Abstract
This paper deals with the theory and applications of spatially-variant mathematical morphology. We formalize the definition of spatially variant dilation/erosion and opening/closing for gray-level images using exclusively the structuring function, without resorting to complement. This sound theoretical framework allows to build morphological operators whose structuring elements can locally adapt their orientation across the dominant direction of image structures. The orientation at each pixel is extracted by means of a diffusion process of the average square gradient field, which regularizes and extends the orientation information from the edges of the objects to the homogeneous areas of the image. The proposed filters are used for enhancement of anisotropic images features such as coherent, flow-like structures.
Access provided by Autonomous University of Puebla. Download to read the full chapter text
Chapter PDF
Similar content being viewed by others
Keywords
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
References
Bazen, A.M., Gerez, S.H.: Systematic methods for the computation of the directional fields and singular points of fingerprints. IEEE Trans. Pattern Anal. Mach. Intell. 24(7), 905–919 (2002)
Beucher, S., Blosseville, J.M., Lenoir, F., Motyka, V., Kraft, C.: TITAN, a traffic measurement system using image processing techniques. In: Proceedings IEE Road Traffic Congress (1989)
Bouaynaya, N., Schonfeld, D.: Theoretical foundations of spatially-variant mathematical morphology part II: Gray-level images. IEEE Trans. Pattern Anal. Mach. Intell. 30, 837–850 (2008)
Breuß, M., Burgeth, B., Weickert, J.: Anisotropic continuous-scale morphology. In: Martí, J., Benedí, J.M., Mendonça, A.M., Serrat, J. (eds.) IbPRIA 2007, Part II. LNCS, vol. 4478, pp. 515–522. Springer, Heidelberg (2007)
Cuisenaire, O.: Locally adaptable mathematical morphology using distance transformations. Pattern Recognition 39, 405–416 (2006)
Dokladal, P., Dokladalova, E.: Grey-scale Morphology with Spatially-Variant Rectangles in Linear Time. In: Blanc-Talon, J., Bourennane, S., Philips, W., Popescu, D., Scheunders, P. (eds.) ACIVS 2008. LNCS, vol. 5259, pp. 674–685. Springer, Heidelberg (2008)
Heijmans, H.J.A.M., Ronse, C.: The algebraic basis of mathematical morphology - part I: Dilations and erosions. Computer Vision, Graphics and Image Processing 50, 245–295 (1990)
Heijmans, H.J.A.M.: Morphological Image Operators. Academic Press, Boston (1994)
Heijmans, H., Buckley, M., Talbot, H.: Path openings and closings. Journal of Mathematical Imaging and Vision 22, 107–119 (2005)
Kass, M., Witkin, A.: Analyzing oriented patterns. Comput. Vision Graph. Image Process. 37(3), 362–385 (1987)
Lerallut, R., Decenciére, E., Meyer, F.: Image filtering using morphological amoebas. Image Vision Comput. 25, 395–404 (2007)
Perona, P.: Orientation diffusions. IEEE Trans. Image Processing 7(3), 457–467 (1998)
Roerdink, J.: Group morphology. Pattern Recognition 33, 877–895 (2000)
Ronse, C., Heijmans, H.J.A.M.: The algebraic basis of mathematical morphology - part II: Openings and closings. Computer Vision, Graphics and Image Processing: Image Understanding 54, 74–97 (1991)
Serra, J.: Image Analysis and Mathematical Morphology, vol. I. Academic Press, London (1982)
Serra, J.: Image Analysis and Mathematical Morphology: Theoretical Advances, vol. II. Academic Press, London (1988)
Serra, J., Suliman, M.D.H., Mahmud, M.: Prediction of Scars in Malaysian Forest fires by means of Random Spreads. In: Proc. of Int. ISPRS Conf. on Techniques and Applications of Optical and SAR Imagery fusion (2007)
Soille, P., Talbot, H.: Directional morphological filtering. IEEE Trans. Pattern Anal. Mach. Intell. 23, 1313–1329 (2001)
Soille, P.: Morphological image analysis. Springer, Heidelberg (1999)
Tankyevych, O., Talbot, H., Dokladal, P.: Curvilinear Morpho-Hessian Filter. In: Proceedings of ISBI 2008, pp. 1011–1014 (2008)
Xu, C., Prince, J.L.: Generalized gradient vector flow external forces for active contours. Signal Processing 71(2), 131–139 (1998)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2009 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Verdú-Monedero, R., Angulo, J., Serra, J. (2009). Spatially-Variant Anisotropic Morphological Filters Driven by Gradient Fields. In: Wilkinson, M.H.F., Roerdink, J.B.T.M. (eds) Mathematical Morphology and Its Application to Signal and Image Processing. ISMM 2009. Lecture Notes in Computer Science, vol 5720. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-03613-2_11
Download citation
DOI: https://doi.org/10.1007/978-3-642-03613-2_11
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-03612-5
Online ISBN: 978-3-642-03613-2
eBook Packages: Computer ScienceComputer Science (R0)