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Sampling, Interpolation and Detection. Applications in Satellite Imaging. Andrés Almansa

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Sampling, Interpolation and Detection. Applications in Satellite Imaging. Andrés Almansa Sampling, interpolation and detection. Applications in satellite imaging. Andrés Almansa To cite this version: Andrés Almansa. Sampling, interpolation and detection. Applications in satellite imaging.. Signal and Image processing. École normale supérieure de Cachan - ENS Cachan, 2002. English. tel-00665725 HAL Id: tel-00665725 https://tel.archives-ouvertes.fr/tel-00665725 Submitted on 2 Feb 2012 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. ¡£¢¥¤§¦©¨ ¤ ¦¨ ¨ ©¨ ¨¨! 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Bernard Rouge´ m'a fait gouterˆ la beaute´ de la theorie´ de Shannon, et il a et´ e´ une source d'inspiration constante. Je ne sais pas comment lui remercier pour les frequentes´ et longues heures de discussion et travail commun qu'il m'a accorde´ a` Cachan et a` Toulouse, malgre´ notre distance geographique.´ J'ai toujours admire´ le grand enthousiasme et l'esprit d'equipe´ que Jean-Michel Morel a su trans- mettre a` ses el´ eves` et collaborateurs, et non moins ai-je appreci´ e´ sa grande disponibi- lite,´ et les innombrables et brillantes idees´ qu'il m'a transmises, avec la plus grande humilite,´ sans memeˆ vouloir en rester le coauteur. Son souci pour mon avenir apres` la these,` ainsi que les multiples relations nationales et internationales desquelles il m'a donne´ l'opportunite´ de faire partie, sont aussi un signe de sa grande gen´ er´ osite.´ Dans ce cadre exceptionnel de travail en equipe,´ j'ai naturellement eu l'occasion d'avoir des discussions tres` eclairantes´ avec virtuellement tous les membres du CMLA et ses visiteurs, et ils meritent´ tous mon plus sincer` e remerciement. Je voudrais sim- plement souligner dans les lignes qui suivent quelques contributions particulier` ement importantes que j'ai eu la graceˆ de recevoir. Tout mon travail sur l'echantillonnage´ regulier´ et la restauration, contenu dans les premiers deux chapitres a et´ e´ le fruit d'une reflexion´ tres` intense, des` le debout de ma these` avec Sylvain Durand et Bernard Rouge.´ Mes travaux sur l'interpolation de modeles` de terrain ont ben´ efici´ e´ de la remarquable collaboration de Fred´ eric´ Cao dans v vi REMERCIEMENTS les aspects EDP, et de la maˆıtrise de Yann Gousseau des aspects statistiques, ainsi que d'un souci commun de trouver la meilleure solution au probleme.` Mon travail sur l'echantillonnage´ irregulier´ n'a aboutit que graceˆ au soutien initial de Stephane´ Jaffard, et le logiciel et commentaires gen´ er´ eusement transmis par Thomas Strohmer, mais sur- tout graceˆ a` l'insistance et persev´ erance´ de Bernard Rouge´ dans la recherche d'une reponse´ a` ses conjectures. Finalement, Jean-Michel Morel, Agnes` Desolneux et Lio- nel Moisan m'ont introduit dans ce monde fascinant de la theorie´ de la Gestalt qui a conduit a` mon travail sur la detection´ de points de fuite, travail dont une grande par- tie a et´ e´ inspiree´ par l'excellent travail de Sebastien´ Vamech, et les discussions qui ont suivi sa participation au groupe de travail sur la geom´ etrie´ integrale.´ Je souhaite egalement´ remercier tres` chaleureusement Vicent Caselles et Andreu Sole,´ pour leur critique constructive a` mon travail sur l'interpolation par EDPs, ainsi que leur aide eclairante´ avec Franc¸ois Malgouyres et Lionel Moisan sur la restaura- tion par variation totale et leur algorithmes de minimisation. Mon travail sur l'in- terpolation a et´ e´ aussi enorm´ ement´ facilite´ par les donnees´ de Carlos Lopez,´ et des discussions avec Pierre Soille et Corinne Vachier sur les distances geod´ esiques.´ Dans l'echantillonnage´ irregulier´ j'ai eu l'honneur de recevoir des tres` precieuses´ sugges- tions de la part de Yves Meyer et de Patrick-Luis Combettes. Finalement les commen- taires et suggestions de Pascal Monasse, ainsi que la soigneuse lecture des rapporteurs anonymes de IEEE PAMI, ont contribue´ a` amelior´ er nettement le dernier chapitre sur la detection´ de points de fuite. Lenny Rudin deserves a very special acknowledgement. I very much enjoyed my visit to his company, and the opportunity to contribute to his excellent video-processing software. My work on vanishing point detection was mainly motivated by the photo- grammetric applications at Cognitech and is due to a large extent to Lenny Rudin's ideas and encouragement. The many discussions he granted me on sampling, restora- tion, and interpolation almost certainly left their traces in this thesis. Les conditions de travail au CMLA ont et´ e´ excellentes. J'en remercie tous les membres du laboratoire, et leurs equipes´ d'administration du systeme,` secretariat´ et bibliotheque,` ainsi qu'aux doctorants de la salle informatique au rez-de-chaussee,´ et tous ceux qui ont contribue´ a` la creation´ d'une atmospher` e de travail tres` conviviale. Plusieurs personnes ont joue´ un roleˆ tres` important dans mon parcours scientifique avant d'arriver au CMLA. I would like to specially thank Tony Lindeberg for he intro- duced me in the field of image processing, for the many things he taught me during my master's thesis, and for his generous help during my transition from MSc to PhD stu- vii dies. Roberto Oliveira-Mattos, Rosario Curbelo y Gustavo Drets merecen mi mas´ sin- cero agradecimiento por el excelente grupo de trabajo que crearon en Uruguay, y por los v´ınculos y medios materiales que me permitieron continuar mis estudios. Cuando deb´ı dejar dicho grupo para comenzar mi tesis, Gregory Randall, Alicia Fernandez,´ Al- varo Gomez, Ana Spangenberg, Sebastian Sas´ıas, Sergio Nemachnov, y muchos otros colegas del CeCal y del IIE asumieron generosa y rapidamente´ muchas de las respon- sabilidades que poco a poco deje atras,´ facilitando as´ı el comienzo de mi tesis. Gregory Randall me ha considerado como un miembro mas´ de su equipo, a la hora de buscar el mejor lugar para mis estudios de doctorado, as´ı como a la hora de hacerme un lu- gar al regreso. Por su amistad, y por el entusiasmo y profesionalismo que el´ ha sabido contagiar a sus colaboradores, quiero expresarle mi mas´ sincero agradecimiento. Des` notre arrivee´ en France, nous avons et´ e´ chaleureusement accueillis par nos amis Noureddine, Raphael,¨ Aurelie,´ Philippe et Kyung Lan. No menor agradecimiento se merecen mis compatriotas Richard y Claudia, Gianfranco, Ana, Pablo, Nico, An- drea, Denis y Luciana, Laura y Laurent, Gonzalo, Miguel y Rosario, Gustavo, y los casi compatriotas Hilda, Claudia y Guillaume, Vincent y Romina, Pierre, Alejandro por su apoyo constante y por hacernos sentir casi como en casa, durante estos anos˜ de tesis. Wie zu Hause haben wir uns auch gefuhlt¨ wahr¨ end unser Besuch der Fami- lien Kohncke¨ und Nolting¨ in Mainz, Dreieich, Hamburg, und Cabrils. Sie sind unsere zweite Familie geworden, wahr¨ end unser Aufenthalt in Europa. Il me tient particulier` ement a` coeur remercier a` chacun des membres de ma com- munaute´ CVX a` Paris, ainsi qu'a` Jean-Marc Fournon, Marika Thomas, Alain Thomas- set, Christian Mellon, Philippe Deterre, le groupe Transgenese,` et la communaute´ de l'Arche a` Paris. Non seulement leur ecoute´ et presence´ tout au long de ces annees´ en France, m'ont permis de croˆıtre personnellement. Ils ont aussi su me donner le soutien necessair´ e aux moments les plus difficiles de cette these.` Quisiera hacer extensivo este agradecimiento a mi hermana Monica,´ a Alejandro, Marcelo, Rafa y Gabriel, quienes de cerca o a la distancia me han sabido apoyar cuando mas los necesitaba. Por ultimo,´ quiero expresar mi mas´ profundo agradecimiento a mi familia y mi esposa.
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