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 LNCS 605616Blum, 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 appear