Abstract
The mathematical background of MNNs can be found in mathematical morphology (MM). Since MM can be conducted very generally in the complete lattice setting, MNNs are closely related to other lattice-based neurocomputing models.
This paper reviews some important types of feedforward morphological neural networks including their mathematical background. In addition, we analyze and compare the performance of feedforward morphological models and conventional multi-layer perceptrons in some classification problems.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Sussner, P., Grana, M.: Guest Editorial: Special Issue on Morphological Neural Networks. Journal of Mathematical Imaging and Vision 19(2), 79–80 (2003)
Heijmans, H.J.A.M.: Morphological Image Operators. Academic Press, New York (1994)
Serra, J.: Image Analysis and Mathematical Morphology. Academic Press, London (1994)
Banon, G., Barrera, J.: Decomposition of Mappings between Complete Lattices by Mathematical Morphology, Part 1. General Lattices. Signal Processing 30 3, 299–327 (1993)
Sussner, P., Valle, M.E.: Gray Scale Morphological Associative Memories. IEEE Transactions on Neural Networks 17(3), 559–570 (2006)
Sussner, P.: Morphological Perceptron Learning. In: Proceedings of IEEE ISIC/CIRA/ISAS Joint Conference, Gaithersburg, MD, September 1998, pp. 477–482 (1998)
Ritter, G.X., Urcid, G.: Lattice Algebra Approach to Single-Neuron Computation. IEEE Transactions on Neural Networks 14(2), 282–295 (2003)
Araújo, R.A., Madeiro, F., Pessoa, L.F.C.: Modular morphological neural network training via adaptive genetic algorithm for design translation invariant operators. In: Proceedings of the IEEE International Conference on Acoustics, Speech and Signal Processing, Toulouse, France (May 2006)
Pessoa, L.F.C., Maragos, P.: Neural networks with hybrid morphological/rank/linear nodes: a unifying framework with applications to handwritten character recognition. Pattern Recognition 33, 945–960 (2000)
Kaburlasos, V.G., Petridis, V.: Fuzzy lattice neurocomputing (FLN) models. Neural Networks 13, 1145–1170 (2000)
Raducanu, B., Graña, M., Albizuri, X.F.: Morphological Scale Spaces and Associative Morphological Memories: Results on Robustness and Practical Applications. Journal of Mathematical Imaging and Vision 19(2), 113–131 (2003)
Sousa, R.P., Pessoa, L.F.C., Carvalho, J.M.: Designing translation invariant operations via neural network training. In: Proceedings of the IEE International Conference on Image Processing, Vancouver, Canada, pp. 908–911 (2000)
Khabou, M.A., Gader, P.D.: Automatic target detection using entropy optimized shared-weight neural networks. IEEE Transactions on Neural Networks 11(1), 186–193 (2000)
Birkhoff, G.: Lattice Theory, 3rd edn. American Mathematical Society, Providence (1993)
Zadeh, L.A.: Fuzzy Sets. Information and Control 8(3), 338–353 (1965)
Carpenter, G.A., Grossberg, S.: ART 3: Hierarchical search using chemical transmitters in self-organizing pattern recognition architectures. Neural Networks 3, 129–152 (1990)
Valle, M.E., Sussner, P.: A General Framework for Fuzzy Morphological Associative Memories. Fuzzy Sets and Systems 159(7), 747–768 (2007)
Ronse, C.: Why Mathematical Morphology Needs Complete Lattices. Signal Processing 21(2), 129–154 (1990)
Sussner, P., Valle, M.E.: Morphological and Certain Fuzzy Morphological Associative Memories with Applications in Classification and Prediction. In: Kaburlasos, V.G., Ritter, G.X. (eds.) Computational Intelligence Based on Lattice Theory. Studies in Computational Intelligence, vol. 67, pp. 149–173. Springer, Heidelberg (2007)
Blake, C.L., Hettich, S., Newman, D.J., Merz, C.J.: UCI Repository of machine learning databases. University of California, Irvine, Dept. of Information and Computer Sciences (1998), http://www.ics.uci.edu/mlearn/MLRepository.html
Porter, R., Harvey, N., Perkins, S., Theiler, J., Brumby, S., Bloch, J., Gokhale, M., Szymanski, J.: Optimizing digital hardware perceptrons for multispectral image classification. Journal of Mathematical Imaging and Vision 19(2), 133–150 (2003)
Ripley, B.D.: Pattern Recognition and Neural Networks. Cambridge University Press, Cambridge (1996)
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 2008 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Monteiro da Silva, A., Sussner, P. (2008). A Brief Review and Comparison of Feedforward Morphological Neural Networks with Applications to Classification. In: Kůrková, V., Neruda, R., Koutník, J. (eds) Artificial Neural Networks - ICANN 2008. ICANN 2008. Lecture Notes in Computer Science, vol 5164. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-87559-8_81
Download citation
DOI: https://doi.org/10.1007/978-3-540-87559-8_81
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-87558-1
Online ISBN: 978-3-540-87559-8
eBook Packages: Computer ScienceComputer Science (R0)