An Algorithm to Train Unrestricted Sequential Discrete Morphological Neural Networks

Author(s)

Marcondes, Diego ; Feldman, Mariana ; Barrera, Junior

• Document type: Journal article
• Source: DISCRETE GEOMETRY AND MATHEMATICAL MORPHOLOGY, DGMM 2024; v. 14605, p. 14-pg., 2024-01-01.

Abstract

There have been attempts to insert mathematical morphology (MM) operators into convolutional neural networks (CNN), and the most successful endeavor to date has been the morphological neural networks (MNN). Although MNN have performed better than CNN in solving some problems, they inherit their black-box nature. Furthermore, in the case of binary images, they are approximations that loose the Boolean lattice structure of MM operators and, thus, it is not possible to represent a specific class of W-operators with desired properties. In a recent work, we proposed the Discrete Morphological Neural Networks (DMNN) for binary image transformation to represent specific classes of W-operators and estimate them via machine learning. We also proposed a stochastic lattice descent algorithm (SLDA) to learn the parameters of Canonical Discrete Morphological Neural Networks (CDMNN), whose architecture is composed only of operators that can be decomposed as the supremum, infimum, and complement of erosions and dilations. In this paper, we propose an algorithm to learn unrestricted sequential DMNN, whose architecture is given by the composition of general W-operators. We illustrate the algorithm in a practical example. (AU)

• FAPESP's process: 22/06211-2 - Machine learning via learning spaces, from theory to practice: how the lack of data may be mitigated by high computational power
• Grantee: Diego Ribeiro Marcondes
• Support Opportunities: Scholarships in Brazil - Post-Doctoral
• FAPESP's process: 23/00256-7 - Prior information in neural networks
• Grantee: Diego Ribeiro Marcondes
• Support Opportunities: Scholarships abroad - Research Internship - Post-doctor
• FAPESP's process: 20/06950-4 - Center for Research and Development on Live Knowledge
• Grantee: João Eduardo Ferreira
• Support Opportunities: Research Grants - Problem-Oriented Research Centers in São Paulo
• FAPESP's process: 14/50937-1 - INCT 2014: on the Internet of the Future
• Grantee: Fabio Kon
• Support Opportunities: Research Projects - Thematic Grants