
This Article  
 
Share  
Bibliographic References  
Add to:  
Digg Furl Spurl Blink Simpy Del.icio.us Y!MyWeb  
Search  
 
ASCII Text  x  
Pierre Soille, Hugues Talbot, "Directional Morphological Filtering," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 23, no. 11, pp. 13131329, November, 2001.  
BibTex  x  
@article{ 10.1109/34.969120, author = {Pierre Soille and Hugues Talbot}, title = {Directional Morphological Filtering}, journal ={IEEE Transactions on Pattern Analysis and Machine Intelligence}, volume = {23}, number = {11}, issn = {01628828}, year = {2001}, pages = {13131329}, doi = {http://doi.ieeecomputersociety.org/10.1109/34.969120}, publisher = {IEEE Computer Society}, address = {Los Alamitos, CA, USA}, }  
RefWorks Procite/RefMan/Endnote  x  
TY  JOUR JO  IEEE Transactions on Pattern Analysis and Machine Intelligence TI  Directional Morphological Filtering IS  11 SN  01628828 SP1313 EP1329 EPD  13131329 A1  Pierre Soille, A1  Hugues Talbot, PY  2001 KW  Image analysis KW  mathematical morphology KW  rank filters KW  directional filters KW  periodic line KW  discrete geometry KW  granulometry KW  orientation field KW  radial decomposition. VL  23 JA  IEEE Transactions on Pattern Analysis and Machine Intelligence ER   
Abstract—We show that a translation invariant implementation of min/max filters along a line segment of slope in the form of an irreducible fraction
[1] A. Dufour and C. Bonnet, “Influence of Unattended Features on the Processing of a Single Line Segment,” Spatial Vision, vol. 9, no. 3, pp. 307324, 1995.
[2] D. Kurylo, A. Reeves, and B. Scharf, “Expectancy of Line Segment Orientation,” Spatial Vision, vol. 10, no. 2, pp. 149162, 1996.
[3] J. Daugman, “Uncertainty Relation for Resolution in Space, Spatial Frequency, and Orientation Optimized by TwoDimensional Visual Cortical Filters,” J. Optical Soc. Am. A, vol. 2, no. 7, pp. 11601169, July 1985.
[4] W.T. Freeman and E.H. Adelson, "The Design and Use of Steerable Filters," IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 13, pp. 891906, 1991.
[5] D. Jeulin and M. Kurdy, “Directional Mathematical Morphology for Oriented Image Restoration and Segmentation,” Acta Stereologica, vol. 11, pp. 545550, 1992.
[6] R. Bamberger and M. Smith, “A Filter Bank for the Directional Decomposition of Images: Theory and Design,” IEEE Trans. Signal Processing, vol. 40, pp. 882893, Apr. 1992.
[7] H. Yamada, K. Yamamoto, and K. Hosokawa, “Directional Mathematical Morphology and Reformalized Hough Transformation for the Analysis of Topographic Maps,” IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 15, no. 4, pp. 380387, Apr. 1993.
[8] E.R. Davies, “Vectorial Strategy for Designing Line Segment Detectors with High Orientation Strategy,” Electronic Letters, vol. 33, no. 21, pp. 17741777, 1997.
[9] P. Soille, E. Breen, and R. Jones, “Recursive Implementation of Erosions and Dilations Along Discrete Lines at Arbitrary Angles,” IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 18, no. 5, pp. 562567, May 1996.
[10] S. Beucher, S. Kozyrev, and D. Gorokhovik, “PréTraitement Morphologique d'Images de Plis Postaux,” Colloque National sur l'Ecrit et le Document, M. Gilloux, ed., pp. 133140, Paris: CNED. 1996.
[11] R. Zwiggelaar and C. Taylor, “Abnormal Masses in Mammograms: Detection Using ScaleOrientation Signatures,” Proc. Medical Image Computing and ComputerAssisted Intervention—MICCAI '98, W. Wells, A. Colchester, and S. Delp, eds., pp. 570577, 1998.
[12] P. Soille and H. Talbot, “Image Structure Orientation Using Mathematical Morphology,” Proc. 14th Int'l Conf. Pattern Recognition, A. Jain, S. Venkatesh, and B. Lovell, eds., vol. 2, pp. 14671469, Aug. 1998.
[13] P. Whelan, P. Soille, and A. Drimbarean, “RealTime Registration of Paper Watermarks,” RealTime Imaging, vol. 7, no. 4, pp. 367380, Aug. 2001.
[14] J. Bresenham, “Algorithm for Computer Control of Digital Plotter,” IBM System J., vol. 4, pp. 2530, 1965.
[15] P. Soille, E. Breen, and R. Jones, “A Fast Algorithm for Min/Max Filters Along Lines of Arbitrary Orientation,” Proc. IEEE Workshop Nonlinear Signal and Image Processing, I. Pitas, ed., pp. 987990, June 1995.
[16] M. van Herk, “A Fast Algorithm for Local Minimum and Maximum Filters on Rectangular and Octogonal Kernels,” Pattern Recognition Letters, vol. 13, pp. 517521, 1992.
[17] J. Gil and M. Werman, “Computing 2D Min, Median, and Max Filters,” IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 15, no. 5, pp. 504507, May 1993.
[18] D. Gevorkian, J. Astola, and S. Atourian, “Improving GilWerman Algorithm for Running Min and Max Filters,” IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 19, no. 5, pp. 526529, May 1997.
[19] P. Soille, “Morphological Image Analysis Applied to Crop Field Mapping,” Image and Vision Computing, vol. 18, no. 13, pp. 10251032, Oct. 2000, see electronic appendix at.
[20] J. Sanchiz, F. Pla, J.A. Marchant, and R. Brivot, “Structure from Motion Techniques Applied to Crop Field Imaging,” Image and Vision Computing, vol. 14, pp. 353363, 1996.
[21] T. Hague, J.A. Marchant, and N. Tillett, “Autonomous Robot Navigation for Precision Horticulture,” Proc. IEEE Int'l Conf. Robotics and Automation, pp. 18801885 Apr. 1997.
[22] J.A. Marchant, R. Tillett, and R. Brivot, “RealTime Segmentation of Plants and Weeds,” RealTime Imaging, vol. 4, pp. 243253, 1998.
[23] G. Garibotto and L. Lambarelli, “Fast OnLine Implementation of Two Dimensional Median Filtering,” Electronic Letters, vol. 15, no. 1, pp. 2425, Jan. 1979.
[24] T. Huang, G. Yang, and G. Tang, “A Fast TwoDimensional Median Filtering Algorithm,” IEEE Trans. Acoustics, Speech, and Signal Processing, vol. 27, no. 1, pp. 1318, Feb. 1979.
[25] P. Soille, “Grey Scale Convex Hulls: Definition, Implementation, and Application,” Mathematical Morphology and Its Applications to Image and Signal Processing, H. Heijmans and J. Roerdink, eds., pp. 8390, Kluwer Academic, 1998.
[26] P. Soille, “From Binary to Grey Scale Convex Hulls,” Fundamenta Informaticae, vol. 41, nos. 12, pp. 131146, Jan. 2000.
[27] P. Soille, Morphological Image Analysis. Berlin, Heidelberg, New York: SpringerVerlag, 1999.
[28] R. Jones and P. Soille, “Periodic Lines: Definition, Cascades, and Application to Granulometries,” Pattern Recognition Letters, vol. 17, no. 10, pp. 10571063, Sept. 1996.
[29] H. Minkowski, “Volumen und Oberfläche,” Mathematische Annalen, vol. 57, pp. 447495, 1903.
[30] G. Matheron, Random Sets and Integral Geometry. New York: Wiley, 1975.
[31] B. Chaudhuri, “An Efficient algorithm for Running Window Pel Grey Level Ranking in 2D Images,” Pattern Recognition Letters, vol. 11, no. 2, pp. 7780, 1990.
[32] M. Van Droogenbroeck and H. Talbot, “Fast Computation of Morphological Operations with Arbitrary Structuring Elements,” Pattern Recognition Letters, vol. 17, no. 14, pp. 14511460, 1996.
[33] G. Heygster, “Rank Filters in Digital Image Processing,” Computer Graphics and Image Processing, vol. 19, no. 2, pp. 148164, June 1982.
[34] J. Serra, “Introduction to Morphological Filters,” Image Analysis and Mathematical Morphology. Vol 2: Theoretical Advances, J. Serra, ed., ch. 5, pp. 101114. Academic Press, 1988.
[35] J. Serra and L. Vincent, “An Overview of Morphological Filtering,” Circuits Systems Signal Process, vol. 11, no. 1, pp. 47108, 1992.
[36] C. Ronse, “Erosion of Narrow Image Features by Combination of Local Low Rank and Max Filters,” Proc. Second IEE Int'l Conf. Image Processing and Its Applications, pp. 7781, 1986.
[37] C. Ronse and H. Heijmans, “The Algebraic Basis of Mathematical Morphology: II. Openings and Closings,” Computer Vision, Graphics, and Image Processing: Image Understanding, vol. 54, no. 1, pp. 7497, 1991.
[38] H. Heijmans, “Morphological Image Operators,” Advances in Electronics and Electron Physics, Boston: Academic Press, 1994.
[39] S. Wilson, “Vector Morphology and Iconic Neural Networks,” IEEE Trans. Systems, Man, and Cybernetics, vol. 19, no. 6, pp. 16361644, 1989.
[40] P. Soille, “On Morphological Operators Based on Rank Filters,” Pattern Recognition, pending publication.
[41] P. Whelan and P. Soille, “Watermark Extraction in Paper Samples,” Proc. Optical Eng. Soc. Ireland and Irish Machine Vision and Image Processing Joint Conf., D. Vernon, ed., pp. 287299, Sept. 1998.
[42] A. Drimbarean, P. Soille, and P. Whelan, “Online Registration of Watermarks from Continuous Web Paper,” Proc. Irish Machine Vision and Image Processing Conf., P. Whelan, ed., pp. 267279, 1999.
[43] E. Isaac and R. Singleton, “Sorting by Address Calculation,” J. ACM, vol. 3, pp. 169174, 1956.
[44] D. Saupe, “Algorithms for Random Fractals,” The Science of Fractal Images, H. Peitgen and D. Saupe, eds., ch. 2, New York: SpringerVerlag, 1988.
[45] J. Farey, “On a Curious Property of Vulgar Fractions,” Philosophical Magazine, 1816, seehttp://ams.egeo.sai.jrc.it/soille/ivc2000http:/ /cuttheknot.com/blueFareyHistory.html for a historical note and a copy of Farey's original letter.
[46] G. Matheron, Eléments pour une Théorie des Milieux Poreux. Paris: Masson, 1967.
[47] J. Serra, Image Analysis and Mathematical Morphology. London: Academic Press, 1982.
[48] P. Maragos, "Pattern Spectrum and Multiscale Shape Representation," IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 11, pp. 701716, 1989.
[49] M. Werman and S. Peleg, “MinMax Operators in Texture Analysis,” IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 7, no. 6, pp. 730733, Nov. 1985.
[50] M. Donahue and S. Rokhlin, “On the Use of Level Curves in Image Analysis,” Computer Vision, Graphics, and Image Processing: Image Understanding, vol. 57, no. 2, pp. 185203, Mar. 1993.
[51] R. Cappelli, A. Lumini, D. Maio, and D. Maltoni, “Fingerprint Classification by Directional Image Partitioning,” IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 21, no. 5, pp. 402421, May 1999.
[52] R. van den Boomgaard and R. van Balen, “Methods for Fast Morphological Image Transforms Using Bitmapped Binary Images,” Computer Vision, Graphics, and Image Processing: Graphical Models and Image Processing, vol. 54, no. 3, pp. 252258, May 1992.
[53] R. Adams, “Radial Decomposition of Discs and Spheres,” Computer Vision, Graphics, and Image Processing: Graphical Models and Image Processing, vol. 55, no. 5, pp. 325332, Sept. 1993.
[54] J.F. Rivest, J. Serra, and P. Soille, “Dimensionality in Image Analysis,” J. Visual Comm. and Image Representation, vol. 3, no. 2, pp. 137146, 1992.
[55] P. Soille and J.F. Rivest, “Dimensionality of Morphological Operators and Cluster Analysis,” Image Algebra and Morphological Image Processing IV, E. Dougherty, P. Gader, and J. Serra, eds., pp. 4353 July 1993.
[56] S. Sternberg, “Grayscale Morphology,” Computer Graphics and Image Processing, vol. 35, pp. 333355, 1986.
[57] P. Soille and R. Jones, “Periodic Lines: Fast Implementation and Extensions to Greyscale Structuring Elements and 3D Images,” technical report, Fraunhofer IPK (Berlin)/CSIRO DMS (Sydney), 1995.
[58] P. Soille, “Morphological Operators with Discrete Line Segments,” Proc. Discrete Geometry for Computer Imagery 2000, G. Borgefors, I. Nyström, and G. Sanniti di Baja, eds., pp. 7898, 2000.
[59] K. Sivakumar, M. Patel, N. Ketharnavaz, Y. Balagurunathan, and E. Dougherty, “A ConstantTime Algorithm for Erosions/Dilations with Applications to Morphological Texture Feature Computation,” RealTime Imaging, vol. 6, pp. 223239, 2000.
[60] R. Jones and P. Soille, “Periodic Lines and Their Applications to Granulometries,” Math. Morphology and Its Applications to Image and Signal Processing, P. Maragos, W. Schafer, and M. Butt, eds., pp. 264272, Kluwer Academic, 1996.