Multilayer feedforward networks are universal approximators
Neural Networks
Optimal mean-square N-observation digital morphological filters: i. optimal binary filters
CVGIP: Image Understanding
Signal Processing
Multiresolution Analysis for Optimal Binary Filters
Journal of Mathematical Imaging and Vision
Translation Invariant Transformations of Discrete Random Sets
SIBGRAPHI '98 Proceedings of the International Symposium on Computer Graphics, Image Processing, and Vision
Morphological algorithm design for binary images using genetic programming
Genetic Programming and Evolvable Machines
Advances in Nonlinear Signal and Image Processing
Advances in Nonlinear Signal and Image Processing
Multilevel Training of Binary Morphological Operators
IEEE Transactions on Pattern Analysis and Machine Intelligence
Learning of Neural Networks Based on Weighted Mean Squares Error Function
ISCID '09 Proceedings of the 2009 Second International Symposium on Computational Intelligence and Design - Volume 01
An Information Theory framework for two-stage binary image operator design
Pattern Recognition Letters
Structuring element adaptation for morphological filters
Journal of Visual Communication and Image Representation
Morphological grayscale reconstruction in image analysis: applications and efficient algorithms
IEEE Transactions on Image Processing
Training feedforward networks with the Marquardt algorithm
IEEE Transactions on Neural Networks
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The design of binary W-operators, morphological operators that are translation-invariant and locally defined by a finite neighborhood window, corresponds to the problem of designing Boolean functions, or their characteristic functions. One of the main issues regarding the automatic design of W-operators, based on samples, is the one of generalization. Considering the designing of W-operators as a particular case of designing a pattern recognition system, in this paper we propose a new approach for the automatic design of binary W-operators. The approach consists on a functional representation of the class membership conditional probability for the whole set of patterns viewed through a given window, instead of generalizing the class labels (or the characteristic function values). The estimation of parameters for the functional representation uses a nonlinear regression performed by an artificial feed-forward neural network. The network training is based on the weighted mean square error cost function, allowing us to use the marginal probability of each pattern viewed by a given window. Experimental results, consisting on noise filtering in images of retinal angiographies, edge detection in noise images, texture identification and character recognition, show that the proposed approach outperforms not only pyramidal multiresolution, the best existing method for generalization of characteristic functions of W-operators, but also classical classifiers based on support vector machines, k-nearest neighbor and convolutional neural networks.