Discrete euclidean skeletons in increased resolution

Orientadores: Roberto de Alencar Lotufo, Michel CouprieTese (doutorado) - Universidade Estadual de Campinas, Faculdade de Engenharia Eletrica e de ComputaçãoResumo: A extração de esqueletos Euclidianos é uma tema de grande importância na área de processamento de imagens e tem sido discutido pela comunidade científica já há mais de 20 anos. Hoje é consenso que os esqueletos Euclidianos devem ter as seguintes características: ï¬?nos, centrados, homotópicos e reversíveis, i.e., suficientes para a reconstrução do objeto original. Neste trabalho, introduzimos o Eixo Mediano Euclidiano Exato em Resolução Aumentada -HMA, com o objetivo de obter um eixo mediano mais ï¬?no do que o obtido pela definição clássica. Combinando o HMA com um eï¬?ciente algoritmo de afinamento paralelo homotópico, propomos um esqueleto Euclidiano que é centrado, homotópico, reversível e mais ï¬?no que os já existentes na literatura. O esqueleto proposto tem a particularidade adicional de ser único e independente de decisões arbitrárias. São dados algoritmos e provas, assim como exemplos de aplicações dos esqueletos propostos em imagens reais, mostrando as vantagens da proposta. O texto inclui também uma revisão bibliográfica sobre algoritmos de transformada de distância, eixo mediano e esqueletos homotópicosAbstract: The extraction of Euclidean skeletons is a subject of great importance in the domain of image processing and it has been discussed by the scientiï¬?c community since more than 20 years.Today it is a consensus that Euclidean skeletons should present the following characteristics: thin, centered, homotopic and reversible, i.e., sufï¬?cient for the reconstruction of the original object. In this work, we introduce the Exact Euclidean Medial Axis in Higher Resolution -HMA, with the objective of obtaining a medial axis which is thinner than the one obtained by the classical medial axis deï¬?nition. By combining the HMA with an efï¬?cient parallel homotopic thinning algorithm we propose an Euclidean skeleton which is centered, homotopic, reversible and thinner than the existing similars in the literature. The proposed skeleton has the additional particularity of being unique and independent of arbitrary choices. Algorithms and proofs are given, as well as applicative examples of the proposed skeletons in real images, showing the advantages of the proposal. The text also includes an overview on algorithms for the Euclidean distance transform algorithms, the medial axis extraction, as well as homotopic skeletonsDoutoradoEngenharia de ComputaçãoDoutor em Engenharia Elétric

Euclidean homotopic skeleton based on critical kernels

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Euclidean Homotopic Skeleton Based On Critical Kernels

Critical kernels constitute a general framework settled in the category of abstract complexes for the study of parallel thinning in any dimension. It allows to easily design parallel thinning algorithms which produce new types of skeletons, with specific geometrical properties, while guaranteeing their topological soundness. In this paper, we demonstrate that it is possible to define a skeleton based on the Euclidean distance, rather than on the common discrete distances, in the context of critical kernels. We provide the necessary definitions as well as an efficient algorithm to compute this skeleton. © 2006 IEEE.307314Bertrand, G., Skeletons in derived grids (1984) In procs. Int. Conf. Patt. Recogn, pp. 326-329Bertrand, G., On critical kernels (2005), Technical Report IGM2005-5, Institut Gaspard-Monge, Université de Marne-la-Vallée, FranceBertrand, G., Couprie, M., New 2d parallel thinning algorithms based on critical kernels (2006) LNCS, 4040, pp. 45-59. , Combinatorial Image Analysis, of, SpringerBlum, H., An associative machine for dealing with the visual field and some of its biological implications (1961) Biological prototypes and synthetic systems, 1, pp. 244-260Blum, H., A transformation for extracting new descriptors of shape (1967) Models for the Perception of Speech and Visual Form, pp. 362-380. , W. Wathendunn, editor, MIT PressCouprie, M., Coeurjolly, D., Zrour, R., Discrete bisector function and Euclidean skeleton in 2d and 3d (2006) Image and Vision Computing, , acceptedDavies, E., Plummer, A., Thinning algorithms: A critique and a new methodology (1981) Pattern Recognition, 14, pp. 53-63de Souza, A.F., (2005) Expansão por dilatação e por erosão visando a extração de esqueletos e contornos em imagens digitais, , PhD thesis, INPE, BrazilHirata, T., A unified linear-time algorithm for computing distance maps (1996) Information Processing Letters, 58 (3), pp. 129-133Rémy, E., Thiel, E., Exact medial axis with Euclidean distance (2005) Image and Vision Computing, 23 (2), pp. 167-175Saúde, A.V., Couprie, M., Lotufo, R., Exact Euclidean medial axis in higher resolution (2006) LNCS, , A. Kuba, K. Palágyi, and L. Nyúl, editors, Discrete Geometry for Computer Imagery, Springer, OctH. Talbot and L. Vincent. Euclidean skeletons and conditional bisectors. In Procs. VCIP'92, SPIE, ume 1818, pages 862-876, 1992Vincent, L., Efficient computation of various types of skeletons (1991) Procs. Medical Imaging V, SPIE, 1445, pp. 297-31

Exact Euclidean Medial Axis In Higher Resolution

The notion of skeleton plays a major role in shape analysis. Some usually desirable characteristics of a skeleton are: sufficient for the reconstruction of the original object, centered, thin and homotopic. The Euclidean Medial Axis presents all these characteristics in a continuous framework. In the discrete case, the Exact Euclidean Medial Axis (MA) is also sufficient for reconstruction and centered. It no longer preserves homotopy but it can be combined with a homotopic thinning to generate homotopic skeletons. The thinness of the MA, however, may be discussed. In this paper we present the definition of the Exact Euclidean Medial Axis on Higher Resolution which has the same properties as the MA but with a better thinness characteristic, against the price of rising resolution. We provide an efficient algorithm to compute it. © Springer-Verlag Berlin Heidelberg 2006.4245 LNCS605616Blum, H., An associative machine for dealing with the visual field and some of its biological implications (1961) Biological Prototypes and Synthetic Systems, 1, pp. 244-260Davies, E., Plummer, A., Thinning algorithms: A critique and a new methodology (1981) Pattern Recognition, 14, pp. 53-63Talbot, H., Vincent, L., Euclidean skeletons and conditional bisectors (1992) Procs. VCIP'92, 1818, pp. 862-876. , SPIECouprie, M., Coeurjolly, D., Zrour, R., Discrete bisector function and euclidean skeleton in 2d and 3d (2006) Image and Vision Computing, , acceptedBertrand, G., Skeletons in derived grids (1984) Procs. Int. Conf. Patt. Recogn., pp. 326-329Kovalevsky, V., Finite topology as applied to image analysis (1989) Computer Vision, Graphics and Image Processing, 48, pp. 141-161Khalimsky, E., Kopperman, R., Meyer, P., Computer graphics and connected topologies on finite ordered sets (1990) Topology and Its Applications, 38, pp. 1-17Kong, T.Y., Kopperman, R., Meyer, P., A topological approach to digital topology (1991) American Mathematical Monthly, 38, pp. 901-917Bertrand, G., New notions for discrete topology (1999) Procs. DGCI, 1568, pp. 216-226. , LNCS, Springer VerlagBertrand, G., Couprie, M., New 3d parallel thinning algorithms based on critical kernels (2006) LNCS, , Kuba, A., Palágyi, K., Nyúl, L., eds.: DGCI, SpringerDanielsson, P., Euclidean distance mapping (1980) Computer Graphics and Image Processing, 14, pp. 227-248Meyer, F., (1979) Cytologie Quantitative et Morphologie Mathématique, , PhD thesis, École des Mines de Paris, FranceSaito, T., Toriwaki, J., New algorithms for euclidean distance transformation of an n-dimensional digitized picture with applications (1994) Pattern Recognition, 27, pp. 1551-1565Hirata, T., A unified linear-time algorithm for computing distance maps (1996) Information Processing Letters, 58 (3), pp. 129-133Meijster, A., Roerdink, J., Hesselink, W., A general algorithm for computing distance transforms in linear time (2000) Computational Imaging and Vision, 18, pp. 331-340. , J. Goutsias, L.V., Bloomberg, D., eds.: Mathematical morphology and its applications to image and signal processing 5th. Kluwer Academic PublishersRémy, E., Thiel, E., Look-up tables for medial axis on squared Euclidean distance transform (2003) Procs. DGCI, 2886, pp. 224-235. , LNCS, Springer VerlagCœurjolly, D., D-dimensional reverse Euclidean distance transformation and Euclidean medial axis extraction in optimal time (2003) Procs. DGCI, 2886, pp. 327-337. , LNCS, Springer VerlagRémy, E., Thiel, E., Exact medial axis with euclidean distance (2005) Image and Vision Computing, 23 (2), pp. 167-175Saúde, A.V., Couprie, M., Lotufo, R., (2006) Exact Euclidean Medial Axis in Higher Resolution, , Technical Report IGM2006-5, IGM, Université de Marne-la-valléeBorgefors, G., Ragnemalm, I., Di Baja, G.S., The Euclidean distance transform: Finding the local maxima and reconstructing the shape (1991) Seventh Scandinavian Conference on Image Analysis, 2, pp. 974-981. , Aalborg, DenmarkHardy, G., Wright, E., (1978) An Introduction to the Theory of Numbers. 5th Edn., , Oxford University PressCouprie, M., Saúde, A.V., Bertrand, G., Euclidean homotopic skeleton based on critical kernels (2006) Procs. SIBGRAPI, , to appea