Communications of the ACM
Binary image algebra and optical cellular logic processor design
Computer Vision, Graphics, and Image Processing
Minimal representations for translation-invariant set mappings by mathematical morphology
SIAM Journal on Applied Mathematics
Automatic morphology
Computational learning theory: an introduction
Computational learning theory: an introduction
Decision theoretic generalizations of the PAC model for neural net and other learning applications
Information and Computation
Computational mathematical morphology
Signal Processing - Special issue on mathematical morphology and its applications to signal processing
Finding optimal sequential decompositions of erosions and dilations
ISMM '98 Proceedings of the fourth international symposium on Mathematical morphology and its applications to image and signal processing
Signal Processing
Fundamentals of Artificial Neural Networks
Fundamentals of Artificial Neural Networks
Enhancement and Restoration of Digital Documents: Statistical Design of Nonlinear Algorithms
Enhancement and Restoration of Digital Documents: Statistical Design of Nonlinear Algorithms
Introduction to Switching Theory and Logical Design
Introduction to Switching Theory and Logical Design
Design of Statistically Optimal Stack Filters
SIBGRAPI '99 Proceedings of the XII Brazilian Symposium on Computer Graphics and Image Processing
Design of optimal binary filters under joint multiresolution-envelope constraint
Pattern Recognition Letters - Special issue: Sibgrapi 2001
A genetic programming based system for the automatic construction of image filters
Integrated Computer-Aided Engineering
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An important aspect of mathematical morphology is the description of complete lattice operators by a formal language, the Morphological Language (ML), whose vocabulary is composed of infimum, supremum, dilations, erosions, anti-dilations and anti-erosions. This language is complete (i.e., it can represent any complete lattice operator) and expressive (i.e., many useful operators can be represented as phrases with relatively few words). Since the sixties special machines, the Morphological Machines (MMachs), have been built to implement the ML restricted to the lattices of binary and gray-scale images. However, designing useful MMach programs is not an elementary task. Recently, much research effort has been addressed to automate the programming of MMachs. The goal of the different approaches for this problem is to find suitable knowledge representation formalisms to describe transformations over geometric structures and to translate them automatically into MMach programs by computational systems. We present here the central ideas of an approach based on the representation of transformations by collections of observed-ideal pairs of images and the estimation of suitable operators from these data. In this approach, the estimation of operators is based on statistical optimization or, equivalently, on a branch of Machine Learning Theory known as PAC Learning. These operators are generated as standard form morphological operators that may be simplified (i.e., transformed into equivalent morphological operators that use fewer vocabulary words) by syntactical transformations.