ISMM 2007 Special Issue

1 This paper will be published in a future issue of Image and Vision Computing. 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,