Image and Vision Computing 28 (2010) 1427–1428
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Editorial
ISMM 2007 Special Issue
Mathematical Morphology (MM) was created in the midsixties by a group led by Georges Matheron and Jean Serra of the Paris School of Mines in Fontainebleau, France. By the end of the seventies, its usefulness for image analysis had been recognized in Europe, in particular within the area of microscopic imaging. Starting in the eighties, with the publication in English of Serra’s books on ‘‘Image Analysis and Mathematical Morphology”, MM spread worldwide. In 1993, the MM community organized the first International Symposium on Mathematical Morphology (ISMM), an event that has been held approximately biennially ever since. In Brazil, MM began to be studied at the National Institute for Space Research (INPE), in the mid-eighties, through a technical cooperation program with France. From the beginning, MM was considered a useful alternative to the linear approach to image processing. In 1987, the first master’s thesis devoted to MM and its applications to Remote Sensing was presented at the INPE graduate program. By the early nineties, MM had spread over many universities and research centers all across Brazil. At that time, the first two books on MM ‘‘Bases da morfologia matemática para a análise de imagens binárias” by G. Banon and J. Barrera, and ‘‘Morfologia matemática: Teoria e exemplos” by J. Facon, were published in Brazil, in Portuguese. Since then, MM has been a very active area of research in Brazil. In July 2005, the ISMM steering committee chose Rio de Janeiro, Brazil, among four other candidates, as the site for the 8th ISMM edition, to be held in October 10–13, 2007. The on-line Proceedings of the 8th ISMM were divided in two volumes: Volume 1 containing full papers, and Volume 2 containing extended abstracts [1,2]. The full papers were also published in a printed book [3]. Among the 38 full papers, 11 papers were selected, and their authors invited to submit an extended and improved version. Out of the 11, a total of 6 papers were accepted for inclusion in this special issue. Each submitted article was reviewed by at least two reviewers. The authors thank the reviewers who dedicated their time reading their assigned articles and suggesting valuable recommendations. We would also like to thank the authors for carefully addressing the reviewers’ comments, which contributed to improving the overall quality of the manuscripts. We also thank the Image and Vision Computing editorial board for their support during the preparation of this issue. This special issue contains the following contributions. Related to the theme of Lattice Theory, Kiselman introduces upper and lower inverses of mappings between complete lattices, analyzes their properties and links with Galois connections, and gives a thorough characterization of them, as well as an extension to upper and lower quotient of two mappings. Still in this theme, 0262-8856/$ - see front matter Ó 2010 Published by Elsevier B.V. doi:10.1016/j.imavis.2010.05.007
based on a partial-order relation defined on tree representations of images, which provide a complete inf-semilattice structure, Vichik et al. derive self-dual morphological operators that can be used as filters for noise reduction. Despite the fact that Discrete Geometry is a separate field of research, it has a large intersection with MM whenever one considers the applications of MM to digital image processing. Within this theme, Serra investigates the conditions for generating granulometries on discrete domains using Steiner sets, as well as conditions on these sets for them to be convex or connected. The main application of MM is Image Processing. The contribution in this theme refers to image simplification. Meyer and Angulo introduce the so-called bilevelings of an image defined on a hexagonal grid, prove that they can be characterized in terms of so-called micro-viscous operators that appear to form adjunctions between set of functions defined on vertices and edges, and verify that they lead to higher levels of simplification than with ordinary levelings1. The watershed method represents a powerful paradigm in image segmentation. Ever since its introduction three decades ago, it has attracted the interest of many investigators and practitioners, and research activity in this area continues unabated today. In this last theme on Watershed Segmentation, two contributions establish relationships between several approaches related to image segmentation. Allène et al. study the links that exist between the watershed and minimum cuts, minimum spanning forests, and shortest-path forests. Audigier and Lotufo use the Image Foresting Transform and the Tie-Zone concept to establish the relationship between several discrete watershed transforms. Among the major developments in MM in the last two decades are the interrelated subjects of connectivity classes and connected operators. Connectivity classes, in their general lattice-theoretical formulation, not only unify in a single axiomatic framework useful but disparate notions of connectivity, but also include new interesting definitions of connectivity not previously possible. Connected operators, on the other hand, have become very popular in image analysis applications due to the fact that these operators can preserve edge information by working at the level of the image flat zones, which are defined using connectivity criteria. In this theme, Crespo examines in detail the equivalence between two important classes of connected operators, namely, set levelings and adjacency-stable operators. References [1] Gerald Jean Francis, Banon, Barrera Jr., Ulisses de Mendonça, Braga-Neto, Nina Sumiko Tomita, Hirata, in: International Symposium on Mathematical
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This paper will be published in a future issue of Image and Vision Computing.
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Editorial / Image and Vision Computing 28 (2010) 1427–1428
Morphology, 8 (ISMM): Volume 1 – Full Papers, INPE, São José dos Campos, 2007. ISBN 978-85-17-00035-5. . [2] Gerald Jean Francis, Banon, Barrera Jr., Ulisses de Mendonça, Braga-Neto, Nina Sumiko Tomita, Hirata, in: International Symposium on Mathematical Morphology, 8 (ISMM): Volume 2 – Extended Abstracts, INPE, São José dos Campos, 2007. ISBN 978-85-17-00035-5. . (accessed 15.10.09). [3] Gerald Jean Francis, Banon, Barrera Jr., Ulisses de Mendonça, Braga-Neto, Nina Sumiko Tomita, Hirata, Mathematical Morphology and its Applications to Signal and Image Processing, São José dos Campos: INPE, 2007, xiv + 475 p. ISBN 97885-17-00032-4.
Gerald Banon Divisão de Processamento de Imagens (DPI), Instituto Nacional de Pesquisas Espaciais (INPE), Av. dos Astronautas, 1758, Jd. Granja, 12227-010 São José dos Campos, SP, Brazil E-mail address:
[email protected]
Ulisses Braga-Neto Department of Electrical and Computer Engineering, Texas A&M University, 214 Zachry Engineering Building, College Station, TX 77843-3128, USA E-mail address:
[email protected] Roberto Marcondes Cesar Jr. Computer Vision Research Group, Instituto de Matemática e Estatística (IME), Universidade de São Paulo (USP), R. do Matão, 1010, Butantã, 05508-090 São Paulo, SP, Brazil E-mail address:
[email protected]
