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Titlebook: Computational Proximity; Excursions in the To James F. Peters Book 2016 Springer International Publishing Switzerland 2016 Description.Desc

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,Helly’s Theorem and Strongly Proximal Helly Theorem,This chapter introduces a strongly proximal version of Helly’s theorem for convex sets and convex bodies. The collection of labelled Voronoï regions in the mesh nerve on the apple surface in Fig. . is an example of a Helly family of convex bodies.
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Connnectedness Patterns,This chapter introduces the study of connectedness patterns, which are collections of sets that exhibit a repetition of strongly connected polygons in a tiling of the plane.
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Image Geometry and Nearness Expressions for Image and Scene Analysis,ected seed (generating or site) points in a digital image. A . is a collection of objects in a visual field that captures our attention. In human vision, a . is the total area in which objects can be seen. A normal visual field is about 60. from the vertical meridian of each eye and about 60. above and 75. below the horizontal meridian.
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Nerve Patterns,ronoï diagram is an ngon that is strongly connected to polygons along the border of the nucleus. The partial ordering relation . on either the number of polygon sides or the areas of the nuclei leads to the arrangement of the nerves in a mesh nerve pattern.
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