans doute sur ce point). Je voudrais remercier Jean-Michel Morel de m’avoir dirigée pendant ces trois ans. Cette thèse a été riche en apprentissages grâce à sa grande disponibilité et sa patience. J’aimerais remercier mon jury : Pierre Alliez, Ron Kimmel et Guillermo Sapiro qui ont accepté de rapporter ma thèse, Jacques Blanc-Talon, Tamy Boubekeur, Frédéric Chazal, Claire Lartigue et Yves Meyer qui ont accepté de faire partie du jury. Cette thèse a été elaborée autour des données fournies par le LURPA que je remercie vivement. J’aimerais aussi remercier la DGA pour avoir financé ces trois ans de recherche. Merci à tous les chercheurs rencontrés au cours de cette thèse et avec qui j’ai pu avoir des conversations très intéressantes : Freddy Bruckstein, Guillermo Sapiro, Pierre Alliez, Frédéric Chazal, Steve Oudot, José-Luis Lisani, Tony Buades, Pascal Monasse et toute l’équipe du projet MISS. Travailler au CMLA a été un vrai plaisir, merci en particulier à Véronique Al- madovar, Micheline Brunetti, Sandra Doucet, Virginie Pauchont et Carine Saint- Prix pour leur efficacité et la bonne humeur qu’elles répandent dans le laboratoire. Tous mes remerciements vont aux thésards qui m’ont accompagnée pendant ces trois ans : Neus Sabater pour des séances piscines intensives et des conseils cuisine pour couronner le tout. Eric Bughin, pour la pause café du matin. Aude Champmartin, pour me rappeler que, non, au labo tout le monde n’est pas sous linux et me trainer à la gym. Adina Ciomaga pour être un peu strrrressée avant les rendez-vous. Bruno Galerne, pour des discussions cinématographiques intenses et tel-00557589, version 1 - 19 Jan 2011 Zhongwei pour m’avoir fait comprendre la stéréorectification (enfin!). Merci aussi à Nicolas, parce que la D sans problème informatique ne serait plus de la D. Merci à Rafa pour une gentillesse et une patience sans borne même quand je repose dix fois les mêmes questions. Merci à tous les thésards et post-docs qui ont rendu la vie au labo très agréable entre pauses café au pavillon des jardins et repas gastronomiques le soir : Adina, Aude, Ayman, Benjamin, Bruno, Eric, Frédéric, Frédérique, Gaël, Ives, Jean-Pascal, Julien, Marc, Mauricio, Miguel, Morgan, Neus, Nicolas C., Nico- las L., Romain, Saad, Yohann et Zhongwei. Merci enfin aux visiteurs : Alex, Anne, Pascal, Gloria et Pablo... Cette thèse a nécessité : • La lecture de 398 articles; • La rédaction de 30 rapports; ii • 3 réinstallations de Linux; • 1 changement de carte mère; • 1 remplacement de disque dur; • x plantages généralisés des serveurs de calcul du labo; • 255009 lignes de code; • 26 programmes; • 11 cahiers; • 25 stylos et crayons divers; • 1350 litres de thé; • 126 litres de café; • 421200 minutes de musique écoutée (dont une bonne moitié de Händel et Rossini). Je voudrais remercier certains professeurs qui m’ont beaucoup marquée par leur grande pédagogie : Jean-Louis Garcin, Jean-Aristide Cavaillès au lycée Chaptal et Francis Schmitt, disparu trop tôt, à Télécom ParisTech. Mes remerciements à Yann Gousseau et Henri Maitre pour leurs conseils d’orientation. Finalement, je voudrais remercier mes parents et mes soeurs, Jeanne et Char- lotte, pour leur soutien sans lequel cette thèse n’aurait pas existé. Merci à Nicolas, qui a réussi à me supporter même pendant que je rédigeais! Merci à Hugo aussi et bon courage pour ta thèse. Merci enfin à tous mes amis télécommiens et non télé- commiens, à ma prof de chant, à mon ensemble vocal et à mon club théâtre, parce que la thèse c’est bien, mais l’oublier une ou deux heures ça permet de prendre du recul. tel-00557589, version 1 - 19 Jan 2011 Et comme il ne faut oublier personne, merci à tous ceux qui ne figurent pas dans ces remerciements. Contents Introduction State of the Art . D Acquisition ............................ .. Stereoscopy .......................... .. Time-of-flight laser scanner ................. .. Triangulation laser scanner ................. . Some acquisition projects ...................... . LURPA acquisition system ...................... . Representation of D data ...................... . From a point cloud to a mesh .................... .. Merging multiple views ................... .. Meshing ........................... .. Remeshing .......................... . Rendering ............................... . Post-processing and line detection .................. . The difference between Image Processing and D surface processing Scale Space Meshing of Raw Data Point Sets . Introduction ............................. .. Building a mesh ....................... tel-00557589, version 1 - 19 Jan 2011 .. Raw data point set processing ................ .. Computing curvatures .................... . Continuous theory .......................... .. Spherical neighborhoods vs cylindrical neighborhoods .. .. Curvature estimation .................... .. Surface motion induced by projections on the regression plane ............................. . The discrete algorithm ........................ .. Higher order regression surfaces ............... . First application: scale space raw data point orientation ...... . Second application: scale space meshing .............. . Comparative experiments on high resolution data ......... . Complexity analysis and computation time measures ........ . Conclusion .............................. iv Contents High Fidelity Scan Merging . Introduction ............................. . Previous Work ............................ .. Rigid Scan registration .................... .. Non-rigid scan registration ................. .. Super-resolution from several scans ............. .. Meshing ........................... . Scan Merging ............................. .. Principle ........................... .. Low/High frequency surface decomposition ........ .. Finding a common smooth basis for all surfaces ...... .. Algorithm .......................... .. One-dimensional study ................... . Implementation and Results ..................... . Conclusion .............................. Filling Holes in Scale Space Meshes . Previous Work ............................ .. Volumetric methods ..................... .. Patch filling methods ..................... .. Inpainting for surfaces, hole filling based on similarity ... .. Point clouds ......................... . A hole filling algorithm ....................... .. Filling the hole: finding an initial patch ........... .. Refining the patch ...................... .. Giving shape to the patch .................. tel-00557589, version 1 - 19 Jan 2011 .. Special holes ......................... . Results on synthetic data ....................... .. Sphere example ........................ . Scale space meshes .......................... The Level Set Tree on Meshes . Introduction ............................. . Mesh Extremal Regions ....................... .. Definition of MSER for D images [MCUP] ....... .. Level set trees: an extension to D mesh surfaces ...... .. Building the component tree for meshes .......... . Extracting maximally stable regions from the component tree ... .. Mesh-MSER: the algorithm ................. .. Triangle classification .................... .. Border extraction from selected region ........... Contents v . Implementation and results ..................... .. Results on mechanical and geometrical shapes ....... .. Archeological pieces: comparative results .......... . Using the same approach with other functions ........... . Conclusion .............................. A numerical
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