. Echantillonnage-en-?, Tout d'abord en ce qui concerne l'´ echantillonnage en ?, il va falloir diviser par cos(?) chaque donné. Ceci correspondàcorrespondà l'espacement entre des lignes successives (` a ? fixé) Ainsi pour ? = 0, l'espacement est de 1, alors que pour ? = ?

. Echantillonnage-en-? and . Pour-l-'´-echantillonnage-en-?,-la-méthode-utilise-?-=-atan, N ? 1 avec N ´ etant la taille de l'image. Il nous faut donc interpoler les données, afin d'avoir un pas régulier. Nous avons donc interpolé les données afin de ne prendre les valeurs qu

. B. Fig, 6 ? Sélection de la composante graphique de la séparation texte/image (graphx est sélectionné dans la fenêtre de gauche)

. De-plus, La vérité terrain est un ensemble de couples (rectangle englobant, ´ etiquette) L'interface permet doncàdoncà l'utilisateur de délimiter une zone de l'image qui contient un symbole et de l'´ etiqueter (Fig B.7) De plus, il est possible d'accéderaccéderà un tableau récapitulatif qui montre toutes les zones contenant des symboles, ce qui permet de vérifier qu'il n'y a pas eu d'erreurs d'´ etiquetage (Fig B.8) et permet de les corriger le caséchéantcaséchéant, ABKJ99 ] Michael Ankerst, Markus M. Breunig, Hans-Peter Kriegel, and J.Sander. OP- TICS : ordering points to identify the clustering structure SIGMOD '99 : Proceedings of the 1999 ACM SIGMOD, International Conference on Management of Data, pp.49-60, 1999.

[. Agrawal, J. Gehrke, D. Gunopulos, and P. Raghavan, Automatic subspace clustering of high dimensional data for data mining applications, SIGMOD '98 : Proceedings of the 1998 ACM SIG- MOD international conference on Management of data, pp.94-105, 1998.

]. D. Ant91 and . Antoine, Interprétation des plans cadastraux françaisfrançaisà partir d'un modèle

J. [. Adam, C. Ogier, J. Cariou, and . Gardes, A Scale and Rotation Parameters Estimator Application to Technical Document Interpretation, Proceedings of 4th IAPR International Workshop on Graphics Recognition, pp.377-380, 2001.
DOI : 10.1007/3-540-45868-9_23

[. Berchtold, C. Bohm, and H. P. , The pyramid-technique : Towards breaking the curse of dimensionality, Proceedings of the ACM SIGMOD International Conference on Management Data, pp.142-153, 1998.

. Bcb-+-92-]-l, V. Boatto, M. D. Consorti, S. Buono, V. Di-zenzo et al., An Interpretation System for Land Register Maps, IEEE COMPUTER Magazine, issue.7, pp.2525-2558, 1992.

]. R. Bel61 and . Bellman, On the Approximation of Curves by Line Segments using Dynamic Programming, Communications of the ACM, vol.4, issue.6, p.284, 1961.

]. A. Ber73 and . Berztiss, A backtrack procedure for isomorphism of directed graphs, Journal of the ACM, vol.20, issue.3, pp.365-377, 1973.

]. P. Ber02 and . Berkhin, Survey of Clustering Data Mining Techniques, 2002.

]. S. Ber04 and . Berrani, Recherche approximative de plus proches voisins avec contrôle probabiliste de la précision ; applicationàapplicationà la recherche d'images par le contenu. thèse, 2004.

]. J. Bez81, . Bezdek-kevin, J. Beyer, R. Goldstein, U. Ramakrishnan et al., Pattern Recognition with Fuzzy Objective Function Algorithms When Is " Nearest Neighbor A clustering technique for summarizing multivariate data The X-Tree : An Index Structure for High-Dimensional Data The R*-tree : An efficient and robust access method for points and rectangles, Proceedings of the 22nd International Conference on Very Large Databases Proceedings of the ACM SIGMOD International Conference on Management of Data, pp.217-235153, 1967.

D. Boley, H. Bozdogan-boz94, ]. H. Bozdogan-bra95, ]. R. Bracewell, M. L. Brady-[-bsa91-]-s et al., Determining the Number of Component Clusters in the Standard Multi-variate Normal Mixture Model Using Model-Selection Criteria ARO Contract DAAG29-820K-0155 Mixture-Model Cluster Analysis Using Model Selection Criteria and a New Informational Measure of Complexity Two-Dimensional Imaging A Fast Discrete Approximation Algorithm For The Radon Transform Pattern Recognition with Moment Invariants : A Comparative Study and New Results Attributed Programmed Graph and Application to Diagram Interpretation A robust and scalable clustering algorithm for mixed type attributes in large database environments, Principal Direction Divisive Partitioning. Data Mining and Knowledge Discovery Proceedings of the First US/Japan Conference on the Frontiers of Statistical Modeling : An Informational Approach Proceedings of the 7th ACM SIGKDD Conte, P. Foggia, C. Sansone, and M. Vento. Thirty years of graph matching in pattern recognition, pp.325-344, 1982.

G. Celeux and G. Govaert, A classification EM algorithm for clustering and two stochastic versions, Computational Statistics & Data Analysis, vol.14, issue.3, pp.315-332, 1992.
DOI : 10.1016/0167-9473(92)90042-E

URL : https://hal.archives-ouvertes.fr/inria-00075196

J. [. Calinski and . Harabasz, A dendrite method for cluster analysis, Communications in statistics, vol.3, issue.1, pp.1-27, 1974.

M. [. Cash and . Hatamian, Optical character recognition by the method of moments, Computer Vision, Graphics, and Image Processing, vol.39, issue.3, pp.291-310, 1987.
DOI : 10.1016/S0734-189X(87)80183-4

]. N. Cho65 and . Chomsky, Aspects of the Theory of Syntax, 1965.

[. Chen, H. Liao, J. Wang, K. Fan, and C. Hsieh, An Interpretation System for Cadastral Maps, Proceedings of the 13th International Conference on Pattern Recognition, pp.711-715, 1996.

]. B. Coü96 and . Coüasnon, Segmentation et reconnaissance de documents guidées par la connaissance a priori : application aux partitions musicales, Thèse de doctorat, 1996.

M. [. Ciacca, P. Patella, and . Zezula, M-Tree : An efficient access method for similarity search in metric spaces, Proceedings of the 23rd International Conference on Very Large Databases, pp.426-435, 1997.

P. [. Chong, R. Raveendran, and . Mukudan, A comparative analysis of algorithms for fast computation of Zernike moments, Pattern Recognition, vol.36, issue.3, pp.731-742, 2003.
DOI : 10.1016/S0031-3203(02)00091-2

M. [. Cordella and . Vento, Symbol recognition in documents: a collection of techniques?, International Journal on Document Analysis and Recognition, vol.3, issue.2, pp.73-88, 2000.
DOI : 10.1007/s100320000036

K. [. Dudani, R. M. Bredding, and . Mcghee, Aircraft Identifiation by Moment Invariants, IEEE Transactions on Computers, vol.26, pp.39-45, 1977.
DOI : 10.1109/tc.1977.5009272

]. S. Dea83 and . Deans, Applications of the Radon Transform, 1983.

R. O. Duda, P. E. Hart, and D. G. Stork, Pattern Classification, Second Edition, 2000.

]. J. Den-hartog, T. K. Kate, and J. J. Gerbrands, An Alternative to Vectorization : Decomposition of Graphics into Primitives, Proceedings of Third Symposium on Document Analysis and Information Retrieval, 1994.

[. Ester, H. Kriegel, J. Sander, and X. Xu, A density-based algorithm for discovering clusters in large spatial databases with noise, Second International Conference on Knowledge Discovery and Data Mining, pp.226-231, 1996.

R. [. Fletcher and . Kasturi, A robust algorithm for text string separation from mixed text/graphics images, IEEE Transactions on Pattern Analysis and Machine Intelligence, vol.10, issue.6, pp.910-918, 1988.
DOI : 10.1109/34.9112

H. Frigui and R. Krishnapuram, A robust competitive clustering algorithm with applications in computer vision, IEEE Transactions on Pattern Analysis and Machine Intelligence, vol.21, issue.5, pp.450-465, 1999.
DOI : 10.1109/34.765656

L. N. Ana, L. Fred, ]. K. Leitao-fu74, ]. K. Fu-fu83, and . Fu, A new cluster isolation criterion based on dissimilarity increments Syntactic Methods in Pattern Recognition A Step Towards Unification of Syntactic and Statistical Pattern Recognition Unsupervise and Semi-supervised Clustering : a Brief Survey, IEEE Transactions on Pattern Analysis and Machine Intelligence Mathematics in Science and Engineering IEEE Transactions on PAMI IEEE Trans. Comput C, vol.25, issue.52, pp.944-958200, 1972.

R. Ganti, J. Ramakrishnan, A. L. Gehrke, J. C. Powell, . S. French et al., Clustering Large Datasets in Arbitrary Metric Spaces CURE : an efficient clustering algorithm for large databases R-trees : A dynamic index structure for spatial searching A New System for the Analysis of Schematic Diagrams The lsd h -tree : An access structure for feature vectors, Proceedings fo the 1998 ACM SIGMOD international conference on Management of data Proceedings of the ACM SIGMOD International Conference on Management of Data Proceedings of 2nd International Conference on Document Analysis and Recognition Proceedings of the 12th International Conference on Data Engineering, pp.502-511, 1984.

A. Hinneburg, D. A. Keim-hse, and A. R. Newton, An Efficient Approach to Clustering in Large Multimedia Databases with Noise Sketched Symbol Recognition using Zernike Moments, Knowledge Discovery and Data Mining Proceedings of the 17th International Conference on Pattern Recognition Hol75 ] J.H. Holland. Adaption in Natural and Artificial Systems, pp.58-65, 1975.

E. Hartuv, R. Shamir-jain, R. Dubes-jain, M. N. Murty, P. J. Flynn-[-kg82-]-f et al., Algorithms for Clustering Data Data clustering : a review Elliptic Fourier Features of Closed Contours Optimization by Simulated Annealing Invariant Image Recognition by Zernike Moments Chameleon : Hierarchical Clustering Using Dynamic Modeling A possibilistic approach to clustering A new region-based shape descriptor Finding Groups in Data : An Introduction to Cluster Analysis Document Image Analysis : An Overview of Techniques for Graphics Recognition The sr-tree : An index structure for highdimensional nearset neighbor queries Invariant Character Recognition with Zernike and Orthogonal Fourier-Mellin Moments The tv-tree : An index structure for high-dimensional data, A clustering algorithm based on graph connectivity . Information Processing Letters IRE Trans. on Information Theory Preproceedings of IAPR Workshop on Syntactic and Structural Pattern Recognition Proceedings of the ACM SIGMOD International Conference on Management Data LJF94 ] K.I. Lin, H.V. Jagadish, and C. Faloutsos LLKM97 ] J. Lladós, J. López-Krahe, and E. Martí. A System to Understand Hand- Drawn Floor Plans Using Subgraph Isomorphism and Hough Transform. Machine Vision and Applications LMG + 98 ] A. Lassaulzais, R. Mullot, J. Gardes, J. M. Ogier, and Y. Lecourtier. Segmentation d'infrastructures de réseau téléphonique Actes du 1 er Colloque International Francophone sur l' ´ Ecrit et le Document, pp.4-6175, 1962.

G. [. Lladós, E. Sánchez, . [. Martí, E. Lladós, G. Valveny et al., Symbol Recognition : Current Advances and Perspectives A general theory of classification sorting strategies Automatic Learning and Recognition of Graphical Symbols in Engineering Drawings An examination of procedures for determining the number of clusters in a data set Some methods for classification and analysis of multivariate observations Arc and Path Consistency Revisited A theory of multiscale, curvaturebased shape representation for planar curves, String Based Method to Recognize Symbols and Structural Textures in Architectural Plans Proceedings of 4th IAPR International Workshop on Graphics Recognition Graphics Recognition?Methods and Applications Proceedings of the fifth Berkeley Symposium on Mathematical Statistics and Probability The EM algorithm and extensions MR95 ] R. Motwani and P. Raghavan. Randomized Algorithms Mur83 ] F. Murtagh. A survey of recent advances in hierarchical clustering algorithms NGC99 ] H. Nagesh, S. Goil, and A. Choudhary. MAFIA : Efficient and scalable subspace clustering for very large data sets, pp.91-103, 1967.

R. T. Ng and J. Han, CLARANS: a method for clustering objects for spatial data mining, NL90 ] V. Nagasamy and N. A. Langrana. Engineering Drawing Processing and Vectorization System. Computer Vision, Graphics and Image Processing, pp.1003-1016, 1990.
DOI : 10.1109/TKDE.2002.1033770

]. A. Okm-+-88, T. Okazaki, K. Kondo, S. Mori, E. Tsunekawa et al., An Automatic Circuit Diagram Reader with Loop-Structure-Based Symbol Recognition, IEEE Transactions on PAMI, vol.10, issue.3, pp.331-341, 1988.

J. [. Peura and . Iivarinen, Efficiency of simple shape descriptors, 3rd International Workshop on Visual Form, pp.28-30, 1997.

L. [. Qjidaa and . Radouane, Robust line fitting in a noisy image by the method of moments, IEEE Transactions on Pattern Analysis and Machine Intelligence, vol.21, issue.11, pp.1216-1223, 1999.
DOI : 10.1109/34.809115

V. Vijay, K. Raghavan, and . Birchard, A clustering strategy based on a formalism of the reproductive process in natural systems, SIGIR '79 : Proceedings of the 2nd annual international ACM SIGIR conference on Information storage and retrieval, pp.10-22, 1979.

]. J. [-ris78 and . Rissanen, Modeling by shortest data description, Automatica, vol.14, pp.464-471, 1978.

R. [. Raymond, C. Klein, and . Dubes, Experiments in projection and clustering by simulated annealing, Pattern Recognition, vol.22, issue.2, pp.213-220, 1989.

]. J. [-rob81 and . Robinson, The k-d-b-tree : A search structure for large multidimensional dynamic indexes, Proceedings of the ACM SIGMOD International Conference on Management Data, pp.10-18, 1981.

R. [. Reeves, S. E. Prokop, and F. P. Andrews, Three-dimensional shape analysis using moments and Fourier descriptors, IEEE Transactions on Pattern Analysis and Machine Intelligence, vol.10, issue.6, pp.937-842, 1988.
DOI : 10.1109/34.9115

H. [. Weber, S. Schek, and . Blott, A quantitative analysis and performance study for similarity-search methods in high-dimensional spaces, Proceedings of the 24th International Conference on Very Large Databases, pp.194-205, 1998.

]. A. Sha69 and . Shaw, A Formal Picture Description Scheme as a Basis for Picture Processing Systems, Information and Control, vol.14, issue.1, pp.9-52, 1969.

]. P. Sne57 and . Sneath, The application of computers to taxonomy, Journal of general microbiology, vol.17, pp.201-226, 1957.

]. T. Sor48 and . Sorensen, The application of computers to taxonomy, Biologiske Skrifter, vol.5, pp.1-34, 1948.

N. [. Sellis, C. Roussopoulos, and . Faloutsos, The R + -tree : A dynamic index for multi-dimensional objects, Proceedings of the 16th International Conference on Very Large data Bases, pp.507-518, 1987.

R. Sharan and R. Shamir, CLICK : Clustering Algorithm with Applications to Gene Expression Analysis, ISMB'00, pp.307-316, 2000.

D. [. Thomopoulos, . Bougoulias, ]. R. Dignet-tea79, R. Teague, A. Torres et al., Image Analysis via the General Theory of Moments A graph-based approach for multiscale shape analysis Feature Extraction Methods for Character Recognition ? A Survey Recognition of Handwritten Symbols [ Tof96 ] P. Toft. The Radon Transform ? Theory and Implementation Technical Symbols Recognition Using the Two-dimensional Radon Transform Binary shape normalization using the Radon transform A new shape descriptor defined on the Radon transform A hybrid approach to detect graphical symbols in documents Filling in the Gaps : The Shape of Subjective Contours and a Model for their Generation Hierarchical grouping to optimize an objective function Estimation and inference by compact coding, Proceedings of the 30th IEEE Conference on Decision and Control Proceedings of the 16th International Conference on Pattern Recognition Proceedings of 11th International Conference on Discrete Geometry for Computer Imagery Document Analysis Systems VI ? Proceedings of 6th IAPR International Workshop on Document Analysis Systems Proceedings of the 12th International Conference on Data Engineering XEKS98 ] Xiaowei Xu-Peter Kriegel, and J. Sander. A Distribution- Based Clustering Algorithm for Mining in Large Spatial Databases Proceedings of the Fourteenth International Conference on Data Engineering, pp.853-858920, 1963.

R. Xu, D. Wunsch, N. Yoneda, K. Kise, S. Takamatsu et al., Handbook of Character Recognition and Document Image Analysis, chapter 19 Symbol Recognition via Statistical Integration of Pixel-Level Constraint Histograms : A New Descriptor A Method of Understanding Conceptual Diagrams A System for Recognizing a Large Class of Engineering Drawings A similarity-based robust clustering method An Analysis Technique for Biological Shape Graph-Theorical methods for detecting and describing gestalt clusters A comparative study of fourier descriptors for shape representation and retrieval Generic Fourier descriptor for shape-based image retrieval Fourier descriptors for planar closed curves, Survey of Clustering Algorihtms. IEEE Transactions on neural networks Paper-Based Map Processing Proceedings of IAPR Workshop on Machine Vision Applications, Kawasaki (Japan) fifth Asian Conference on Computer Vision Proceedings of the IEEE International Conference on Multimedia and Expo Accepted for presentation at 18th International Conference on Pattern Recognition ZRL96 ] T. Zhang, R. Ramakrishnan, and L. Livny. BIRCH : an efficient data clustering method for vey large databases Proceedings of the 1996 ACM SIGMOD international conference on Management of data, pp.645-678, 1971.

J. Zunic, N. Sladoje-zt06a, ]. D. Zuwala, and S. Tabbone, Efficiency of characterizing ellipses and ellipsoids by discrete moments, Document Analysis Systems VII : Proceedings of 7th International Workshop on Document Analysis Bibliographie Systems, pp.407-414, 2000.
DOI : 10.1109/34.845384