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Issue No.12 - Dec. (2012 vol.34)
pp: 2379-2392
B. Kerautret , LORIA, Univ. of Lorraine, Vandoeuvre-les-Nancy, France
J-O Lachaud , Lab. de Math. (LAMA), Univ. of Savoie, Le-Bourget-du-Lac, France
The automatic detection of noisy or damaged parts along digital contours is a difficult problem since it is hard to distinguish between information and perturbation without further a priori hypotheses. However, solving this issue has a great impact on numerous applications, including image segmentation, geometric estimators, contour reconstruction, shape matching, or image edition. We propose an original strategy to detect what the relevant scales are at which each point of the digital contours should be considered. It relies on theoretical results of asymptotic discrete geometry. A direct consequence is the automatic detection of the noisy or damaged parts of the contour, together with its quantitative evaluation (or noise level). Apart from a given maximal observation scale, the proposed approach does not require any parameter tuning and is easy to implement. We demonstrate its effectiveness on several datasets. We present different direct applications of this local measure to contour smoothing and geometric estimators whose algorithms initially required a noise/scale parameter to tune: They show the pertinence of the proposed measure for digital shape analysis and reconstruction.
smoothing methods, geometry, image segmentation, object detection, shape recognition, digital shape analysis, meaningful scales detection, digital contours, unsupervised local noise estimation, image segmentation, geometric estimators, contour reconstruction, shape matching, image edition, asymptotic discrete geometry, noisy part automatic detection, damaged part automatic detection, contour smoothing, noise-scale parameter, Noise measurement, Shape analysis, Decision support systems, Noise measurement, Geometry, Approximation methods, shape analysis, Local noise detection, discrete geometry, maximal segments
B. Kerautret, J-O Lachaud, "Meaningful Scales Detection along Digital Contours for Unsupervised Local Noise Estimation", IEEE Transactions on Pattern Analysis & Machine Intelligence, vol.34, no. 12, pp. 2379-2392, Dec. 2012, doi:10.1109/TPAMI.2012.38
[1] I. Debled-Rennesson, F. Feschet, and J. Rouyer-Degli, "Optimal Blurred Segments Decomposition of Noisy Shapes in Linear Times," Computers and Graphics, vol. 30, pp. 30-36, 2006.
[2] T. Nguyen and I. Debled-Rennesson, "Curvature Estimation in Noisy Curves," Proc. 12th Int'l Conf. Computer Analysis of Images and Patterns, pp. 474-481, 2007.
[3] B. Kerautret and J.-O. Lachaud, "Curvature Estimation along Noisy Digital Contours by Approximate Global Optimization," Pattern Recognition, vol. 42, no. 10, pp. 2265-2278, Oct. 2009.
[4] R. Malgouyres, F. Brunet, and S. Fourey, "Binomial Convolutions and Derivatives Estimations from Noisy Discretizations," Proc. 14th Int'l Conf. Discrete Geometry for Computer Imagery, pp. 370-379, Apr. 2008.
[5] M. Marji, "On the Detection of Dominant Points on Digital Planar Curves," PhD dissertation, Wayne State Univ., 2003.
[6] L. Rudin, S. Osher, and E. Fatemi, "Nonlinear Total Variation Based Noise Removal Algorithms," Physica D, vol. 60, pp. 259-268, 1992.
[7] A.P. Witkin, "Scale-Space Filtering," Proc. Eight Int'l Joint Conf. Artificial Intelligence, pp. 1019-1022, 1983.
[8] J.J. Koenderink, "The Structure of Images," Biological Cybernetics, vol. 50, pp. 363-370, 1984.
[9] H. Jeong and C. Kim, "Adaptive Determination of Filter Scales for Edge Detection," IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 14, no. 5, pp. 579-585, May 1992.
[10] D. Mumford and J. Shah, "Optimal Approximations by Piecewise Smooth Functions and Associated Variational Problems," Comm. Pure Applied Math., vol. 42, pp. 577-684, 1989.
[11] J. Elder and S.W. Zucker, "Local Scale Control for Edge Detection and Blur Estimation," IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 20, no. 7, pp. 669-716, July 1998.
[12] C. Kervrann, "An Adaptive Window Approach for Image Smoothing and Structures Preserving," Proc. Ninth European Conf. Computer Vision, pp. 132-144, 2004.
[13] P. Perona and J. Malik, "Scale-Space and Edge Detection Using Anisotropic Diffusion," IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 12, no. 7, pp. 629-639, July 1990.
[14] D. Barash, "A Fundamental Relationship between Bilateral Filtering, Adaptive Smoothing and the Nonlinear Diffusion Equation," IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 24, no. 6, pp. 844-847, June 2002.
[15] K. Chen, "Adaptive Smoothing via Contextual and Local Discontinuities," IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 27, no. 10, pp. 1552-1566, Oct. 2005.
[16] A. Goshtasby and M. Satter, "An Adaptive Window Mechanism for Image Smoothing," Computer Vision and Image Understanding, vol. 111, pp. 155-169, 2008.
[17] J.-O. Lachaud, A. Vialard, and F. de Vieilleville, "Fast, Accurate and Convergent Tangent Estimation on Digital Contours," Image Vision Computing, vol. 25, no. 10, pp. 1572-1587, Oct. 2007.
[18] P. Bhowmick and B.B. Bhattacharya, "Fast Polygonal Approximation of Digital Curves Using Relaxed Straightness Properties," IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 29, no. 9, pp. 1590-1602, Sept. 2007.
[19] H. Liu, L.J. Latecki, and W. Liu, "A Unified Curvature Definition for Regular, Polygonal, and Digital Planar Curves," Int'l J. Computer Vision, vol. 80, no. 1, pp. 104-124, 2008.
[20] C. Couprie, L. Grady, L. Najman, and H. Talbot, "Power Watersheds: A Unifying Graph-Based Optimization Framework," IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 33, no. 7, pp. 1384-1399, July 2011.
[21] B. Kerautret and J.-O. Lachaud, "MS Online Demonstration," http://kerrecherche.iutsd.uhp-nancy.frMeaningfulBoxes , 2010.
[22] A. Rosenfeld, "Digital Straight Line Segments," IEEE Trans. Computers, vol. 23, no. 12, pp. 1264-1269, Dec. 1974.
[23] L. Dorst and A. Smeulders, "Discrete Representation of Straight Line," IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 6, no. 4, pp. 450-463, July 1984.
[24] A. Bruckstein, "Self-Similarity Properties of Digitized Straight Lines," Contemporary Math., vol. 119, pp. 1-20, 1991.
[25] R. Klette and A. Rosenfeld, "Digital Straightness—A Review," Discrete Applied Math., vol. 139, nos. 1-3, pp. 197-230, 2004.
[26] I.D. Rennesson and J.-P. Reveilles, "A Linear Algorithm for Segmentation of Digital Curves," Int'l J. Pattern Recognition Artificial Intelligence, vol. 9, no. 6, pp. 635-662, 1995.
[27] R. Klette and A. Rosenfeld, "Grids and Digitization," Digital Geometry: Geometric Methods for Digital Picture Analysis, chapter 2, Morgan Kaufmann, 2004.
[28] J.-O. Lachaud, "Espaces Non-Euclidiens et Analyse d'Image: Modèles Déformables Riemanniens et Discrets, Topologie et Géométrie Discrète," Habilitation à Diriger des Recherches, Université Bordeaux 1, in French, 2006.
[29] B. Kerautret and J.-O. Lachaud, "Online Annex of Article: Meaningful Scales Detection along Digital Contours for Unsupervised Local Noise Estimation," , Oct. 2011.
[30] B. Kerautret and J.-O. Lachaud, "Multi-Scale Analysis of Discrete Contours for Unsupervised Noise Detection," Proc. 13th Int'l Workshop Combinatorial Image Analysis, pp. 187-200, 2009.
[31] F. de Vieilleville, J.-O. Lachaud, and F. Feschet, "Maximal Digital Straight Segments and Convergence of Discrete Geometric Estimators," J. Math. Imaging Vision, vol. 27, no. 2, pp. 471-502, Feb. 2007.
[32] T. Kanungo, "Document Degradation Models and a Methodology for Degradation Model Validation," PhD dissertation, Univ. of Washington, 1996.
[33] A.C. Bovik, Handbook of Image and Video Processing. Academic Press, 2005.
[34] T.V. Hoang, E.H. Barney Smith, and S. Tabbone, "Edge Noise Removal in Bilevel Graphical Document Images Using Sparse Representation," Proc. IEEE 18th Int'l Conf. Image Processing, 2011.
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