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Mathematical morphology in graphs: methods and applications in data visualization

Grant number: 14/12815-1
Support Opportunities:Scholarships in Brazil - Post-Doctoral
Effective date (Start): January 01, 2015
Effective date (End): August 31, 2017
Field of knowledge:Physical Sciences and Mathematics - Computer Science - Computing Methodologies and Techniques
Principal Investigator:Afonso Paiva Neto
Grantee:Fábio Augusto Salve Dias
Host Institution: Instituto de Ciências Matemáticas e de Computação (ICMC). Universidade de São Paulo (USP). São Carlos , SP, Brazil
Associated research grant:11/22749-8 - Challenges in exploratory visualization of multidimensional data: paradigms, scalability and applications, AP.TEM
Associated scholarship(s):16/04391-2 - Mathematical morphology operators for the visual analytics of urban data, BE.EP.PD

Abstract

The main objective of this project is the representation, processing and visualization of heterogeneous, multidimensional, information using mathematical morphology. The framework of mathematical morphology provides powerful non-linear operators for signal processing. This framework has been recently extended to digital objects, such as graphs. One of the objectives of this project is to continue the exploration of morphological operators in the graph space, considering applications in visualization and visual data analysis, where large multidimensional graphs play a significant role. To the best of our knowledge, the theory of mathematical morphology was not considered for such applications and we hope this change in semantic context inspire new kinds of operators. We also believe that the solid mathematical framework provided by mathematical morphology will stimulate the development of new methods for visualization and visual data analysis. There are several morphological operators that are suitable to such applications, especially for pre-processing, analysis and comparison of graphs. To the best of our knowledge, albeit the known flexibility of the morphological operators, this approach was not explored in the literature.

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Scientific publications (5)
(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)
SAGRISTA, ANTONI; JORDAN, STEFAN; JUST, ANDREAS; DIAS, FABIO; NONATO, LUIS GUSTAVO; SADLO, FILIP. Topological Analysis of Inertial Dynamics. IEEE TRANSACTIONS ON VISUALIZATION AND COMPUTER GRAPHICS, v. 23, n. 1, p. 950-959, . (13/07375-0, 14/12815-1, 11/22749-8)
DIAS, MARKUS DIEGO; MANSOUR, MOUSSA R.; DIAS, FABIO; PETRONETTO, FABIANO; SILVA, CLAUDIO T.; NONATO, L. GUSTAVO; IEEE. A Hierarchical Network Simplification Via Non-Negative Matrix Factorization. 2017 30TH SIBGRAPI CONFERENCE ON GRAPHICS, PATTERNS AND IMAGES (SIBGRAPI), v. N/A, p. 8-pg., . (14/12815-1, 16/04190-7, 11/22749-8, 13/07375-0, 16/04391-2)
DAL COL, ALCEBIADES; VALDIVIA, PAOLA; PETRONETTO, FABIANO; DIAS, FABIO; SILVA, CLAUDIO T.; GUSTAVO NONATO, L.. Wavelet-Based Visual Analysis of Dynamic Networks. IEEE TRANSACTIONS ON VISUALIZATION AND COMPUTER GRAPHICS, v. 24, n. 8, p. 2456-2469, . (14/12815-1, 13/14089-3, 15/03330-7, 16/04391-2, 11/22749-8)
DIAS, FABIO; MANSOUR, MOUSSA R.; VALDIVIA, PAOLA; COUSTY, JEAN; NAJMAN, LAURENT; ANGULO, J; VELASCOFORERO, S; MEYER, F. Watersheds on Hypergraphs for Data Clustering. MATHEMATICAL MORPHOLOGY AND ITS APPLICATIONS TO SIGNAL AND IMAGE PROCESSING (ISMM 2017), v. 10225, p. 11-pg., . (15/14426-5, 13/14089-3, 16/04391-2, 11/22749-8, 14/12815-1)
DAL COL, ALCEBIADES; VALDIVIA, PAOLA; PETRONETTO, FABIANO; DIAS, FABIO; SILVA, CLAUDIO T.; GUSTAVO NONATO, L.. Wavelet-Based Visual Analysis for Data Exploration. COMPUTING IN SCIENCE & ENGINEERING, v. 19, n. 5, p. 7-pg., . (11/22749-8, 15/03330-7, 16/04391-2, 16/04190-7, 14/12815-1, 13/14089-3)

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