Publications de Ian Jermyn

Résultat de la recherche dans la liste des publications :

• 12 Articles
• 46 Articles de conférence
• 9 Rapports de recherche et Rapports techniques
• 2 Articles de collection ou Chapitres de livres

nouvelle recherche | bibtex

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46 Articles de conférence

29 - Shape Moments for Region-Based Active Contours. P. Horvath et A. Bhattacharya et I. H. Jermyn et J. Zerubia et Z. Kato. Dans Proc. Hungarian-Austrian Conference on Image Processing and Pattern Recognition, Szeged, Hungary, mai 2005. @INPROCEEDINGS{horvath_hacippr05, author = {Horvath, P. and Bhattacharya, A. and Jermyn, I. H. and Zerubia, J. and Kato, Z.}, title = {Shape Moments for Region-Based Active Contours}, year = {2005}, month = {mai}, booktitle = {Proc. Hungarian-Austrian Conference on Image Processing and Pattern Recognition}, address = {Szeged, Hungary}, keyword = {} }

30 - Multimodal statistics of adaptive wavelet packet coefficients: experimental evidence and theory. R. Cossu et I. H. Jermyn et J. Zerubia. Dans Proc. Physics in Signal and Image Processing, Toulouse, France, janvier 2005. Mots-clés : Bimodale, Statistics, Paquet d'ondelettes, Adaptatif, Texture. @INPROCEEDINGS{cossu_psip05, author = {Cossu, R. and Jermyn, I. H. and Zerubia, J.}, title = {Multimodal statistics of adaptive wavelet packet coefficients: experimental evidence and theory}, year = {2005}, month = {janvier}, booktitle = {Proc. Physics in Signal and Image Processing}, address = {Toulouse, France}, pdf = {http://www-sop.inria.fr/members/Ian.Jermyn/publications/Cossu05psip.pdf}, keyword = {Bimodale, Statistics, Paquet d'ondelettes, Adaptatif, Texture} } Abstract : In recent work, it was noted that although the subband histograms for standard wavelet coefcients take on a generalized Gaussian form, this is no longer true for wavelet packet bases adapted to a given texture. Instead, three types of subband statistics are observed: Gaussian, generalized Gaussian, and interestingly, in some subbands, bi- or multi-modal histograms. Motivated by this observation, we provide additional experimental conrmation of the existence of multimodal subbands, and provide a theoretical explanation for their occurrence. The results reveal the connection of such subbands with the characteristic structure in a texture, and thus confirm the importance of such subbands for image modelling and applications.

31 - Texture discrimination using multimodal wavelet packet subbands. R. Cossu et I. H. Jermyn et J. Zerubia. Dans Proc. IEEE International Conference on Image Processing (ICIP), Singapore, octobre 2004. Mots-clés : Bimodale, Adaptatif, probabilistic, Paquet d'ondelettes, Texture. @INPROCEEDINGS{cossu_icip04, author = {Cossu, R. and Jermyn, I. H. and Zerubia, J.}, title = {Texture discrimination using multimodal wavelet packet subbands}, year = {2004}, month = {octobre}, booktitle = {Proc. IEEE International Conference on Image Processing (ICIP)}, address = {Singapore}, pdf = {http://www-sop.inria.fr/members/Ian.Jermyn/publications/Cossu04icip.pdf}, keyword = {Bimodale, Adaptatif, probabilistic, Paquet d'ondelettes, Texture} } Abstract : The subband histograms of wavelet packet bases adapted to individual texture classes often fail to display the leptokurtotic behaviour shown by the standard wavelet coefcients of `natural' images. While many subband histograms remain leptokurtotic in adaptive bases, some subbands are Gaussian. Most interestingly, however, some subbands show multimodal behaviour, with no mode at zero. In this paper, we provide evidence for the existence of these multimodal subbands and show that they correspond to narrow frequency bands running throughout images of the texture. They are thus closely linked to the texture's structure. As such, they seem likely to possess superior descriptive and discriminative power as compared to unimodal subbands. We demonstrate this using both Brodatz and remote sensing images.

32 - Gap closure in (road) networks using higher-order active contours. M. Rochery et I. H. Jermyn et J. Zerubia. Dans Proc. IEEE International Conference on Image Processing (ICIP), Singapore, octobre 2004. Mots-clés : Contour actif, Gap closure, Ordre superieur, Forme, Reseaux routiers. @INPROCEEDINGS{Rochery04, author = {Rochery, M. and Jermyn, I. H. and Zerubia, J.}, title = {Gap closure in (road) networks using higher-order active contours}, year = {2004}, month = {octobre}, booktitle = {Proc. IEEE International Conference on Image Processing (ICIP)}, address = {Singapore}, pdf = {ftp://ftp-sop.inria.fr/ariana/Articles/rochery_icip04.pdf}, keyword = {Contour actif, Gap closure, Ordre superieur, Forme, Reseaux routiers} } Abstract : We present a new model for the extraction of networks from images in the presence of occlusions. Such occlusions cause gaps in the extracted network that need to be closed. Using higher-order active contours, which allow the incorporation of sophisticated geometric information, we introduce a new, non-local, `gap closure' force that causes pairs of network extremities that are close together to extend towards one another and join, thus closing the gap between them. We demonstrate the benefits of the model using the problem of road network extraction, presenting results on aerial images.

33 - Texture analysis using adaptative biorthogonal wavelet packets. G.C.K. Abhayaratne et I. H. Jermyn et J. Zerubia. Dans Proc. IEEE International Conference on Image Processing (ICIP), Singapore, octobre 2004. Mots-clés : Adaptatif, Paquet d'ondelettes, Biorthogonal, Texture, Statistics. @INPROCEEDINGS{Abhayratne_icip04, author = {Abhayaratne, G.C.K. and Jermyn, I. H. and Zerubia, J.}, title = {Texture analysis using adaptative biorthogonal wavelet packets}, year = {2004}, month = {octobre}, booktitle = {Proc. IEEE International Conference on Image Processing (ICIP)}, address = {Singapore}, pdf = {http://www-sop.inria.fr/members/Ian.Jermyn/publications/Abhayaratne04icip.pdf}, keyword = {Adaptatif, Paquet d'ondelettes, Biorthogonal, Texture, Statistics} } Abstract : We discuss the use of adaptive biorthogonal wavelet packet bases in a probabilistic approach to texture analysis, thus combining the advantages of biorthogonal wavelets (FIR, linear phase) with those of a coherent texture model. The computation of the probability uses both the primal and dual coefcients of the adapted biorthogonal wavelet packet basis. The computation of the biorthogonal wavelet packet coefcients is done using a lifting scheme, which is very efficient. The model is applied to the classification of mosaics of Brodatz textures, the results showing improvement over the performance of the corresponding orthogonal wavelets.

34 - Texture analysis using probabilistic models of the unimodal and multimodal statistics of adaptative wavelet packet coefficients. R. Cossu et I. H. Jermyn et J. Zerubia. Dans Proc. IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), Montreal, Canada, mai 2004. Mots-clés : Bimodale, Adaptatif, Paquet d'ondelettes, Texture, Mixture de gaussiennes, Statistics. @INPROCEEDINGS{cossu04a, author = {Cossu, R. and Jermyn, I. H. and Zerubia, J.}, title = {Texture analysis using probabilistic models of the unimodal and multimodal statistics of adaptative wavelet packet coefficients}, year = {2004}, month = {mai}, booktitle = {Proc. IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)}, address = {Montreal, Canada}, pdf = {http://www-sop.inria.fr/members/Ian.Jermyn/publications/Cossu04icassp.pdf}, keyword = {Bimodale, Adaptatif, Paquet d'ondelettes, Texture, Mixture de gaussiennes, Statistics} } Abstract : Although subband histograms of the wavelet coefficients of natural images possess a characteristic leptokurtotic form, this is no longer true for wavelet packet bases adapted to a given texture. Instead, three types of subband statistics are observed: Gaussian, leptokurtotic, and interestingly, in some subbands, multimodal histograms. These subbands are closely linked to the structure of the texture, and guarantee that the most probable image is not flat. Motivated by these observations, we propose a probabilistic model that takes them into account. Adaptive wavelet packet subbands are modelled as Gaussian, generalized Gaussian, or a constrained Gaussian mixture. We use a Bayesian methodology, finding MAP estimates for the adaptive basis, for subband model selection, and for subband model parameters. Results confirm the effectiveness of the proposed approach, and highlight the importance of multimodal subbands for texture discrimination and modelling.

35 - Wavelet-Based Superresolution in Astronomy. R. Willett et I. H. Jermyn et R. Nowak et J. Zerubia. Dans Proc. Astronomical Data Analysis Software and Systems, Strasbourg, France, octobre 2003. Mots-clés : Superresolution, Ondelettes, Astronomy. @INPROCEEDINGS{Willett03, author = {Willett, R. and Jermyn, I. H. and Nowak, R. and Zerubia, J.}, title = {Wavelet-Based Superresolution in Astronomy}, year = {2003}, month = {octobre}, booktitle = {Proc. Astronomical Data Analysis Software and Systems}, address = {Strasbourg, France}, pdf = {http://www-sop.inria.fr/members/Ian.Jermyn/publications/Willett03adass.pdf}, keyword = {Superresolution, Ondelettes, Astronomy} } Abstract : High-resolution astronomical images can be reconstructed from several blurred and noisy low-resolution images using a computational process known as superresolution reconstruction. Superresolution reconstruction is closely related to image deconvolution, except that the low-resolution images are not registered and their relative translations and rotations must be estimated in the process. The novelty of our approach to the superresolution problem is the use of wavelets and related multiresolution methods within an expectation-maximization reconstruction process to improve the accuracy and visual quality of the reconstructed image. Simulations demonstrate the effectiveness of the proposed method, including its ability to distinguish between tightly grouped stars with a small set of observations.

36 - Higher Order Active Contours and their Application to the Detection of Line Networks in Satellite Imagery. M. Rochery et I. H. Jermyn et J. Zerubia. Dans Proc. IEEE Workshop Variational, Geometric and Level Set Methods in Computer Vision, at ICCV, Nice, France, octobre 2003. Mots-clés : Ordre superieur, Contour actif, Forme, Reseaux routiers, Segmentation, A priori. @INPROCEEDINGS{Rochery03a, author = {Rochery, M. and Jermyn, I. H. and Zerubia, J.}, title = {Higher Order Active Contours and their Application to the Detection of Line Networks in Satellite Imagery}, year = {2003}, month = {octobre}, booktitle = {Proc. IEEE Workshop Variational, Geometric and Level Set Methods in Computer Vision}, address = {at ICCV, Nice, France}, pdf = {ftp://ftp-sop.inria.fr/ariana/Articles/rochery_vlsm03.pdf}, keyword = {Ordre superieur, Contour actif, Forme, Reseaux routiers, Segmentation, A priori} } Abstract : We present a novel method for the incorporation of shape information into active contour models, and apply it to the extraction of line networks (e.g. road, water) from satellite imagery. The method is based on a new class of contour energies. These energies are quadratic on the space of one-chains in the image, as opposed to classical energies, which are linear. They can be expressed as double integrals on the contour, and thus incorporate non-trivial interactions between different contour points. The new energies describe families of contours that share complex geometric properties, without making reference to any particular shape. Networks fall into such a family, and to model them we make a particular choice of quadratic energy whose minima are reticulated. To optimize the energies, we use a level set approach. The forces derived from the new energies are non-local however, thus necessitating an extension of standard level set methods. Promising experimental results are obtained using real images.

37 - Texture Analysis: An Adaptive Probabilistic Approach. K. Brady et I. H. Jermyn et J. Zerubia. Dans Proc. IEEE International Conference on Image Processing (ICIP), Barcelona, Spain, septembre 2003. Mots-clés : Adaptatif, Paquet d'ondelettes, Statistics, Texture. @INPROCEEDINGS{Brady03, author = {Brady, K. and Jermyn, I. H. and Zerubia, J.}, title = {Texture Analysis: An Adaptive Probabilistic Approach}, year = {2003}, month = {septembre}, booktitle = {Proc. IEEE International Conference on Image Processing (ICIP)}, address = {Barcelona, Spain}, pdf = {http://www-sop.inria.fr/members/Ian.Jermyn/publications/Brady03icip.pdf}, keyword = {Adaptatif, Paquet d'ondelettes, Statistics, Texture} } Abstract : Two main issues arise when working in the area of texture segmentation: the need to describe the texture accurately by capturing its underlying structure, and the need to perform analyses on the boundaries of textures. Herein, we tackle these problems within a consistent probabilistic framework. Starting from a probability distribution on the space of infinite images, we generate a distribution on arbitrary finite regions by marginalization. For a Gaussian distribution, the computational requirement of diagonalization and the modelling requirement of adaptivity together lead naturally to adaptive wavelet packet models that capture the ‘significant amplitude features’ in the Fourier domain. Undecimated versions of the wavelet packet transform are used to diagonalize the Gaussian distribution efficiently, albeit approximately. We describe the implementation and application of this approach and present results obtained on several Brodatz texture mosaics.

38 - Étude D'une Nouvelle Classe de Contours Actifs Pour la Détection de Routes Dans Des Images de Télédétection. M. Rochery et I. H. Jermyn et J. Zerubia. Dans Proc. GRETSI Symposium on Signal and Image Processing, Paris, France, septembre 2003. @INPROCEEDINGS{Rochery03, author = {Rochery, M. and Jermyn, I. H. and Zerubia, J.}, title = {Étude D'une Nouvelle Classe de Contours Actifs Pour la Détection de Routes Dans Des Images de Télédétection}, year = {2003}, month = {septembre}, booktitle = {Proc. GRETSI Symposium on Signal and Image Processing}, address = {Paris, France}, pdf = {ftp://ftp-sop.inria.fr/ariana/Articles/rochery_gretsi03.pdf}, keyword = {} }

39 - Adaptive Probabilistic Models of Wavelet Packets for the Analysis and Segmentation of Textured Remote Sensing Images. K. Brady et I. H. Jermyn et J. Zerubia. Dans Proc. British Machine Vision Conference (BMVC), Norwich, U. K., septembre 2003. Mots-clés : probabilistic, Adaptatif, wavelet, Texture. @INPROCEEDINGS{Brady03a, author = {Brady, K. and Jermyn, I. H. and Zerubia, J.}, title = {Adaptive Probabilistic Models of Wavelet Packets for the Analysis and Segmentation of Textured Remote Sensing Images}, year = {2003}, month = {septembre}, booktitle = {Proc. British Machine Vision Conference (BMVC)}, address = {Norwich, U. K.}, pdf = {http://www-sop.inria.fr/members/Ian.Jermyn/publications/Brady03bmvc.pdf}, keyword = {probabilistic, Adaptatif, wavelet, Texture} } Abstract : Remote sensing imagery plays an important role in many elds. It has become an invaluable tool for diverse applications ranging from cartography to ecosystem management. In many of the images processed in these types of applications, semantic entities in the scene are correlated with textures in the image. In this paper, we propose a new method of analysing such textures based on adaptive probabilistic models of wavelet packets. Our approach adapts to the principal periodicities present in the textures, and can capture long-range correlations while preserving the independence of the wavelet packet coefcients. This technique has been applied to several remote sensing images, the results of which are presented.

40 - Gaussian Mixture Models of Texture and Colour for Image Database Retrieval. H. Permuter et J.M. Francos et I. H. Jermyn. Dans Proc. IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), Hong Kong, avril 2003. Mots-clés : Texture, Mixture de gaussiennes, Classification, Aerial images. @INPROCEEDINGS{Permuter03, author = {Permuter, H. and Francos, J.M. and Jermyn, I. H.}, title = {Gaussian Mixture Models of Texture and Colour for Image Database Retrieval}, year = {2003}, month = {avril}, booktitle = {Proc. IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)}, address = {Hong Kong}, pdf = {http://www-sop.inria.fr/members/Ian.Jermyn/publications/Permuter03icassp.pdf}, keyword = {Texture, Mixture de gaussiennes, Classification, Aerial images} } Abstract : We introduce Gaussian mixture models of ‘structure’ and colour features in order to classify coloured textures in images, with a view to the retrieval of textured colour images from databases. Classifications are performed separately using structure and colour and then combined using a confidence criterion. We apply the models to the VisTex database and to the classification of man-made and natural areas in aerial images. We compare these models with others in the literature, and show an overall improvement in performance.

41 - Unsupervised Image Segmentation via Markov Trees and Complex Wavelets. C. Shaffrey et N. Kingsbury et I. H. Jermyn. Dans Proc. IEEE International Conference on Image Processing (ICIP), Rochester, USA, septembre 2002. Mots-clés : Segmentation, Hidden Markov Model, Texture, Couleur. @INPROCEEDINGS{ijking, author = {Shaffrey, C. and Kingsbury, N. and Jermyn, I. H.}, title = {Unsupervised Image Segmentation via Markov Trees and Complex Wavelets}, year = {2002}, month = {septembre}, booktitle = {Proc. IEEE International Conference on Image Processing (ICIP)}, address = {Rochester, USA}, pdf = {http://www-sop.inria.fr/members/Ian.Jermyn/publications/Shaffrey02icip.pdf}, keyword = {Segmentation, Hidden Markov Model, Texture, Couleur} } Abstract : The goal in image segmentation is to label pixels in an image based on the properties of each pixel and its surrounding region. Recently Content-Based Image Retrieval (CBIR) has emerged as an application area in which retrieval is attempted by trying to gain unsupervised access to the image semantics directly rather than via manual annotation. To this end, we present an unsupervised segmentation technique in which colour and texture models are learned from the image prior to segmentation, and whose output (including the models) may subsequently be used as a content descriptor in a CBIR system. These models are obtained in a multiresolution setting in which Hidden Markov Trees (HMT) are used to model the key statistical properties exhibited by complex wavelet and scaling function coefficients. The unsupervised Mean Shift Iteration (MSI) procedure is used to determine a number of image regions which are then used to train the models for each segmentation class.

42 - Psychovisual Evaluation of Image Segmentation Algorithms. C. Shaffrey et I. H. Jermyn et N. Kingsbury. Dans Proc. Advanced Concepts for Intelligent Vision Systems, Ghent, Belgique, septembre 2002. @INPROCEEDINGS{kingij, author = {Shaffrey, C. and Jermyn, I. H. and Kingsbury, N.}, title = {Psychovisual Evaluation of Image Segmentation Algorithms}, year = {2002}, month = {septembre}, booktitle = {Proc. Advanced Concepts for Intelligent Vision Systems}, address = {Ghent, Belgique}, keyword = {} }

43 - Evaluation Methodologies for Image Retrieval Systems. I. H. Jermyn et C. Shaffrey et N. Kingsbury. Dans Proc. Advanced Concepts for Intelligent Vision Systems, Ghent, Belgique, septembre 2002. @INPROCEEDINGS{shaffreyij, author = {Jermyn, I. H. and Shaffrey, C. and Kingsbury, N.}, title = {Evaluation Methodologies for Image Retrieval Systems}, year = {2002}, month = {septembre}, booktitle = {Proc. Advanced Concepts for Intelligent Vision Systems}, address = {Ghent, Belgique}, keyword = {} }

44 - Region extraction from multiple images. H. Ishikawa et I. H. Jermyn. Dans Proc. IEEE International Conference on Computer Vision (ICCV), Vancouver, Canada, juillet 2001. Mots-clés : Stereo, Motion, global, optimum, Graphe, Cycle. @INPROCEEDINGS{IJ01a, author = {Ishikawa, H. and Jermyn, I. H.}, title = {Region extraction from multiple images}, year = {2001}, month = {juillet}, booktitle = {Proc. IEEE International Conference on Computer Vision (ICCV)}, address = {Vancouver, Canada}, pdf = {http://www-sop.inria.fr/members/Ian.Jermyn/publications/Jermyn01iccv.pdf}, keyword = {Stereo, Motion, global, optimum, Graphe, Cycle} } Abstract : We present a method for region identification in multiple images. A set of regions in different images and the correspondences on their boundaries can be thought of as a boundary in the multi-dimensional space formed by the product of the individual image domains. We minimize an energy functional on the space of such boundaries, thereby identifying simultaneously both the optimal regions in each image and the optimal correspondences on their boundaries. We use a ratio form for the energy functional, thus enabling the global minimization of the energy functional using a polynomial time graph algorithm, among other desirable properties. We choose a simple form for this energy that favours boundaries that lie on high intensity gradients in each image, while encouraging correspondences between boundaries in different images that match intensity values. The latter tendency is weighted by a novel heuristic energy that encourages the boundaries to lie on disparity or optical flow discontinuities, although no dense optical flow or disparity map is computed.

45 - Judging whether multiple silhouettes can come from the same object. D. Jacobs et P. Belhumeur et I. H. Jermyn. Dans Int. Workshop on Visual Form, Springer-Verlag Lecture Notes in Computer Science 2059, Capri, Italie, mai 2001. @INPROCEEDINGS{IJ01b, author = {Jacobs, D. and Belhumeur, P. and Jermyn, I. H.}, title = {Judging whether multiple silhouettes can come from the same object}, year = {2001}, month = {mai}, booktitle = {Int. Workshop on Visual Form, Springer-Verlag Lecture Notes in Computer Science 2059}, address = {Capri, Italie}, pdf = {http://www-sop.inria.fr/members/Ian.Jermyn/publications/Jacobs01iwvf.pdf}, keyword = {} } Abstract : We consider the problem of recognizing an object from its silhouette. We focus on the case in which the camera translates, and rotates about a known axis parallel to the image, such as when a mo- bile robot explores an environment. In this case we present an algorithm for determining whether a new silhouette could come from the same ob- ject that produced two previously seen silhouettes. In a basic case, when cross-sections of each silhouette are single line segments, we can check for consistency between three silhouettes using linear programming. This provides the basis for methods that handle more complex cases. We show many experiments that demonstrate the performance of these methods when there is noise, some deviation from the assumptions of the algo- rithms, and partial occlusion. Previous work has addressed the problem of precisely reconstructing an object using many silhouettes taken under controlled conditions. Our work shows that recognition can be performed without complete reconstruction, so that a small number of images can be used, with viewpoints that are only partly constrained.

46 - Globally optimal regions and boundaries. I. H. Jermyn et H. Ishikawa. Dans Proc. IEEE International Conference on Computer Vision (ICCV), 1999. Mots-clés : global, optimum, Graphe, Cycle, Ratio, Segmentation. Copyright : @INPROCEEDINGS{Jermyn99iccv, author = {Jermyn, I. H. and Ishikawa, H.}, title = {Globally optimal regions and boundaries}, year = {1999}, booktitle = {Proc. IEEE International Conference on Computer Vision (ICCV)}, pdf = {http://www-sop.inria.fr/members/Ian.Jermyn/publications/Jermyn99iccv.pdf}, keyword = {global, optimum, Graphe, Cycle, Ratio, Segmentation} } Abstract : We propose a new form of energy functional for the segmentation of regions in images, and an efficient method for finding its global optima. The energy can have contributions from both the region and its boundary, thus combining the best features of region- and boundary-based approaches to segmentation. By transforming the region energy into a boundary energy, we can treat both contributions on an equal footing, and solve the global optimization problem as a minimum mean weight cycle problem on a directed graph. The simple, polynomial-time algorithm requires no initialization and is highly parallelizable.

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9 Rapports de recherche et Rapports techniques

1 - Probabilistic Models of Adaptive Mother Wavelets for Texture Description. G.C.K. Abhayaratne et I. H. Jermyn et J. Zerubia. Research Report, INRIA, France, décembre 2006. @TECHREPORT{Abhayaratne, author = {Abhayaratne, G.C.K. and Jermyn, I. H. and Zerubia, J.}, title = {Probabilistic Models of Adaptive Mother Wavelets for Texture Description}, year = {2006}, month = {décembre}, institution = {INRIA}, type = {Research Report}, address = {France}, keyword = {} }

2 - A higher-order active contour model of a `gas of circles' and its application to tree crown extraction. P. Horvath et I. H. Jermyn et Z. Kato et J. Zerubia. Research Report 6026, INRIA, France, novembre 2006. Mots-clés : Extraction de Houppiers, Aerial images, Ordre superieur, Contour actif, Gaz de cercles, Forme. @TECHREPORT{Horvath05, author = {Horvath, P. and Jermyn, I. H. and Kato, Z. and Zerubia, J.}, title = {A higher-order active contour model of a `gas of circles' and its application to tree crown extraction}, year = {2006}, month = {novembre}, institution = {INRIA}, type = {Research Report}, number = {6026}, address = {France}, url = {http://hal.inria.fr/inria-00115631}, pdf = {ftp://ftp-sop.inria.fr/ariana/Articles/2006_Horvath05.pdf}, keyword = {Extraction de Houppiers, Aerial images, Ordre superieur, Contour actif, Gaz de cercles, Forme} } Abstract : Many image processing problems involve identifying the region in the image domain occupied by a given entity in the scene. Automatic solution of these problems requires models that incorporate significant prior knowledge about the shape of the region. Many methods for including such knowledge run into difficulties when the topology of the region is unknown a priori, for example when the entity is composed of an unknown number of similar objects. Higher-order active contours (HOACs) represent one method for the modelling of non-trivial prior knowledge about shape without necessarily constraining region topology, via the inclusion of non-local interactions between region boundary points in the energy defining the model. The case of an unknown number of circular objects arises in a number of domains, \eg medical, biological, nanotechnological, and remote sensing imagery. Regions composed of an a priori unknown number of circles may be referred to as a `gas of circles'. In this report, we present a HOAC model of a `gas of circles'. In order to guarantee stable circles, we conduct a stability analysis via a functional Taylor expansion of the HOAC energy around a circular shape. This analysis fixes one of the model parameters in terms of the others and constrains the rest. In conjunction with a suitable likelihood energy, we apply the model to the extraction of tree crowns from aerial imagery, and show that the new model outperforms other techniques.

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