Amincissement-sans-segmentation et rehaussement des images de niveau de gris par un filtre de chocs utilisant des champs de diffusion
Segmentation-Free Thinning and Enhancement of Grayscale Images by Shock Filter and Diffusion Fields
OPEN ACCESS
In the scope of gray-level image processing and understanding, thinning is certainly a central shape descriptor for image analysis and pattern recognition. Enhancement is also an essential tool in facilitating the visual interpretation and understanding of images, especially for noisy and blurry ones. The lack of general unified frameworks necessitates the investigation of these problems in a coherent fashion, using partial differential equations. In this paper, we present a method for thinning and enhancing images by using a shock filter derived from our previously work introduced on enhancement. This new filter incorporates specific diffusion fields and since each such field is characteristic of a given application, it brings a new degree of freedom to the shock filters, in order to address problems of greater practical interests. Probative results on handwritten documents illustrate the performance and efficiency of our model. Other applications have been added in order to highlight its efficiency.
Résumé
L’amincissement est assurément un descripteur de forme majeur pour l’analyse d’image et la reconnaissance de forme. Le rehaussement est aussi un outil essentiel pour faciliter l’interprétation visuelle et la compréhension des images de documents notamment celles qui sont bruitées et floues. Nous décrivons dans cet article une méthode d’amincissement et de rehaussement utilisant un filtre de chocs dérivant de celui introduit par Remaki et Cheriet pour le rehaussement. Ce nouveau filtre utilise un champ de diffusion spécifique initial. L’utilisation de tels champs apporte un nouveau degré de liberté aux filtres de chocs, puisque ceux-ci sont spécifiques aux applications (amincissement, rehaussement) et permettent ainsi au même filtre d’être utilisé pour différentes applications. Nous illustrons la performance de notre méthode par des résultats probants obtenus sur des images manuscrites.
Partial Differential Equations (PDE’s), thinning, enhancement, diffusion field, mathematical morphology, grayscale images
Mots clés
Équation aux dérivées partielles (EDP), amincissement, rehaussement, champ de diffusion, morphologie mathématique, images manuscrites
[1] L. ALVAREZ, F. GUICHARD, P.L. LIONS, J.M. MOREL, “Axioms and fundamental equations of image processing”, Arch. Rational Mechanics, Vol. 123, 1993, p. 199-257.
[2] H. BLUM, “Biological shape and visual science”, Journal of Theoretical Biology, Vol. 38, 1973, p. 205-287.
[3] M. CHERIET, J.N. SAID, C.Y. SUEN, “A Recursive Thresholding Technique for Image Segmentation”, IEEE Transaction on Image Processing, Vol. 7, #6, 1998, p. 918-921.
[4] M. CHERIET, J.C.DEMERS, S. DEBLOIS, “Shock filter-Based Diffusion Fields-Application to Grayscale Character Image Processing”, (In press) International Journal of Image and Graphics (SI), Vol. 5, #1, Invited Paper, 2004, p. 209-246.
[5] M. CHERIET, L. REMAKI, “Enhanced and restored signals as a generalized solution for shock filter models. Part II - Numerical study”, Journal of Mathematical Analysis and Applications, Vol. 279, 2003, p. 398-418.
[6] G. Sanniti DI BAJA, I. NYSTRÖM, “2D Grey-level Skeleton Computation: A Discret 3D Approach”’, 17th International Conference on Pattern Recognition(ICPR’04), Vol. 2, Août 2004, p. 455-458.
[7] D.H. CHUNG, G. SAPIRO, “Segmentation-free skeletonization of gray-scale images via pde’s”, ICIP00 International Conference on Image Processing, Vol. 2, Septembre 2000, p. 927-930.
[8] J.J. KOENDERINK, “The Structure of Images”, Biological Cybernetics, Vol. 53, 1984, p. 363-370.
[9] P.C.K. KWOK, V. RANJAN, “A Survey of 3-D Thinning Algorithms”, vision interface ‘91.
[10] L. LAM, S.W. LEE, C.Y. SUEN, “Thinning Methodologies-A comprehensive survey”, IEEE Trans. on Patt. Anal. and Mach. Intell., Vol. 14, #9, 1992, p. 869-885.
[11] C.W. NIBLACK, P.B. GIBBONS, “Generating Skeletons and Centerlines from the Distance Transform”, CVGIP: Graphical Models and image processing, Vol. 54, #5, Septembre 1992, p. 420-437.
[12] S. OSHER, L. RUDIN, “Feature Oriented Image Enhancement Using Shock Filters”, SIAM Journal on Numerical Analysis, Vol. 27, 1990, p. 919-940.
[13] N. OTSU, “A Threshold Selection Method from Grey-Level Histograms”, IEEE Transaction on Systems, Man, and Cybernetics, Vol. SMC-8, 1978, p. 62-66.
[14] P. PERONA, J. MALIK, “Scale space and edge detection using anisotropic diffusion”, Proc. IEEE comp. Soc. Workshop on computer vision, Miami beach, Novembre 1987, IEEE Computer Society Press, Washington, 1987, p. 16-22.
[15] L. REMAKI, M. CHERIET, “Numerical Schemes of Schock Filter Models for Image Enhancement and Restoration”, Journal of Mathematical Imaging and Vision 18, Vol. 2, 2003, p. 129-143.
[16] L. REMAKI, M. CHERIET, “Kcs-New Kernel Family with Compact Support in Scale Space: Formulation and Impact”, IEEE Transactions on Image Processing, Vol. 9, #6, 2000, p. 970-981.
[17] L. REMAKI, M. CHERIET, “Enhanced and restored signals as a generalized solution for shock filter models. Part I – Existence and uniqueness result of the Cauchy problem”, Journal of Mathematical Analysis and Applications, Vol. 279, #1, 2003, p. 189-209.
[18] H. TALBOT, L. VINCENT, “Euclidean Skeletons and Conditional Bisectors”, Visual Communications and image processing’92, SPIE, Vol. 1818, p. 862-876.
[19] X.G. YOU, Y.Y. TANG, L. SUN, “Skeletonization of Ribbon-like Shapes With New Wavelet Function”, Proc. of the first Inter. Conf. on Machine learning and Cybernetics, Vol. 25, #9, 2003, p. 1118-1133.
[20] Z. YU, C. BAJAJ, “A Segmentation-Free Approach for Skeletonization of Gray-Scale Images via Anisotropic Vectore Diffusion”, Proc. of 2004 IEEE Inter. Conf. on Comp. Vision and Patt. Recognition (CVPR’04),Washington DC, Juin 2004, p. 1063-1069.