Mathematical Morphology and Morphological Neural Networks for Multivalued Data

• Grant number: 19/02278-2
• Support Opportunities: Regular Research Grants
• Start date: May 01, 2019
• End date: April 30, 2021
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Applied Mathematics
• Principal Investigator: Marcos Eduardo Ribeiro Do Valle Mesquita
• Grantee: Marcos Eduardo Ribeiro Do Valle Mesquita
• Host Institution: Instituto de Matemática, Estatística e Computação Científica (IMECC). Universidade Estadual de Campinas (UNICAMP). Campinas , SP, Brazil

Abstract

Mathematical morphology is a nonlinear theory with applications in image processing and analysis. A neural network whose neurons perform elementary operations of mathematical morphology is called a morphological neural network. Such as traditional neural networks, morphological neural networks can be used for classification and regression.In this research project, we aim to contribute by developing morphological operators for multi-valued images. Particular attention will be given to morphological operators obtained using a supervised reduced order. We will also address the uncertainties that arise in natural images as well as the vagueness in describing the values of a multi-valued image.As a straightforward application of the results obtained for multi-valued mathematical morphology, we intend to develop morphological neural networks for multi-valued data. Neural networks for multi-valued data represent an active research topic and include, for example, hypercomplex neural networks and capsule networks. In particular, we plan to investigate complete lattice projection autoassociative memories which, besides the low computational cost and theoretical simplicity, presented promising results in face recognition problems. (AU)

Scientific publications

(10)

(References retrieved automatically from Web of Science and SciELO through information on FAPESP grants and their corresponding numbers as mentioned in the publications by the authors)

VIEIRA, GUILHERME; VALLE, MARCOS EDUARDO; IEEE. Extreme Learning Machines on Cayley-Dickson Algebra Applied for Color Image Auto-Encoding. 2020 INTERNATIONAL JOINT CONFERENCE ON NEURAL NETWORKS (IJCNN), v. N/A, p. 8-pg., 2020-01-01. (19/02278-2)

VALLE, MARCOS EDUARDO. Reduced Dilation-Erosion Perceptron for Binary Classification. MATHEMATICS, v. 8, n. 4, APR 2020. (19/02278-2)

SANGALLI, MATEUS; VALLE, MARCOS EDUARDO; BURGETH, B; KLEEFELD, A; NAEGEL, B; PASSAT, N; PERRET, B. Approaches to Multivalued Mathematical Morphology Based on Uncertain Reduced Orderings. MATHEMATICAL MORPHOLOGY AND ITS APPLICATIONS TO SIGNAL AND IMAGE PROCESSING, ISMM 2019, v. 11564, p. 13-pg., 2019-01-01. (19/02278-2)

DO NASCIMENTO, ARLYSON ALVES; VALLE, MARCOS EDUARDO; BURGETH, B; KLEEFELD, A; NAEGEL, B; PASSAT, N; PERRET, B. Characterization and Statistics of Distance-Based Elementary Morphological Operators. MATHEMATICAL MORPHOLOGY AND ITS APPLICATIONS TO SIGNAL AND IMAGE PROCESSING, ISMM 2019, v. 11564, p. 13-pg., 2019-01-01. (19/02278-2)

GARIMELLA, RAMA MURTHY; VALLE, MARCOS EDUARDO; VIEIRA, GUILHERME; RAYALA, ANIL; MUNUGOTI, DILEEP. Vector-Valued Hopfield Neural Networks and Distributed Synapse Based Convolutional and Linear Time-Variant Associative Memories. NEURAL PROCESSING LETTERS, v. N/A, p. 20-pg., 2022-09-23. (19/02278-2)

VALLE, MARCOS EDUARDO; LOBO, RODOLFO ANIBAL. Quaternion-valued recurrent projection neural networks on unit quaternions. THEORETICAL COMPUTER SCIENCE, v. 843, p. 17-pg., 2020-12-02. (19/02278-2)

VALLE, MARCOS EDUARDO; FRANCISCO, SAMUEL; GRANERO, MARCO AURELIO; VELASCO-FORERO, SANTIAGO. Irregularity Index for Vector-Valued Morphological Operators. Journal of Mathematical Imaging and Vision, v. N/A, p. 17-pg., 2022-04-27. (19/02278-2)

VALLE, MARCOS EDUARDO; LOBO, RODOLFO ANIBAL. Hypercomplex-valued recurrent correlation neural networks. Neurocomputing, v. 432, p. 111-123, APR 7 2021. (19/02278-2)

DE CASTRO, FIDELIS ZANETTI; VALLE, MARCOS EDUARDO. A broad class of discrete-time hypercomplex-valued Hopfield neural networks. NEURAL NETWORKS, v. 122, p. 54-67, FEB 2020. (19/02278-2)

VIEIRA, GUILHERME; VALLE, MARCOS EDUARDO; IEEE. Acute Lymphoblastic Leukemia Detection Using Hypercomplex-Valued Convolutional Neural Networks. 2022 INTERNATIONAL JOINT CONFERENCE ON NEURAL NETWORKS (IJCNN), v. N/A, p. 8-pg., 2022-01-01. (19/02278-2)