The Community for Technology Leaders
RSS Icon
Issue No.04 - April (2009 vol.31)
pp: 707-720
Nina S. T. Hirata , University of São Paulo, São Paulo
The design of binary morphological operators that are translation-invariant and locally defined by a finite neighborhood window corresponds to the problem of designing Boolean functions. As in any supervised classification problem, morphological operators designed from training sample also suffer from overfitting. Large neighborhood tends to lead to performance degradation of the designed operator. This work proposes a multi-level design approach to deal with the issue of designing large neighborhood based operators. The main idea is inspired from stacked generalization (a multi-level classifier design approach) and consists in, at each training level, combining the outcomes of the previous level operators. The final operator is a multi-level operator that ultimately depends on a larger neighborhood than of the individual operators that have been combined. Experimental results show that two-level operators obtained by combining operators designed on subwindows of a large window consistently outperforms the single-level operators designed on the full window. They also show that iterating two-level operators is an effective multi-level approach to obtain better results.
Morphological, Statistical, Classifier design and evaluation, Simplification of expressions, Concept learning, Machine learning, Pattern Recognition, Image Processing and Computer Vision
Nina S. T. Hirata, "Multilevel Training of Binary Morphological Operators", IEEE Transactions on Pattern Analysis & Machine Intelligence, vol.31, no. 4, pp. 707-720, April 2009, doi:10.1109/TPAMI.2008.118
[1] G. Matheron, Random Sets and Integral Geometry. John Wiley, 1975.
[2] J. Serra, Image Analysis and Mathematical Morphology. Academic Press, 1982.
[3] P. Soille, Morphological Image Analysis, second ed. Springer-Verlag, 2003.
[4] R.M. Haralick, S.R. Sternberg, and X. Zhuang, “Image Analysis Using Mathematical Morphology,” IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 9, no. 4, pp. 532-550, July 1987.
[5] E.R. Dougherty and R.A. Lotufo, Hands-On Morphological Image Processing. SPIE Press, 2003.
[6] I. Tăbuş, D. Petrescu, and M. Gabbouj, “A Training Framework for Stack and Boolean Filtering—Fast Optimal Design Procedures and Robustness Case Study,” IEEE Trans. Image Processing, vol. 5, no. 6, pp. 809-826, June 1996.
[7] N.R. Harvey and S. Marshall, “The Use of Genetic Algorithms in Morphological Filter Design,” Signal Processing: Image Comm., vol. 8, no. 1, pp. 55-71, Jan. 1996.
[8] J. Barrera, E.R. Dougherty, and N.S. Tomita, “Automatic Programming of Binary Morphological Machines by Design of Statistically Optimal Operators in the Context of Computational Learning Theory,” Electronic Imaging, vol. 6, no. 1, pp. 54-67, Jan. 1997.
[9] N.S.T. Hirata, E.R. Dougherty, and J. Barrera, “Iterative Design of Morphological Binary Image Operators,” Optical Eng., vol. 39, no. 12, pp. 3106-3123, Dec. 2000.
[10] R. Hirata Jr., M. Brun, J. Barrera, and E.R. Dougherty, “Multiresolution Design of Aperture Operators,” J. Math. Imaging and Vision, vol. 6, no. 3, pp. 199-222, 2002.
[11] J. Yoo, K.L. Fong, J.-J. Huang, E.J. Coyle, and G.B. Adams III, “A Fast Algorithm for Designing Stack Filters,” IEEE Trans. Image Processing, vol. 8, no. 8, pp. 1014-1028, Aug. 1999.
[12] E.J. Coyle and J.-H. Lin, “Stack Filters and the Mean Absolute Error Criterion,” IEEE Trans. Acoustics, Speech, and Signal Processing, vol. 36, no. 8, pp. 1244-1254, Aug. 1988.
[13] D. Dellamonica Jr., P.J.S. Silva, C. Humes Jr., N.S.T. Hirata, and J. Barrera, “An Exact Algorithm for Optimal MAE Stack Filter Design,” IEEE Trans. Image Processing, vol. 16, no. 2, pp. 453-462, 2007.
[14] I. Yoda, K. Yamamoto, and H. Yamada, “Automatic Acquisition of Hierarchical Mathematical Morphology Procedures by Genetic Algorithms,” Image and Vision Computing, vol. 17, no. 10, pp. 749-760, Aug. 1999.
[15] M.I. Quintana, R. Poli, and E. Claridge, “Morphological Algorithm Design for Binary Images Using Genetic Programming,” Genetic Programming and Evolvable Machines, vol. 7, no. 1, pp. 81-102, 2006.
[16] R. Hirata Jr., E.R. Dougherty, and J. Barrera, “Aperture Filters,” Signal Processing, vol. 80, no. 4, pp. 697-721, Apr. 2000.
[17] P. Salembier, “Structuring Element Adaptation for Morphological Filters,” Visual Comm. and Image Representation, vol. 3, no. 2, pp.115-136, 1992.
[18] G.J.F. Banon and J. Barrera, “Decomposition of Mappings between Complete Lattices by Mathematical Morphology, Part I: General Lattices,” Signal Processing, vol. 30, pp. 299-327, 1993.
[19] H.J.A.M. Heijmans, Morphological Image Operators. Academic Press, 1994.
[20] J. Barrera, R. Terada, R. Hirata Jr., and N.S.T. Hirata, “Automatic Programming of Morphological Machines by PAC Learning,” Fundamenta Informaticae, vol. 41, no. 1-2, pp. 229-258, Jan. 2000.
[21] G.J.F. Banon and J. Barrera, “Minimal Representations for Translation-Invariant Set Mappings by Mathematical Morphology,” SIAM J. Applied Math., vol. 51, no. 6, pp. 1782-1798, Dec. 1991.
[22] 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, July 1996.
[23] T. Hastie, R. Tibshirani, and J. Friedman, The Elements of Statistical Learning. Springer-Verlag, 2001.
[24] T.M. Mitchell, Machine Learning. McGraw-Hill, 1997.
[25] N.S.T. Hirata, J. Barrera, R. Terada, and E.R. Dougherty, “The Incremental Splitting of Intervals Algorithm for the Design of Binary Image Operators,” Proc. Sixth Int'l Symp. Math. Morphology, H.Talbot and R. Beare, eds., pp. 219-228, 2002.
[26] E.R. Dougherty and J. Barrera, “Prior Information in the Design of Optimal Binary Filters,” Proc. Int'l Symp. Math. Morphology, pp.259-266, 1998.
[27] L.I. Kuncheva, Combining Pattern Classifiers: Methods and Algorithms. Wiley, 2004.
[28] D.H. Wolpert, “Stacked Generalization,” Neural Networks, vol. 5, pp. 241-259, 1992.
[29] N.S.T. Hirata, “Binary Image Operator Design Based on Stacked Generalization,” Proc. 18th Brazilian Symp. Computer Graphics and Image Processing, A.C. Frery and M.A.F. Rodrigues, eds., pp. 63-70, 2005.
[30] E.R. Dougherty, “Optimal Mean-Square N-Observation Digital Morphological Filters, I: Optimal Binary Filters,” CVGIP: Image Understanding, vol. 55, no. 1, pp. 36-54, Jan. 1992.
[31] F.J. Hill and G.R. Peterson, Computer Aided Logical Design with Emphasis on VLSI, fourth ed. John Wiley & Sons, 1993.
[32] E.R. Dougherty and J. Barrera, “Logical Image Operators,” Nonlinear Filters for Image Processing, E.R. Dougherty and J.T.Astola, eds., pp. 1-60, SPIE and IEEE Press, 1999.
[33] N.S.T. Hirata, E.R. Dougherty, and J. Barrera, “A Switching Algorithm for Design of Optimal Increasing Binary Filters over Large Windows,” Pattern Recognition, vol. 33, no. 6, pp. 1059-1081, June 2000.
[34] D.C. Martins Jr., R.M. Cesar Jr., and J. Barrera, “W-Operator Window Design by Minimization of Mean Conditional Entropy,” Pattern Analysis and Applications, vol. 9, pp. 139-153, 2006.
[35] A. Jain and D. Zongker, “Feature Selection: Evaluation, Application, and Small Sample Performance,” IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 19, no. 2, pp. 153-158, Feb. 1997.
27 ms
(Ver 2.0)

Marketing Automation Platform Marketing Automation Tool