Publications about Shape

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• 4 Articles
• 1 PhD Thesis and Habilitation
• 15 Conference articles
• 3 Technical and Research Reports

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4 Articles

1 - Looking for shapes in two-dimensional, cluttered point clouds. A. Srivastava and I. H. Jermyn. IEEE Trans. Pattern Analysis and Machine Intelligence, 31(9): pages 1616-1629, September 2009. Keywords : Shape, Bayesian, Point cloud, Diffeomorphism, Sampling, Fisher-Rao. Copyright : ©2008 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE. @ARTICLE{SrivastavaJermyn09, author = {Srivastava, A. and Jermyn, I. H.}, title = {Looking for shapes in two-dimensional, cluttered point clouds}, year = {2009}, month = {September}, journal = {IEEE Trans. Pattern Analysis and Machine Intelligence}, volume = {31}, number = {9}, pages = {1616-1629}, url = {http://dx.doi.org/10.1109/TPAMI.2008.223}, pdf = {http://www-sop.inria.fr/members/Ian.Jermyn/publications/SrivastavaJermyn09.pdf}, keyword = {Shape, Bayesian, Point cloud, Diffeomorphism, Sampling, Fisher-Rao} } Abstract : We study the problem of identifying shape classes in point clouds. These clouds contain sampled contours and are corrupted by clutter and observation noise. Taking an analysis-by-synthesis approach, we simulate high-probability configurations of sampled contours using models learnt from training data to evaluate the given test data. To facilitate simulations, we develop statistical models for sources of (nuisance) variability: (i) shape variations within classes, (ii) variability in sampling continuous curves, (iii) pose and scale variability, (iv) observation noise, and (v) points introduced by clutter. The variability in sampling closed curves into finite points is represented by positive diffeomorphisms of a unit circle. We derive probability models on these functions using their squareroot forms and the Fisher-Rao metric. Using a Monte Carlo approach, we simulate configurations from a joint prior on the shape-sample space and compare them to the data using a likelihood function. Average likelihoods of simulated configurations lead to estimates of posterior probabilities of different classes and, hence, Bayesian classification.

2 - A higher-order active contour model of a ‘gas of circles' and its application to tree crown extraction. P. Horvath and I. H. Jermyn and Z. Kato and J. Zerubia. Pattern Recognition, 42(5): pages 699-709, May 2009. Keywords : Shape, Higher-order, Active contour, Gas of circles, Tree Crown Extraction, Bayesian. @ARTICLE{Horvath09, 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 = {2009}, month = {May}, journal = {Pattern Recognition}, volume = {42}, number = {5}, pages = {699-709}, url = {http://dx.doi.org/10.1016/j.patcog.2008.09.008}, pdf = {http://www-sop.inria.fr/members/Ian.Jermyn/publications/Horvathetal09.pdf}, keyword = {Shape, Higher-order, Active contour, Gas of circles, Tree Crown Extraction, Bayesian} } Abstract : We present a model of a ‘gas of circles’: regions in the image domain composed of a unknown number of circles of approximately the same radius. The model has applications to medical, biological, nanotechnological, and remote sensing imaging. The model is constructed using higher-order active contours (HOACs) in order to include non-trivial prior knowledge about region shape without constraining topology. The main theoretical contribution is an analysis of the local minima of the HOAC energy that allows us to guarantee stable circles, fix one of the model parameters, and constrain the rest. We apply the model to tree crown extraction from aerial images of plantations. Numerical experiments both confirm the theoretical analysis and show the empirical importance of the prior shape information.

3 - 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.

4 - Higher Order Active Contours. M. Rochery and I. H. Jermyn and J. Zerubia. International Journal of Computer Vision, 69(1): pages 27--42, August 2006. Keywords : Active contour, Shape, Higher-order, Prior, Road network. @ARTICLE{mr_ijcv_06, author = {Rochery, M. and Jermyn, I. H. and Zerubia, J.}, title = {Higher Order Active Contours}, year = {2006}, month = {August}, journal = {International Journal of Computer Vision}, volume = {69}, number = {1}, pages = {27--42}, url = {http://dx.doi.org/10.1007/s11263-006-6851-y}, pdf = {ftp://ftp-sop.inria.fr/ariana/Articles/2006_mr_ijcv_06.pdf}, keyword = {Active contour, Shape, Higher-order, Prior, Road network} } Abstract : We introduce a new class of active contour models that hold great promise for region and shape modelling, and we apply a special case of these models to the extraction of road networks from satellite and aerial imagery. The new models are arbitrary polynomial functionals on the space of boundaries, and thus greatly generalize the linear functionals used in classical contour energies. While classical energies are expressed as single integrals over the contour, the new energies incorporate multiple integrals, and thus describe long-range interactions between different sets of contour points. As prior terms, they describe families of contours that share complex geometric properties, without making reference to any particular shape, and they require no pose estimation. As likelihood terms, they can describe multi-point interactions between the contour and the data. 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. Networks are a shape family of great importance in a number of applications, including remote sensing imagery. To model them, we make a particular choice of prior quadratic energy that describes reticulated structures, and augment it with a likelihood term that couples the data at pairs of contour points to their joint geometry. Promising experimental results are shown on real images.

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PhD Thesis and Habilitation

1 - Shape recognition for image scene analysis. M. S. Kulikova. PhD Thesis, Universite de Nice - Sophia-Antipolis, December 2009. Keywords : tree crown , Classification, Shape, multiple object extraction, Marked point process, Shape prior. @PHDTHESIS{mkulikova_phd09, author = {Kulikova, M. S.}, title = {Shape recognition for image scene analysis}, year = {2009}, month = {December}, school = {Universite de Nice - Sophia-Antipolis}, url = {http://tel.archives-ouvertes.fr/docs/00/48/20/19/PDF/phd_mkulikova_2009.pdf}, keyword = {tree crown , Classification, Shape, multiple object extraction, Marked point process, Shape prior} } Résumé : Cette thèse est composée de deux parties principales. La première partie est dédiée au problème de la classification d’espèces d’arbres en utilisant des descripteurs de forme, en combainison ou non, avec ceux de radiométrie ou de texture. Nous montrons notamment que l’information sur la forme améliore la performance d’un classifieur. Pour ce faire, dans un premier temps, une étude des formes de couronnes d’arbres extraites à partir d’images aériennes, en infrarouge couleur, est eectuée en utilisant une méthodologie d’analyse de formes des courbes continues fermées dans un espace de formes, en utilisant la notion de chemin géodésique sous deux métriques dans des espaces appropriés : une métrique non-élastique en utilisant la reprèsentation par la fonction d’angle de la courbe, ainsi qu’une métrique élastique induite par une représentation par la racinecarée appelée q-fonction. Une étape préliminaire nécessaire à la classification est l’extraction des couronnes d’arbre. Dans une seconde partie, nous abordons donc le problème de l’extraction d’objets de forme complexe arbitraire, à partir d’images de télédétection à très haute résolution. Nous construisons un modèle fondé sur les processus ponctuels marqués. Son originalité tient dans sa prise en compte d’objets de forme arbitraire par rapport aux objets de forme paramétrique, e.g. ellipses ou rectangles. Les formes sélectionnées sont obtenues par la minimisation locale d’une énergie de type contours actifs avec diérents a priori sur la forme incorporé. Les objets de la configuration finale (optimale) sont ensuite sélectionnés parmi les candidats par une dynamique de naissances et morts multiples, couplée à un schéma de recuit simulé. L’approche est validée sur des images de zones forestières à très haute résolution fournies par l’Université d’Agriculture de Suède. Abstract : This thesis includes two main parts. In the first part we address the problem of tree crown classification into species using shape features, without, or in combination with, those of radiometry and texture, to demonstrate that shape information improves classification performance. For this purpose, we first study the shapes of tree crowns extracted from very high resolution colour aerial infra-red images. For our study, we choose a methodology based on the shape analysis of closed continuous curves on shape spaces using geodesic paths under the bending metric with the angle-function curve representation, and the elastic metric with the square root q-function representation. A necessary preliminary step to classification is extraction of the tree crowns. In the second part, we address thus the problem of extraction of multiple objects with complex, arbitrary shape from remote sensing images of very high resolution. We develop a model based on marked point processes. Its originality lies in its use of arbitrarily-shaped objects as opposed to parametric shape objects, e.g. ellipses or rectangles. The shapes considered are obtained by local minimisation of an active contour energy with weak and then strong shape prior knowledge included. The objects in the final (optimal) configuration are then selected from amongst these candidates by a multiple birth-and-death dynamics embedded in an annealing scheme. The approach is validated on very high resolution images of forest provided by the Swedish University of Agriculture.

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15 Conference articles

1 - A phase field higher-order active contour model of directed networks. A. El Ghoul and I. H. Jermyn and J. Zerubia. In 2nd IEEE Workshop on Non-Rigid Shape Analysis and Deformable Image Alignment, at ICCV, Kyoto, Japan, September 2009. Keywords : Geometric prior, Shape, Higher-order actif contours, Phase Field, Directed networks. Copyright : ©2009 IEEE. @INPROCEEDINGS{ElGhoul09b, author = {El Ghoul, A. and Jermyn, I. H. and Zerubia, J.}, title = {A phase field higher-order active contour model of directed networks}, year = {2009}, month = {September}, booktitle = {2nd IEEE Workshop on Non-Rigid Shape Analysis and Deformable Image Alignment, at ICCV}, address = {Kyoto, Japan}, url = {https://hal.inria.fr/inria-00409910}, pdf = {http://hal.inria.fr/docs/00/40/99/10/PDF/nordia09aymenelghoul.pdf}, keyword = {Geometric prior, Shape, Higher-order actif contours, Phase Field, Directed networks} } Abstract : The segmentation of directed networks is an important problem in many domains, e.g. medical imaging (vascular networks) and remote sensing (river networks). Directed networks carry a unidirectional flow in each branch, which leads to characteristic geometric properties. In this paper, we present a nonlocal phase field model of directed networks. In addition to a scalar field representing a region by its smoothed characteristic function and interacting nonlocally so as to favour network configurations, the model contains a vector field representing the ‘flow’ through the network branches. The vector field is strongly encouraged to be zero outside, and of unit magnitude inside the region; and to have zero divergence. This prolongs network branches; controls width variation along a branch; and produces asymmetric junctions for which total incoming branch width approximately equals total outgoing branch width. In conjunction with a new interaction function, it also allows a broad range of stable branch widths. We analyse the energy to constrain the parameters, and show geometric experiments confirming the above behaviour. We also show a segmentation result on a synthetic river image.

2 - Inflection point model under phase field higher-order active contours for network extraction from VHR satellite images. A. El Ghoul and I. H. Jermyn and J. Zerubia. In Proc. European Signal Processing Conference (EUSIPCO), Glasgow, Scotland, August 2009. Keywords : Geometric prior, Shape, Higher-order active contour, Phase Field, remote sensing. Copyright : EURASIP @INPROCEEDINGS{ElGhoul09a, author = {El Ghoul, A. and Jermyn, I. H. and Zerubia, J.}, title = {Inflection point model under phase field higher-order active contours for network extraction from VHR satellite images}, year = {2009}, month = {August}, booktitle = {Proc. European Signal Processing Conference (EUSIPCO)}, address = {Glasgow, Scotland}, url = {http://hal.inria.fr/inria-00390446/fr/}, pdf = {http://hal.inria.fr/docs/00/39/04/46/PDF/eusipco09aymenelghoul.pdf}, keyword = {Geometric prior, Shape, Higher-order active contour, Phase Field, remote sensing} } Abstract : The segmentation of networks is important in several imaging domains, and models incorporating prior shape knowledge are often essential for the automatic performance of this task. We incorporate such knowledge via phase fields and higher-order active contours (HOACs). In this paper: we introduce an improved prior model, the phase field HOAC ‘inflection point’ model of a network; we present an improved data term for the segmentation of road networks; we confirm the robustness of the resulting model to choice of gradient descent initialization; and we illustrate these points via road network extraction results on VHR satellite images.

3 - Phase diagram of a long bar under a higher-order active contour energy: application to hydrographic network extraction from VHR satellite images. A. El Ghoul and I. H. Jermyn and J. Zerubia. In International Conference on Pattern Recognition (ICPR), Tampa, Florida, December 2008. Keywords : Phase diagram, Higher-order actif contours, Shape, river extraction. @INPROCEEDINGS{ElGhoul08b, author = {El Ghoul, A. and Jermyn, I. H. and Zerubia, J.}, title = {Phase diagram of a long bar under a higher-order active contour energy: application to hydrographic network extraction from VHR satellite images}, year = {2008}, month = {December}, booktitle = {International Conference on Pattern Recognition (ICPR)}, address = {Tampa, Florida}, url = {https://hal.inria.fr/inria-00316619}, pdf = {http://hal.inria.fr/docs/00/31/66/19/PDF/icpr08aymenelghoul.pdf}, keyword = {Phase diagram, Higher-order actif contours, Shape, river extraction} } Abstract : The segmentation of networks is important in several imaging domains, and models incorporating prior shape knowledge are often essential for the automatic performance of this task. Higher-order active contours provide a way to include such knowledge, but their behaviour can vary significantly with parameter values: e.g. the same energy can model networks or a ‘gas of circles’. In this paper, we present a stability analysis of a HOAC energy leading to the phase diagram of a long bar. The results, which are confirmed by numerical experiments, enable the selection of parameter values for the modelling of network shapes using the energy. We apply the resulting model to the problem of hydrographic network extraction from VHR satellite images.

4 - Diagramme de phase d'une énergie de type contours actifs d'ordre supérieur : le cas d'une barre longue. A. El Ghoul and I. H. Jermyn and J. Zerubia. In 16ème congrès francophone AFRIF-AFIA Reconnaissance des Formes et Intelligence Artificielle (RFIA), Amiens, France, January 2008. Keywords : Diagramme de phase, Contours actifs d'ordre supérieur, Shape, geometric prior, Télédétection. @INPROCEEDINGS{ElGhoul08, author = {El Ghoul, A. and Jermyn, I. H. and Zerubia, J.}, title = {Diagramme de phase d'une énergie de type contours actifs d'ordre supérieur : le cas d'une barre longue}, year = {2008}, month = {January}, booktitle = {16ème congrès francophone AFRIF-AFIA Reconnaissance des Formes et Intelligence Artificielle (RFIA)}, address = {Amiens, France}, url = {https://hal.inria.fr/inria-00319575}, pdf = {http://hal.inria.fr/docs/00/31/95/75/PDF/rfia08aymenelghoul.pdf}, keyword = {Diagramme de phase, Contours actifs d'ordre supérieur, Shape, geometric prior, Télédétection} } Résumé : Dans cet article, nous présentons l’analyse de stabilité du modèle des “contours actifs d’ordre supérieur” (CAOS), pour l’extraction des réseaux routiers présents dans des images de télédétection. Le modèle énergétique des CAOS à minimiser présente des comportements différents en fonction des valeurs des paramètres du modèle. Il s’est avéré que deux structures géométriques sont favorisées par ce modèle : des structures linéiques et circulaires. Nous nous intéressons ici à la détermination du diagramme de phase, qui définit les gammes des valeurs des paramètres du modèle des CAOS, permettant d’obtenir des structures linéiques. Abstract : In this paper, we present a stability analysis of a “higher-order active contour” (HOAC) model for road network extraction from remotely sensed images. The HOAC energy presents several different behaviours depending on the model parameter values. Two types of geometric structure are favoured, namely line networks and circles. In this work, we derive the phase diagram giving the parameter ranges of the HOAC model that allow stable linear structures.

5 - 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.

6 - 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.

7 - A Novel Representation for Riemannian Analysis of Elastic Curves in R^n. S. Joshi and E. Klassen and A. Srivastava and I. H. Jermyn. In Proc. IEEE Computer Vision and Pattern Recognition (CVPR), Minneapolis, USA, June 2007. Keywords : Shape, Metric, Geodesic, Prior. @INPROCEEDINGS{Joshi07a, author = {Joshi, S. and Klassen, E. and Srivastava, A. and Jermyn, I. H.}, title = {A Novel Representation for Riemannian Analysis of Elastic Curves in R^n}, year = {2007}, month = {June}, booktitle = {Proc. IEEE Computer Vision and Pattern Recognition (CVPR)}, address = {Minneapolis, USA}, url = {http://dx.doi.org/10.1109/CVPR.2007.383185}, pdf = {ftp://ftp-sop.inria.fr/ariana/Articles/2007_Joshi07a.pdf}, keyword = {Shape, Metric, Geodesic, Prior} } Abstract : We propose an efficient representation for studying shapes of closed curves in R^n. This paper combines the strengths of two important ideas---elastic shape metric and path-straightening methods---and results in a very fast algorithm for finding geodesics in shape spaces. The elastic metric allows for optimal matching of features between the two curves while path-straightening ensures that the algorithm results in geodesic paths. For the novel representation proposed here, the elastic metric becomes the simple L^2 metric, in contrast to the past usage where more complex forms were used. We present the step-by-step algorithms for computing geodesics and demonstrate them with 2-D as well as 3-D examples.

8 - Urban road extraction from VHR images using a multiscale image model and a phase field model of network geometry. T. Peng and I. H. Jermyn and V. Prinet and J. Zerubia. In Proc. Urban, Paris, France, April 2007. Keywords : Road network, Very high resolution, Multiscale, Higher-order, Active contour, Shape. @INPROCEEDINGS{Peng07_urban, author = {Peng, T. and Jermyn, I. H. and Prinet, V. and Zerubia, J.}, title = {Urban road extraction from VHR images using a multiscale image model and a phase field model of network geometry}, year = {2007}, month = {April}, booktitle = {Proc. Urban}, address = {Paris, France}, pdf = {http://www-sop.inria.fr/members/Ian.Jermyn/publications/Peng07urban.pdf}, keyword = {Road network, Very high resolution, Multiscale, Higher-order, Active contour, Shape} } Abstract : This paper addresses the problem of automatically extracting the main road network in a dense urban area from a very high resolution optical satellite image using a variational approach. The model energy has two parts: a phase field higherorder active contour energy that describes our prior knowledge of road network geometry, i.e. that it is composed of elongated structures with roughly parallel borders that meet at junctions; and a multi-scale statistical image model describing the image we expect to see given a road network. By minimizing the model energy, an estimate of the road network is obtained. Promising results on 0.6m QuickBird Panchromatic images are presented, and future improvements to the models are outlined.

9 - Circular object segmentation using higher-order active contours. P. Horvath and I. H. Jermyn and Z. Kato and J. Zerubia. In In Proc. Conference of the Hungarian Association for Image Analysis and Pattern Recognition (KEPAF'07), Debrecen, Hungary, January 2007. Note : In Hungarian Keywords : Higher-order, Tree Crown Extraction, Shape. @INPROCEEDINGS{Horvath07a, author = {Horvath, P. and Jermyn, I. H. and Kato, Z. and Zerubia, J.}, title = {Circular object segmentation using higher-order active contours}, year = {2007}, month = {January}, booktitle = {In Proc. Conference of the Hungarian Association for Image Analysis and Pattern Recognition (KEPAF'07)}, address = {Debrecen, Hungary}, note = {In Hungarian}, pdf = {ftp://ftp-sop.inria.fr/ariana/Articles/2007_Horvath07a.pdf}, keyword = {Higher-order, Tree Crown Extraction, Shape} }

10 - An improved 'gas of circles' higher-order active contour model and its application to tree crown extraction. P. Horvath and I. H. Jermyn and Z. Kato and J. Zerubia. In Proc. Indian Conference on Computer Vision, Graphics, and Image Processing (ICVGIP), Madurai, India, December 2006. Keywords : Tree Crown Extraction, Aerial images, Higher-order, Active contour, Gas of circles, Shape. @INPROCEEDINGS{Horvath06_icvgip, author = {Horvath, P. and Jermyn, I. H. and Kato, Z. and Zerubia, J.}, title = {An improved 'gas of circles' higher-order active contour model and its application to tree crown extraction}, year = {2006}, month = {December}, booktitle = {Proc. Indian Conference on Computer Vision, Graphics, and Image Processing (ICVGIP)}, address = {Madurai, India}, url = {http://dx.doi.org/10.1007/11949619_14}, pdf = {ftp://ftp-sop.inria.fr/ariana/Articles/2006_Horvath06_icvgip.pdf}, keyword = {Tree Crown Extraction, Aerial images, Higher-order, Active contour, Gas of circles, Shape} } Abstract : A central task in image processing is to find the region in the image corresponding to an entity. In a number of problems, the region takes the form of a collection of circles, eg tree crowns in remote sensing imagery; cells in biological and medical imagery. In~citeHorvath06b, a model of such regions, the `gas of circles' model, was developed based on higher-order active contours, a recently developed framework for the inclusion of prior knowledge in active contour energies. However, the model suffers from a defect. In~citeHorvath06b, the model parameters were adjusted so that the circles were local energy minima. Gradient descent can become stuck in these minima, producing phantom circles even with no supporting data. We solve this problem by calculating, via a Taylor expansion of the energy, parameter values that make circles into energy inflection points rather than minima. As a bonus, the constraint halves the number of model parameters, and severely constrains one of the two that remain, a major advantage for an energy-based model. We use the model for tree crown extraction from aerial images. Experiments show that despite the lack of parametric freedom, the new model performs better than the old, and much better than a classical active contour.

11 - A Higher-Order Active Contour Model for Tree Detection. P. Horvath and I. H. Jermyn and Z. Kato and J. Zerubia. In Proc. International Conference on Pattern Recognition (ICPR), Hong Kong, August 2006. Keywords : Active contour, Gas of circles, Higher-order, Shape, Prior, Tree Crown Extraction. @INPROCEEDINGS{horvath_icpr06, author = {Horvath, P. and Jermyn, I. H. and Kato, Z. and Zerubia, J.}, title = {A Higher-Order Active Contour Model for Tree Detection}, year = {2006}, month = {August}, booktitle = {Proc. International Conference on Pattern Recognition (ICPR)}, address = {Hong Kong}, pdf = {ftp://ftp-sop.inria.fr/ariana/Articles/2006_horvath_icpr06.pdf}, keyword = {Active contour, Gas of circles, Higher-order, Shape, Prior, Tree Crown Extraction} } Abstract : We present a model of a ‘gas of circles’, the ensemble of regions in the image domain consisting of an unknown number of circles with approximately fixed radius and short range repulsive interactions, and apply it to the extraction of tree crowns from aerial images. The method uses the re- cently introduced ‘higher order active contours’ (HOACs), which incorporate long-range interactions between contour points, and thereby include prior geometric information without using a template shape. This makes them ideal when looking for multiple instances of an entity in an image. We study an existing HOAC model for networks, and show via a stability calculation that circles stable to perturbations are possible for constrained parameter sets. Combining this prior energy with a data term, we show results on aerial imagery that demonstrate the effectiveness of the method and the need for prior geometric knowledge. The model has many other potential applications.

12 - Phase field models and higher-order active contours. M. Rochery and I. H. Jermyn and J. Zerubia. In Proc. IEEE International Conference on Computer Vision (ICCV), Beijing, China, October 2005. Keywords : Active contour, Higher-order, Shape, Line networks, Road network, Phase Field. @INPROCEEDINGS{rochery_iccv05, author = {Rochery, M. and Jermyn, I. H. and Zerubia, J.}, title = {Phase field models and higher-order active contours}, year = {2005}, month = {October}, booktitle = {Proc. IEEE International Conference on Computer Vision (ICCV)}, address = {Beijing, China}, pdf = {ftp://ftp-sop.inria.fr/ariana/Articles/rochery_iccv05.pdf}, keyword = {Active contour, Higher-order, Shape, Line networks, Road network, Phase Field} } Abstract : The representation and modelling of regions is an important topic in computer vision. In this paper, we represent a region via a level set of a `phase field' function. The function is not constrained, eg to be a distance function; nevertheless, phase field energies equivalent to classical active contour energies can be defined. They represent an advantageous alternative to other methods: a linear representation space; ease of implementation (a PDE with no reinitialization); neutral initialization; greater topological freedom. We extend the basic phase field model with terms that reproduce `higher-order active contour' energies, a powerful way of including prior geometric knowledge in the active contour framework via nonlocal interactions between contour points. In addition to the above advantages, the phase field greatly simplifies the analysis and implementation of the higher-order terms. We define a phase field model that favours regions composed of thin arms meeting at junctions, combine this with image terms, and apply the model to the extraction of line networks from remote sensing images.

13 - New Higher-order Active Contour Energies for Network Extraction. M. Rochery and I. H. Jermyn and J. Zerubia. In Proc. IEEE International Conference on Image Processing (ICIP), Genoa, Italy, September 2005. Keywords : Gap closure, Shape, Prior, Higher-order, Active contour. @INPROCEEDINGS{rochery_icip05, author = {Rochery, M. and Jermyn, I. H. and Zerubia, J.}, title = {New Higher-order Active Contour Energies for Network Extraction}, year = {2005}, month = {September}, booktitle = {Proc. IEEE International Conference on Image Processing (ICIP)}, address = {Genoa, Italy}, pdf = {ftp://ftp-sop.inria.fr/ariana/Articles/rochery_icip05.pdf}, keyword = {Gap closure, Shape, Prior, Higher-order, Active contour} } Abstract : Using the framework of higher-order active contours, we present a new quadratic em continuation energy for the extraction of line networks (e.g. road, hydrographic, vascular) in the presence of occlusions. Occlusions create gaps in the data that frequently translate to gaps in the extracted network. The new energy penalizes earby opposing extremities of the network, and thus favours the closure of the gaps created by occlusions. Nearby opposing extremities are identified using a sophisticated interaction between pairs of points on the contour. This new model allows the extraction of fully connected networks, even though occlusions violate common assumptions about the homogeneity of the interior, and high contrast with the exterior, of the network. We present experimental results on real aerial images that demonstrate the effectiveness of the new model for network extraction tasks.

14 - Gap closure in (road) networks using higher-order active contours. M. Rochery and I. H. Jermyn and J. Zerubia. In Proc. IEEE International Conference on Image Processing (ICIP), Singapore, October 2004. Keywords : Active contour, Gap closure, Higher-order, Shape, Road network. @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 = {October}, booktitle = {Proc. IEEE International Conference on Image Processing (ICIP)}, address = {Singapore}, pdf = {ftp://ftp-sop.inria.fr/ariana/Articles/rochery_icip04.pdf}, keyword = {Active contour, Gap closure, Higher-order, Shape, Road network} } 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.

15 - Higher Order Active Contours and their Application to the Detection of Line Networks in Satellite Imagery. M. Rochery and I. H. Jermyn and J. Zerubia. In Proc. IEEE Workshop Variational, Geometric and Level Set Methods in Computer Vision, at ICCV, Nice, France, October 2003. Keywords : Higher-order, Active contour, Shape, Road network, Segmentation, Prior. @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 = {October}, 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 = {Higher-order, Active contour, Shape, Road network, Segmentation, Prior} } 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.

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