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 Vorono? 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,rono? 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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