3 research outputs found
Discrete Morphological Neural Networks
A classical approach to designing binary image operators is Mathematical
Morphology (MM). We propose the Discrete Morphological Neural Networks (DMNN)
for binary image analysis to represent W-operators and estimate them via
machine learning. A DMNN architecture, which is represented by a Morphological
Computational Graph, is designed as in the classical heuristic design of
morphological operators, in which the designer should combine a set of MM
operators and Boolean operations based on prior information and theoretical
knowledge. Then, once the architecture is fixed, instead of adjusting its
parameters (i.e., structural elements or maximal intervals) by hand, we propose
a lattice gradient descent algorithm (LGDA) to train these parameters based on
a sample of input and output images under the usual machine learning approach.
We also propose a stochastic version of the LGDA that is more efficient, is
scalable and can obtain small error in practical problems. The class
represented by a DMNN can be quite general or specialized according to expected
properties of the target operator, i.e., prior information, and the semantic
expressed by algebraic properties of classes of operators is a differential
relative to other methods. The main contribution of this paper is the merger of
the two main paradigms for designing morphological operators: classical
heuristic design and automatic design via machine learning. Thus, conciliating
classical heuristic morphological operator design with machine learning. We
apply the DMNN to recognize the boundary of digits with noise, and we discuss
many topics for future research