[en] Several efficient algorithms for computing erosions and openings have been proposed recently.
They improve on VAN HERK's algorithm in terms of number of comparisons for large structuring
elements. In this paper we introduce a theoretical framework of anchors that aims at a better
understanding of the process involved in the computation of erosions and openings. It is shown
that the knowledge of opening anchors of a signal f is sufficient to perform both the erosion and
the opening of f.
Then we propose an algorithm for one-dimensional erosions and openings which exploits
opening anchors. This algorithm improves on the fastest algorithms available in literature by
approximately 30% in terms of computation speed, for a range of structuring element sizes and
image contents
Disciplines :
Ingénierie électrique & électronique
Auteur, co-auteur :
Van Droogenbroeck, Marc ; Université de Liège - ULiège > Dép. d'électric., électron. et informat. (Inst.Montefiore) > Télécommunications
Buckley, Michael
Langue du document :
Anglais
Titre :
Morphological erosions and openings: fast algorithms based on anchors
G. Arce and N. Gallagher, "State description for the root-signal set of median filters," IEEE Transactions on Acoustics, Speech and Signal Processing, Vol. 30, No. 6, pp. 894-902, 1982.
G. Arce and M. McLoughlin, "Theoretical analysis of the max/median filter," IEEE Transactions on Acoustics, Speech and Signal Processing, Vol. 35, No. 1, pp. 60-69, 1987.
J. Astola, P. Heinonen, and Y. Neuvo, "On root structures of median and median-type filters," IEEE Transactions on Acoustics, Speech and Signal Processing, Vol. 35, No. 8, pp. 1199-1201, 1987.
J. Barrera and G.P. Salas, "Set operations on closed intervals and their applications to the automatic programming of morphological machines," Electronic Imaging, Vol. 5, No. 3, pp. 335-352, 1996.
S. Beucher and C. Lantuéjoul, "Use of watersheds in contour detection," in International Workshop on Image Processing, Rennes, CCETT/IRISA, Sept. 1979, pp. 2.1-2.12.
E.J. Breen and R. Jones, "Attribute openings, thinnings, and granulometries," Computer Vision and Image Understanding, Vol. 64, No. 3, pp. 377-389, 1996.
M. Brookes, "Algorithms for max and min niters with improved worst-case performance," IEEE Transactions on Circuits and Systems II: Analog and Digital Signal Processing, Vol. 47, No. 9, pp. 930-935, 2000.
B. Chaudhuri, "An efficient algorithm for running window pel gray level ranking in 2-D images," Pattern Recognition Letters, Vol. 11, No. 2, pp. 77-80, 1990.
D. Coltuc and I. Pitas, "On fast running max-min filtering," IEEE Transactions on Circuits and Systems II: Analog and Digital Signal Processing, Vol. 44, No. 8, pp. 660-663, 1997.
S. Douglas, "Running max/min calculation using a pruned ordered list," IEEE Transactions on Signal Processing, Vol. 44, No. 11, pp. 2872-2877, 1996.
D. Eberly, H. Longbotham, and J. Aragon, "Complete classification of roots to one-dimensional median and rank-order filters," IEEE Transactions on Acoustics, Speech and Signal Processing, Vol. 39, No. 1, pp. 197-200, 1991.
U. Eckhardt, "Root images of median filters," Journal of Mathematical Imaging and Vision, Vol. 19, No. 1, pp. 63-70, 2003.
J. Fitch, E. Coyle, and N. Gallagher, "Threshold decomposition of multidimensional ranked order operations," IEEE Transactions on Circuits and Systems, Vol. 32, pp. 445-450, 1985.
N. Gallagher and G. Wise, "A theoretical analysis of the properties of median filters," IEEE Transactions on Acoustics, Speech and Signal Processing, Vol. 29, No. 6, pp. 1136-1141, 1981.
D. Gevorkian, J. Astola, and S. Atourian, "Improving Gil-Werman algorithm for running min and max filters," IEEE Transactions on Pattern Analysis and Machine Intelligence, Vol. 19, No. 5, pp. 526-529, 1997.
J. Gil and R. Kimmel, "Efficient dilation, erosion, opening and closing algorithms," in Mathematical Morphology and its Applications to Image and Signal Processing V, J. Goutsias, L. Vincent, and D. Bloomberg (Eds.), Palo-Alto, USA, Kluwer Academic Publishers, June 2000, pp. 301-310.
J. Gil and R. Kimmel, "Efficient dilation, erosion, opening, and closing algorithms," IEEE Transactions on Pattern Analysis and Machine Intelligence, Vol. 24, No. 12, pp. 1606-1617, 2002.
J. Gil and M. Werman, "Computing 2-D min, median, and max filters," IEEE Transactions on Pattern Analysis and Machine Intelligence, Vol. 15, No. 5, pp. 504-507, 1993.
R. Haralick, S. Sternberg, and X. Zhuang, "Image analysis using mathematical morphology," IEEE Transactions on Pattern Analysis and Machine Intelligence, Vol. 9, No. 4, pp. 532-550, 1987.
H. Heijmans, Morphological Image Operators, Advances in Electronics and Electron Physics, Academic Press, 1994.
H. Heijmans and C. Ronse, "The algebraic basis of mathematical morphology: I. Dilations and erosions," Computer Vision, Graphics, and Image Processing, Vol. 50, pp. 245-295, 1990.
T. Huang, G. Yang, and G. Tang, "A fast two-dimensional median filtering algorithm," IEEE Transactions on Acoustics, Speech and Signal Processing, Vol. 27, No. 1, pp. 13-18, 1979.
P. Maragos, "Pattern spectrum and multiscale shape representation," IEEE Transactions on Pattern Analysis and Machine Intelligence, Vol. 11, No. 7, pp. 701-716, 1989.
P. Maragos and R. Schafer, "Morphological filters - Part II: Their relations to median, order-statistic, and stack filters," IEEE Transactions on Acoustics, Speech, and Signal Processing, Vol. 35, No. 8, pp. 1170-1184, 1987.
G. Matheron, Random Sets and Integral Geometry, Wiley: New York, 1975.
T. Miyatake, M. Ejiri, and H. Matsushima, "A fast algorithm for maximum-minimum image filtering," Systems and Computers in Japan, Vol. 27, No. 13, pp. 74-85, 1996.
J. Pecht, "Speeding up successive Minkowski operations," Pattern Recognition Letters, Vol. 3, No. 2, pp. 113-117, 1985.
I. Pitas, "Fast algorithms for running ordering and max/min calculations," IEEE Transactions on Circuits and Systems, Vol. 36, No. 6, pp. 795-804, 1989.
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. 74-97, 1991.
C. Ronse and H. Heijmans, "A lattice-theoretical framework for annular filters in morphological image processing," Applicable Analysis in Engineering, Communication, and Computing, Vol. 9, No. 1, pp. 45-89, 1998.
P. Salembier and J. Serra, "Flat zones filtering, connected operators, and filters by reconstruction," IEEE Transactions on Image Processing, Vol. 4, No. 8, pp. 1153-1160, 1995.
J. Serra, Image Analysis and Mathematical Morphology, Academic Press: London, 1982.
P. Soille and H. Talbot, "Directional morphological filtering," IEEE Transactions on Pattern Analysis and Machine Intelligence, Vol. 23, No. 11, pp. 1313-1329, 2001.
R. van den Boomgaard, "Mathematical morphology: Extensions towards computer vision," Ph.D. thesis, Amsterdam University, March 1992.
M. Van Droogenbroeck, "Traitement d'images numériques au moyen d'algorithmes utilisant la morphologie mathématique et la notion d'objet : application au codage," Ph.D. thesis, Catholic University of Louvain, May 1994.
M. Van Droogenbroeck, "On the implementation of morphological operations," in Mathematical Morphology and its Applications to Image Processing, J. Serra and P. Soille (Eds.), Kluwer Academic Publishers: Dordrecht, 1994, pp. 241-248.
M. van Droogenbroeck and H. Talbot, "Fast computation of morphological operations with arbitrary structuring elements," Pattern Recognition Letters, Vol. 17, No. 14, pp. 1451-1460, 1996.
M. van Herk, "A fast algorithm for local minimum and maximum filters on rectangular and octogonal kernels," Pattern Recognition Letters, Vol. 13, No. 7, pp. 517-521, 1992.
L. Vincent, "Morphological area openings and closings for grayscale images," in Proc. Shape in Picture '92, NATO Workshop, Driebergen, The Netherlands, Springer-Verlag, Sept. 1992.
L. Vincent, "Granulometries and opening trees," Fundamenta Informaticae, Vol. 41, No. 1-2, pp. 57-90, 2000.
L. Vincent and P. Soille, "Watersheds in digital spaces: an efficient algorithm based on immersion simulations," IEEE Transactions on Pattern Analysis and Machine Intelligence, Vol. 13, No. 6, pp. 583-598, 1991.
