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From 21.03.04 to 26.03.04, the Dagstuhl Seminar 04131 Geometric Properties from Incomplete Data was held in the International Conference and Research Center (IBFI), Schloss Dagstuhl. During the seminar, several participants presented their current research, and ongoing work and open problems were discussed. Abstracts of the presentations given during the seminar as well as abstracts of seminar results and ideas are put together in this paper. The rst section describes the seminar topics andfatcat:nv3fc5navvgrdk3gilv6jq2mai