Publications of 2007

Result of the query in the list of publications :

• 6 Articles
• 3 PhD Thesis and Habilitations
• 28 Conference articles
• 6 Technical and Research Reports
• 1 Collection article or Book chapter

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6 Articles

1 - Higher-Order Active Contour Energies for Gap Closure. M. Rochery and I. H. Jermyn and J. Zerubia. Journal of Mathematical Imaging and Vision, 29(1): pages 1-20, September 2007. Keywords : Gap closure, Higher-order, Active contour, Shape, Prior, Road network. @ARTICLE{Rochery07, author = {Rochery, M. and Jermyn, I. H. and Zerubia, J.}, title = {Higher-Order Active Contour Energies for Gap Closure}, year = {2007}, month = {September}, journal = {Journal of Mathematical Imaging and Vision}, volume = {29}, number = {1}, pages = {1-20}, url = {http://dx.doi.org/10.1007/s10851-007-0021-x}, pdf = {ftp://ftp-sop.inria.fr/ariana/Articles/2007_Rochery07.pdf}, keyword = {Gap closure, Higher-order, Active contour, Shape, Prior, Road network} } Abstract : One of the main difficulties in extracting line networks from images, and in particular road networks from remote sensing images, is the existence of interruptions in the data caused, for example, by occlusions. These can lead to gaps in the extracted network that do not correspond to gaps in the real network. In this paper, we describe a higher-order active contour energy that in addition to favouring network-like regions, includes a prior term penalizing networks containing ‘nearby opposing extremities’, thereby making gaps in the extracted network less likely. The new energy term causes such extremities to attract one another during gradient descent. They thus move towards one another and join, closing the gap. To minimize the energy, we develop specific techniques to handle the high-order derivatives that appear in the gradient descent equation. We present the results of automatic extraction of networks from real remote-sensing images, showing the ability of the model to overcome interruptions.

2 - Gaussian approximations of fluorescence microscope point-spread function models. B. Zhang and J. Zerubia and J.C. Olivo-Marin. Applied Optics, 46(10): pages 1819-1829, April 2007. Copyright : © 2007 Optical Society of America @ARTICLE{jz_applied_photo, author = {Zhang, B. and Zerubia, J. and Olivo-Marin, J.C.}, title = {Gaussian approximations of fluorescence microscope point-spread function models}, year = {2007}, month = {April}, journal = {Applied Optics}, volume = {46}, number = {10}, pages = {1819-1829}, keyword = {} } Abstract : We comprehensively study the least-squares Gaussian approximations of the diffraction-limited 2D-3D paraxial-nonparaxial point-spread functions (PSFs) of the wide field fluorescence microscope (WFFM), the laser scanning confocal microscope (LSCM), and the disk scanning confocal microscope (DSCM). The PSFs are expressed using the Debye integral. Under an L∞ constraint imposing peak matching, optimal and near-optimal Gaussian parameters are derived for the PSFs. With an L1 constraint imposing energy conservation, an optimal Gaussian parameter is derived for the 2D paraxial WFFM PSF. We found that (1) the 2D approximations are all very accurate; (2) no accurate Gaussian approximation exists for 3D WFFM PSFs; and (3) with typical pinhole sizes, the 3D approximations are accurate for the DSCM and nearly perfect for the LSCM. All the Gaussian parameters derived in this study are in explicit analytical form, allowing their direct use in practical applications.

3 - Building Outline Extraction from Digital Elevation Models using Marked Point Processes. M. Ortner and X. Descombes and J. Zerubia. International Journal of Computer Vision, 72(2): pages 107-132, April 2007. Keywords : RJMCMC, Buildings, Stochastic geometry, Marked point process, Digital Elevation Model (DEM). @ARTICLE{ortner_ijcv_05, author = {Ortner, M. and Descombes, X. and Zerubia, J.}, title = {Building Outline Extraction from Digital Elevation Models using Marked Point Processes}, year = {2007}, month = {April}, journal = {International Journal of Computer Vision}, volume = {72}, number = {2}, pages = {107-132}, url = {http://www.springerlink.com/content/d563v16957427102/?p=873bd324c7c14049a45cc1f2905b5a86&pi=0}, keyword = {RJMCMC, Buildings, Stochastic geometry, Marked point process, Digital Elevation Model (DEM)} }

4 - ant colony optimization for image regularization based on a non-stationary Markov modeling. S. Le Hegarat-Mascle and A. Kallel and X. Descombes. IEEE Trans. on Image Processing, 16(3): pages 865-878, March 2007. Keywords : Markov Random Fields, Ants colonization. @ARTICLE{Ants07, author = {Le Hegarat-Mascle, S. and Kallel, A. and Descombes, X.}, title = {ant colony optimization for image regularization based on a non-stationary Markov modeling}, year = {2007}, month = {March}, journal = {IEEE Trans. on Image Processing}, volume = {16}, number = {3}, pages = {865-878}, keyword = {Markov Random Fields, Ants colonization} } Abstract : Ant colony optimization (ACO) has been proposed as a promising tool for regularization in image classification. The algorithm is applied here in a different way than the classical transposition of the graph color affectation problem. The ants collect information through the image, from one pixel to the others. The choice of the path is a function of the pixel label, favoring paths within the same image segment. We show that this corresponds to an automatic adaptation of the neighborhood to the segment form, and that it outperforms the fixed-form neighborhood used in classical Markov random field regularization techniques. The performance of this new approach is illustrated on a simulated image and on actual remote sensing images

5 - Détection de feux de forêt par analyse statistique d'évènements rares à partir d'images infrarouges thermiques. F. Lafarge and X. Descombes and J. Zerubia and S. Mathieu. Traitement du Signal, 24(1), 2007. Note : copyright Traitement du Signal Keywords : Gaussian Field, Rare event, DT-caracteristic, Intensity peak. @ARTICLE{lafarge_ts06, author = {Lafarge, F. and Descombes, X. and Zerubia, J. and Mathieu, S.}, title = {Détection de feux de forêt par analyse statistique d'évènements rares à partir d'images infrarouges thermiques}, year = {2007}, journal = {Traitement du Signal}, volume = {24}, number = {1}, note = {copyright Traitement du Signal}, pdf = {ftp://ftp-sop.inria.fr/ariana/Articles/2007_lafarge_ts06.pdf}, keyword = {Gaussian Field, Rare event, DT-caracteristic, Intensity peak} }

6 - Computing Statistics from Man-Made Structures on the Earth's Surface for Indexing Satellite Images. A. Bhattacharya and M. Roux and H. Maitre and I. H. Jermyn and X. Descombes and J. Zerubia. International Journal of Simulation Modelling, 6(2): pages 73--83, 2007. @ARTICLE{Bhattacharya07, author = {Bhattacharya, A. and Roux, M. and Maitre, H. and Jermyn, I. H. and Descombes, X. and Zerubia, J.}, title = {Computing Statistics from Man-Made Structures on the Earth's Surface for Indexing Satellite Images}, year = {2007}, journal = {International Journal of Simulation Modelling}, volume = {6}, number = {2}, pages = {73--83}, url = {http://www.ijsimm.com/Full_Papers/Fulltext2007/text6-2_73-83.pdf}, pdf = {ftp://ftp-sop.inria.fr/ariana/Articles/2007_Bhattacharya07.pdf}, keyword = {} } Abstract : Indexing and retrieval from remote sensing image databases relies on the extraction of appropriate information from the data about the entity of interest (e.g. land cover type) and on the robustness of this extraction to nuisance variables. Other entities in an image may be strongly correlated with the entity of interest and their properties can therefore be used to characterize this entity. The road network contained in an image is one example. The properties of road networks vary considerably from one geographical environment to another, and they can therefore be used to classify and retrieve such environments. In this paper, we define several such environments, and classify them with the aid of geometrical and topological features computed from the road networks occurring in them. The relative failure of network extraction methods in certain types of urban area obliges us to segment such areas and to add a second set of geometrical and topological features computed from the segmentations. To validate the approach, feature selection and SVM linear kernel classification are performed on the feature set arising from a diverse image database.

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3 PhD Thesis and Habilitations

1 - The 'Gas of circles' model and its application to tree crown extraction. P. Horvath. PhD Thesis, Universite de Szeged, Universite de Nice Sophia Antipolis, December 2007. Keywords : geometric prior, Contours actifs d'ordre supérieur, Phase Field, Gas of circles. @PHDTHESIS{horvath_these, author = {Horvath, P.}, title = {The 'Gas of circles' model and its application to tree crown extraction}, year = {2007}, month = {December}, school = {Universite de Szeged, Universite de Nice Sophia Antipolis}, pdf = {ftp://ftp-sop.inria.fr/ariana/Articles/2007_horvath_these.pdf}, keyword = {geometric prior, Contours actifs d'ordre supérieur, Phase Field, Gas of circles} }

2 - Modèles stochastiques pour la reconstruction tridimensionnelle d'environnements urbains. F. Lafarge. PhD Thesis, Ecole des Mines de Paris, October 2007. Keywords : 3D reconstruction, Urban areas, Satellite images, Structural approach, Simulated Annealing, MCMC. @PHDTHESIS{lafarge_phd07, author = {Lafarge, F.}, title = {Modèles stochastiques pour la reconstruction tridimensionnelle d'environnements urbains}, year = {2007}, month = {October}, school = {Ecole des Mines de Paris}, url = {http://tel.archives-ouvertes.fr/tel-00179695/en/}, keyword = {3D reconstruction, Urban areas, Satellite images, Structural approach, Simulated Annealing, MCMC} } Résumé : Cette thèse aborde le problème de la reconstruction tridimensionnelle de zones urbaines à partir d'images satellitaires très haute résolution. Le contenu informatif de ce type de données est insuffisant pour permettre une utilisation efficace des nombreux algorithmes développés pour des données aériennes. Dans ce contexte, l'introduction de connaissances a priori fortes sur les zones urbaines est nécessaire. Les outils stochastiques sont particulièrement bien adaptés pour traiter cette problématique. Nous proposons une approche structurelle pour aborder ce sujet. Cela consiste à modéliser un bâtiment comme un assemblage de modules urbains élémentaires extraits d'une bibliothèque de modèles 3D paramétriques. Dans un premier temps, nous extrayons les supports 2D de ces modules à partir d'un Modèle Numérique d' Elévation (MNE). Le résultat est un agencement de quadrilatères dont les éléments voisins sont connectés entre eux. Ensuite, nous reconstruisons les bâtiments en recherchant la configuration optimale de modèles 3D se fixant sur les supports précédemment extraits. Cette configuration correspond à la réalisation qui maximise une densité mesurant la cohérence entre la réalisation et le MNE, mais également prenant en compte des connaissances a priori telles que des lois d'assemblage des modules. Nous discutons enfin de la pertinence de cette approche en analysant les résultats obtenus à partir de données satellitaires (simulations PLEIADES). Des expérimentations sont également réalisées à partir d'images aériennes mieux résolues.

3 - Indexing of satellite images using structural information. A. Bhattacharya. PhD Thesis, Ecole Nationale Supérieure des Télécommunications, 2007. Keywords : Landscape, Segmentation, Features, Extraction, Classification, Data mining. @PHDTHESIS{bhattacharya_these, author = {Bhattacharya, A.}, title = {Indexing of satellite images using structural information}, year = {2007}, school = {Ecole Nationale Supérieure des Télécommunications}, pdf = {ftp://ftp-sop.inria.fr/ariana/Articles/2007_bhattacharya_these.pdf}, keyword = {Landscape, Segmentation, Features, Extraction, Classification, Data mining} }

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28 Conference articles

1 - Forest Fire Detection based on Gaussian field analysis. F. Lafarge and X. Descombes and J. Zerubia. In Proc. European Signal Processing Conference (EUSIPCO), Poznan, Poland, September 2007. Note : Copyright EURASIP Keywords : Gaussian Field, DT-caracteristic, Forest fires. @INPROCEEDINGS{lafarge_eusipco07, author = {Lafarge, F. and Descombes, X. and Zerubia, J.}, title = {Forest Fire Detection based on Gaussian field analysis}, year = {2007}, month = {September}, booktitle = {Proc. European Signal Processing Conference (EUSIPCO)}, address = {Poznan, Poland}, note = {Copyright EURASIP}, pdf = {ftp://ftp-sop.inria.fr/ariana/Articles/2007_lafarge_eusipco07.pdf}, keyword = {Gaussian Field, DT-caracteristic, Forest fires} }

2 - 3D city modeling based on Hidden Markov Model. F. Lafarge and X. Descombes and J. Zerubia and M. Pierrot-Deseilligny. In Proc. IEEE International Conference on Image Processing (ICIP), San Antonio, U.S., September 2007. Note : Copyright IEEE Keywords : 3D reconstruction, Building, Hidden Markov Model. @INPROCEEDINGS{lafarge_icip07, author = {Lafarge, F. and Descombes, X. and Zerubia, J. and Pierrot-Deseilligny, M.}, title = {3D city modeling based on Hidden Markov Model}, year = {2007}, month = {September}, booktitle = {Proc. IEEE International Conference on Image Processing (ICIP)}, address = {San Antonio, U.S.}, note = {Copyright IEEE}, url = {http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=4379207}, keyword = {3D reconstruction, Building, Hidden Markov Model} }

3 - A `Gas of Circles' Phase Field Model and its Application to Tree Crown Extraction. P. Horvath and I. H. Jermyn. In Proc. European Signal Processing Conference (EUSIPCO), Poznan, Poland, September 2007. Keywords : Phase Field, Tree Crown Extraction. @INPROCEEDINGS{Horvath07d, author = {Horvath, P. and Jermyn, I. H.}, title = {A `Gas of Circles' Phase Field Model and its Application to Tree Crown Extraction}, year = {2007}, month = {September}, booktitle = {Proc. European Signal Processing Conference (EUSIPCO)}, address = {Poznan, Poland}, pdf = {ftp://ftp-sop.inria.fr/ariana/Articles/2007_Horvath07d.pdf}, keyword = {Phase Field, Tree Crown Extraction} } Abstract : The problem of extracting the region in the image domain corresponding to an a priori unknown number of circular objects occurs in several domains. We propose a new model of a `gas of circles', the ensemble of regions in the image domain composed of circles of a given radius. The model uses the phase field reformulation of higher-order active contours (HOACs). Phase fields possess several advantages over contour and level set approaches to region modelling, in particular for HOAC models. The reformulation allows us to benefit from these advantages without losing the strengths of the HOAC framework. Combined with a suitable likelihood energy, and applied to the tree crown extraction problem, the new model shows markedly improved performance, both in quality of results and in computation time, which is two orders of magnitude less than the HOAC level set implementation.

4 - A Phase Field Model Incorporating Generic and Specific Prior Knowledge Applied to Road Network Extraction from VHR Satellite Images. T. Peng and I. H. Jermyn and V. Prinet and J. Zerubia and B. Hu. In Proc. British Machine Vision Conference (BMVC), Warwick, UK, September 2007. Keywords : Road network, Very high resolution, Higher-order, Active contour, Shape, Prior. @INPROCEEDINGS{Peng07a, author = {Peng, T. and Jermyn, I. H. and Prinet, V. and Zerubia, J. and Hu, B.}, title = {A Phase Field Model Incorporating Generic and Specific Prior Knowledge Applied to Road Network Extraction from VHR Satellite Images}, year = {2007}, month = {September}, booktitle = {Proc. British Machine Vision Conference (BMVC)}, address = {Warwick, UK}, pdf = {ftp://ftp-sop.inria.fr/ariana/Articles/2007_Peng07a.pdf}, keyword = {Road network, Very high resolution, Higher-order, Active contour, Shape, Prior} } Abstract : We address the problem of updating road maps in dense urban areas by extracting the main road network from a very high resolution (VHR) satellite image. Our model of the region occupied by the road network in the image is innovative. It incorporates three different types of prior geometric knowledge: generic boundary smoothness constraints, equivalent to a standard active contour prior; knowledge of the geometric properties of road networks (i.e. that they occupy regions composed of long, low-curvature segments joined at junctions), equivalent to a higher-order active contour prior; and knowledge of the road network at an earlier date derived from GIS data, similar to other ‘shape priors’ in the literature. In addition, we represent the road network region as a ‘phase field’, which offers a number of important advantages over other region modelling frameworks. All three types of prior knowledge prove important for overcoming the complexity of geometric ‘noise’ in VHR images. Promising results and a comparison with several other techniques demonstrate the effectiveness of our approach.

5 - Apprentissage non supervisé des SVM par un algorithme des K-moyennes entropique pour la détection de zones brûlées. O. Zammit and X. Descombes and J. Zerubia. In Proc. GRETSI Symposium on Signal and Image Processing, Troyes, France, September 2007. Keywords : Satellite images, Forest fires, Burnt areas, Classification, Support Vector Machines, Learning base. @INPROCEEDINGS{zammit_gretsi_07, author = {Zammit, O. and Descombes, X. and Zerubia, J.}, title = {Apprentissage non supervisé des SVM par un algorithme des K-moyennes entropique pour la détection de zones brûlées}, year = {2007}, month = {September}, booktitle = {Proc. GRETSI Symposium on Signal and Image Processing}, address = {Troyes, France}, pdf = {ftp://ftp-sop.inria.fr/ariana/Articles/2007_zammit_gretsi_07.pdf}, keyword = {Satellite images, Forest fires, Burnt areas, Classification, Support Vector Machines, Learning base} }

6 - Rectangular Road Marking Detection with Marked Point Processes. O. Tournaire and N. Paparoditis and F. Lafarge. In ISPRS Conference Photogrammetric Image Analysis (PIA), Vol. 36, pages 149--154, Org. IAPRS, Munich, Germany, September 2007. @INPROCEEDINGS{tournaire_pia07, author = {Tournaire, O. and Paparoditis, N. and Lafarge, F.}, title = {Rectangular Road Marking Detection with Marked Point Processes}, year = {2007}, month = {September}, booktitle = {ISPRS Conference Photogrammetric Image Analysis (PIA)}, volume = {36}, pages = {149--154}, organization = {IAPRS}, address = {Munich, Germany}, pdf = {http://www-sop.inria.fr/ariana/Publis/2007-tournaire-pia.pdf}, keyword = {} }

7 - A Multi-Layer MRF Model for Object-Motion Detection in Unregistered Airborne Image-Pairs. C. Benedek and T. Szirányi and Z. Kato and J. Zerubia. In Proc. IEEE International Conference on Image Processing (ICIP), Vol. 6, pages 141--144, San Antonio, Texas, USA, September 2007. Keywords : Change detection, Aerial images, Camera motion, MRF. Copyright : Copyright IEEE @INPROCEEDINGS{benedek_ICIP07, author = {Benedek, C. and Szirányi, T. and Kato, Z. and Zerubia, J.}, title = {A Multi-Layer MRF Model for Object-Motion Detection in Unregistered Airborne Image-Pairs}, year = {2007}, month = {September}, booktitle = {Proc. IEEE International Conference on Image Processing (ICIP)}, volume = {6}, pages = {141--144}, address = {San Antonio, Texas, USA}, url = {http://ieeexplore.ieee.org/search/srchabstract.jsp?arnumber=4379541&isnumber=4379494&punumber=4378863&k2dockey=4379541@ieeecnfs&query=%28benedek+%3Cin%3E+metadata%29+%3Cand%3E+%284379494+%3Cin%3E+isnumber%29&pos=0}, pdf = {http://web.eee.sztaki.hu/~bcsaba/Publications/Pdf/benedek_icip2007.pdf}, keyword = {Change detection, Aerial images, Camera motion, MRF} } Abstract : In this paper, we give a probabilistic model for automatic change detection on airborne images taken with moving cameras. To ensure robustness, we adopt an unsupervised coarse matching instead of a precise image registration. The challenge of the proposed model is to eliminate the registration errors, noise and the parallax artifacts caused by the static objects having considerable height (buildings, trees, walls etc.) from the difference image. We describe the background membership of a given image point through two different features, and introduce a novel three-layerMarkov Random Field (MRF) model to ensure connected homogenous regions in the segmented image.

8 - Sur la complexite et la rapidite d’algorithmes pour la minimisation de la variation totale sous contraintes. P. Weiss and L. Blanc-Féraud and G. Aubert. In Proc. Symposium on Signal and Image Processing (GRETSI), Troyes, France, September 2007. Keywords : l1 norm minimization, compression noise denoising, optimal algorithm, convex analysis, Total variation, nesterov scheme. @INPROCEEDINGS{Pierre Weiss, author = {Weiss, P. and Blanc-Féraud, L. and Aubert, G.}, title = {Sur la complexite et la rapidite d’algorithmes pour la minimisation de la variation totale sous contraintes}, year = {2007}, month = {September}, booktitle = {Proc. Symposium on Signal and Image Processing (GRETSI)}, address = {Troyes, France}, url = {http://www.math.univ-toulouse.fr/~weiss/Publis/Conferences/Gretsi_WeissBlancFeraudAubert_2010.PDF}, pdf = {ftp://ftp-sop.inria.fr/ariana/Articles/2007_Pierre Weiss.pdf}, keyword = {l1 norm minimization, compression noise denoising, optimal algorithm, convex analysis, Total variation, nesterov scheme} }

9 - A Multispectral Data Model for Higher-Order Active Contours and its Application to Tree Crown Extraction. P. Horvath. In Proc. Advanced Concepts for Intelligent Vision Systems, Delft, Netherlands, August 2007. Keywords : Higher-order, Tree Crown Extraction, Colour. @INPROCEEDINGS{Horvath07c, author = {Horvath, P.}, title = {A Multispectral Data Model for Higher-Order Active Contours and its Application to Tree Crown Extraction}, year = {2007}, month = {August}, booktitle = {Proc. Advanced Concepts for Intelligent Vision Systems}, address = {Delft, Netherlands}, pdf = {ftp://ftp-sop.inria.fr/ariana/Articles/2007_Horvath07c.pdf}, keyword = {Higher-order, Tree Crown Extraction, Colour} } Abstract : Forestry management makes great use of statistics concerning the individual trees making up a forest, but the acquisition of this information is expensive. Image processing can potentially both reduce this cost and improve the statistics. The key problem is the delineation of tree crowns in aerial images. The automatic solution of this problem requires considerable prior information to be built into the image and region models. Our previous work has focused on including shape information in the region model; in this paper we examine the image model. The aerial images involved have three bands. We study the statistics of these bands, and construct both multispectral and single band image models. We combine these with a higher-order active contour model of a `gas of circles' in order to include prior shape information about the region occupied by the tree crowns in the image domain. We compare the results produced by these models on real aerial images and conclude that multiple bands improves the quality of the segmentation. The model has many other potential applications, e.g. to nano-technology, microbiology, physics, and medical imaging.

10 - A New Phase Field Model of a `Gas of Circles' for Tree Crown Extraction from Aerial Images. P. Horvath and I. H. Jermyn. In Proc. International Conference on Computer Analysis of Images and Patterns (CAIP), Vienna, Austria, August 2007. Keywords : Phase Field, Tree Crown Extraction. @INPROCEEDINGS{Horvath07b, author = {Horvath, P. and Jermyn, I. H.}, title = {A New Phase Field Model of a `Gas of Circles' for Tree Crown Extraction from Aerial Images}, year = {2007}, month = {August}, booktitle = {Proc. International Conference on Computer Analysis of Images and Patterns (CAIP)}, address = {Vienna, Austria}, pdf = {ftp://ftp-sop.inria.fr/ariana/Articles/2007_Horvath07b.pdf}, keyword = {Phase Field, Tree Crown Extraction} } Abstract : We describe a model for tree crown extraction from aerial images, a problem of great practical importance for the forestry industry. The novelty lies in the prior model of the region occupied by tree crowns in the image, which is a phase field version of the higher-order active contour inflection point `gas of circles' model. The model combines the strengths of the inflection point model with those of the phase field framework: it removes the `phantom circles' produced by the original `gas of circles' model, while executing two orders of magnitude faster than the contour-based inflection point model. The model has many other areas of application e.g., to imagery in nanotechnology, biology, and physics.

11 - Removing Shape-Preserving Transformations in Square-Root Elastic (SRE) Framework for Shape Analysis of Curves. S. Joshi and E. Klassen and A. Srivastava and I. H. Jermyn. In Proc. Energy Minimization Methods in Computer Vision and Pattern Recognition (EMMCVPR), Ezhou, China, August 2007. Keywords : Shape, Reparameterization, Metric, Geodesic. Copyright : The original publication is available at www.springerlink.com. @INPROCEEDINGS{Joshi07b, author = {Joshi, S. and Klassen, E. and Srivastava, A. and Jermyn, I. H.}, title = {Removing Shape-Preserving Transformations in Square-Root Elastic (SRE) Framework for Shape Analysis of Curves}, year = {2007}, month = {August}, booktitle = {Proc. Energy Minimization Methods in Computer Vision and Pattern Recognition (EMMCVPR)}, address = {Ezhou, China}, pdf = {ftp://ftp-sop.inria.fr/ariana/Articles/2007_Joshi07b.pdf}, keyword = {Shape, Reparameterization, Metric, Geodesic} } Abstract : This paper illustrates and extends an efficient framework, called the square-root-elastic (SRE) framework, for studying shapes of closed curves, that was first introduced in [2]. This framework combines the strengths of two important ideas - elastic shape metric and path-straightening methods - for finding geodesics in shape spaces of curves. The elastic metric allows for optimal matching of features between curves while path-straightening ensures that the algorithm results in geodesic paths. This paper extends this framework by removing two important shape preserving transformations: rotations and re-parameterizations, by forming quotient spaces and constructing geodesics on these quotient spaces. These ideas are demonstrated using experiments involving 2D and 3D curves.

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