DGCI'2006 
13th International Conference onDiscrete Geometry for Computer Imagery October 2527, 2006



Invited SpeakersDuality and Geometry Straightness, Characterization and Envelope Duality applied to geometrical problems is widely used in many applications in computer vision or computational geometry. A classical example is the Hough Transform to detect linear structures in images. In this lecture, we focus on two kinds of duality/polarity applied to geometrical problems: digital straightness detection and envelope computation. T. Yung Kong, New York, IAPR Distinguished Speaker Minimal NonSimple and Minimal NonCosimple Sets in Binary Images on Cell The concepts of weak component and simple 1 are generalizations, to binary images on the ncells of ndimensional cell complexes, of the standard concepts of "26component" and "26simple" 1 in binary images on the 3cells of a 3D cubical complex; the concepts of strong component and cosimple 1 are generalizations of the concepts of "6component" and "6simple" 1. Over the past 20 years, the problems of determining just which sets of 1's can be minimal nonsimple, just which sets can be minimal noncosimple, and just which sets can be minimal nonsimple (minimal noncosimple) without being a weak (strong) foreground component have been solved for the 2D cubical and hexagonal, 3D cubical and facecenteredcubical, and 4D cubical complexes. This lecture solves these problems in much greater generality, for a very large class of cell complexes of dimension less than or equal to 4. Geometric representations and algorithms The study of geometrically defined graphs, and of the reverse question, the construction of geometric representations of graphs, leads to unexpected connections between geometry, graph theory, and algorithms. A large variety of graph properties, seemingly with no relation to geometry, are related to the existence of certain geometric representations, and the construction of such representations leads, in turn, to efficient algorithms to test for these properties. 

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