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Issue No.10 - October (2008 vol.30)
pp: 1800-1813
Morphological attribute filters have not previously been parallelized, mainly because they are both global and non-separable. We propose a parallel algorithm which achieves efficient parallelism for a large class of attribute filters, including attribute openings, closings, thinnings and thickenings, based on Salembier's Max-Trees and Min-trees. The image or volume is first partitioned in multiple slices. We then compute the Max-trees of each slice using any sequential Max-Tree algorithm. Subsequently, the Max-trees of the slices can be merged to obtain the Max-tree of the image. A C-implementation yielded good speed-ups on both a 16-processor MIPS 14000 parallel machine, and a dual-core Opteron-based machine. It is shown that the speed-up of the parallel algorithm is a direct measure of the gain with respect to the sequential algorithm used. Furthermore, the concurrent algorithm shows a speed gain of up to 72% on a single-core processor, due to reduced cache thrashing.
Filtering, Enhancement Parallel algorithms, mathematical morphology, connected filters
Michael H.F. Wilkinson, Hui Gao, Wim H. Hesselink, Jan-Eppo Jonker, Arnold Meijster, "Concurrent Computation of Attribute Filters on Shared Memory Parallel Machines", IEEE Transactions on Pattern Analysis & Machine Intelligence, vol.30, no. 10, pp. 1800-1813, October 2008, doi:10.1109/TPAMI.2007.70836
[1] F.J. Seinstra, D. Koelma, and J.M. Geusebroek, “A Software Architecture for User Transparent Parallel Image Processings,” Parallel Computing, vol. 28, pp. 967-993, 2002.
[2] T. Hirata, “A Unified Linear-Time Algorithm for Computing Distance Maps,” Information Processing Letters, vol. 58, pp. 129-133, 1996.
[3] A. Meijster, J.B.T.M. Roerdink, and W.H. Hesselink, “A General Algorithm for Computing Distance Transforms in Linear Time,” Proc. Int'l Symp. Math. Morphology (ISMM '00), pp. 331-340, June 2000.
[4] P. Salembier and J. Serra, “Flat Zones Filtering, Connected Operators, and Filters by Reconstruction,” IEEE Trans. Image Processing, vol. 4, pp. 1153-1160, 1995.
[5] E.J. Breen and R. Jones, “Attribute Openings, Thinnings and Granulometries,” Computer Visualization and Image Understanding, vol. 64, no. 3, pp. 377-389, 1996.
[6] H.J.A.M. Heijmans, “Connected Morphological Operators for Binary Images,” Computer Visualization and Image Understanding, vol. 73, pp. 99-120, 1999.
[7] J.C. Klein, “Conception et Réalisation d'une Unité Logique Pour l'analyse Quantitative d'images,” PhD dissertation, Nancy Univ., 1976.
[8] L. Vincent, “Morphological Grayscale Reconstruction in Image Analysis: Application and Efficient Algorithm,” IEEE Trans. Image Processing, vol. 2, pp. 176-201, 1993.
[9] F. Cheng and A.N. Venetsanopoulos, “An Adaptive Morphological Filter for Image Processing,” IEEE Trans. Image Processing, vol. 1, pp. 533-539, 1992.
[10] L. Vincent, “Morphological Area Openings and Closings for Grey-Scale Images,” Proc. NATO Shape in Picture Workshop: Math. Description of Shape in Grey-Level Images, Y.-L. O, A. Toet, D. Foster, H.J.A.M. Heijmans, and P. Meer, eds., pp. 197-208, 1993.
[11] P. Salembier, A. Oliveras, and L. Garrido, “Anti-Extensive Connected Operators for Image and Sequence Processing,” IEEE Trans. Image Processing, vol. 7, pp. 555-570, 1998.
[12] E.R. Urbach and M.H.F. Wilkinson, “Shape-Only Granulometries and Grey-Scale Shape Filters,” Proc. Int'l Symp. Math. Morphology (ISMM '02), pp. 305-314, 2002.
[13] E.R. Urbach, J.B.T.M. Roerdink, and M.H.F. Wilkinson, “Connected Shape-Size Pattern Spectra for Rotation and Scale-Invariant Classification of Gray-Scale Images,” IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 29, pp. 272-285, 2007.
[14] M.H.F. Wilkinson and M.A. Westenberg, “Shape Preserving Filament Enhancement Filtering,” Proc. Medical Image Computing and Computer-Assisted Intervention (MICCAI '01), W.J. Niessen and M.A. Viergever, eds., pp. 770-777, 2001.
[15] A. Meijster and M.H.F. Wilkinson, “A Comparison of Algorithms for Connected Set Openings and Closings,” IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 24, no. 4, pp. 484-494, Apr. 2002.
[16] R.E. Tarjan, “Efficiency of a Good But Not Linear Set Union Algorithm,” J. ACM, vol. 22, pp. 215-225, 1975.
[17] R. Jones, “Connected Filtering and Segmentation Using Component Trees,” Computer Visualization and Image Understanding, vol. 75, pp. 215-228, 1999.
[18] L. Najman and M. Couprie, “Building the Component Tree in Quasi-Linear Time,” IEEE Trans. Image Processing, vol. 15, pp.3531-3539, 2006.
[19] S. Morse, “Concepts of Use in Computer Map Processing,” Comm. ACM, vol. 12, pp. 147-152, 1969.
[20] J. Roubal and T.K. Peucker, “Automated Contour Labeling and the Contour Tree,” Proc. Int'l Symp. Computer-Assisted Cartography (AUTOCARTO '85), pp. 472-481, 1985.
[21] M. van Kreveld, R. van Oostrum, C. Bajaj, V. Pascucci, and D. Schikore, “Contour Trees and Small Seed Sets for Iso-Surface Traversal,” Proc. 13th Ann. Symp. Computational Geometry, pp. 212-220, 1997.
[22] H. Carr, J. Snoeyink, and U. Axen, “Computing Contour Trees in All Dimensions,” Computational Geometry, vol. 24, pp. 75-94, 2003.
[23] V. Pascucci and K. Cole-McLaughlin, “Efficient Computation of the Topology of Level Sets,” Proc. IEEE Visualization, pp. 187-194, 2002.
[24] P. Monasse and F. Guichard, “Fast Computation of a Contrast Invariant Image Representation,” IEEE Trans. Image Processing, vol. 9, pp. 860-872, 2000.
[25] G. Bertrand, “On Topological Watersheds,” J. Math. Imaging and Vision, vol. 22, pp. 217-230, 2005.
[26] M. Couprie, L. Najman, and G. Bertrand, “Quasi-Linear Algorithms for the Topological Watershed,” J. Math. Imaging and Vision, vol. 22, pp. 231-249, 2005.
[27] U. Braga-Neto and J. Goutsias, “A Theoretical Tour of Connectivity in Image Processing and Analysis,” J. Math. Imaging and Vision, vol. 19, pp. 5-31, 2003.
[28] J. Serra, “Connectivity on Complete Lattices,” J. Math. Imaging and Vision, vol. 9, pp. 231-251, 1998.
[29] P. Maragos and R.D. Ziff, “Threshold Decomposition in Morphological Image Analysis,” IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 12, no. 5, pp. 498-504, May 1990.
[30] W.H. Hesselink, A. Meijster, and C. Bron, “Concurrent Determination of Connected Components,” Science of Computer Programming, vol. 41, pp. 173-194, 2001.
[31] C. Berger, T. Geraud, R. Levillain, N. Widynski, A. Baillard, and E. Bertin, “Effective Component Tree Computation with Application to Pattern Recognition in Astronomical Imaging,” Proc. Int'l Conf. Image Processing, Sept. 2007.
[32] C. Fiorio and J. Gustedt, “Two Linear Time Union-Find Strategies for Image Processing,” Theoretical Computer Science (A), vol. 154, pp. 165-181, 1996.
[33] B.A. Galler and M.J. Fischer, “An Improved Equivalence Algorithm,” Comm. ACM, vol. 7, pp. 301-303, 1964.
[34] S. Owicki and D. Gries, “An Axiomatic Proof Technique for Parallel Programs,” Acta Informatica, vol. 6, pp. 319-340, 1976.
[35] W.H. Hesselink, “Salembier's Min-Tree Algorithm Turned into Breadth First Search,” Information Processing Letters, vol. 88, no. 5, pp. 225-229, 2003.
[36] M.K. Hu, “Visual Pattern Recognition by Moment Invariants,” IRE Trans. Information Theory, vol. 8, pp. 179-187, 1962.
[37] A. Kanitsar, T. Theussl, L. Mroz, M. Sramek, A.V. Bartoli, B. Csebfalvi, J. Hladuvka, D. Fleischmann, M. Knapp, R. Wegenkittl, P. Felkel, S. Roettger, W.P. Stefan Guthe, and M.E. Groeller, “Christmas Tree Case Study: Computed Tomography as a Tool for Mastering Complex Real World Objects with Applications in Computer Graphics,” Proc. Visualization, pp. 489-492, 2002.
[38] G.K. Ouzounis and M.H.F. Wilkinson, “Mask-Based Second Generation Connectivity and Attribute Filters,” IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 29, pp. 990-1004, 2007.
[39] G.K. Ouzounis and M.H.F. Wilkinson, “A Parallel Dual-Input Max-Tree Algorithm for Shared Memory Machines,” Proc. Int'l Symp. Math. Morphology (ISMM '07), pp. 449-460, 2007.
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