Spatially referenced methods of processing raster and vector data

摘要

The authors consider a general method of constructing addressing and arithmetic systems for two-dimensional image data using the hierarchy of ‘molecular’ tilings based on an original isohedral ‘atomic’ tiling. (Each molecular title at level k is formed from a constant number of tiles at level k−1; this is termed the ‘aperture’ property of the hierarchy.) In addition they present 11 objective criteria (which are of significance in cartographic image processing), by which these hierarchies and tilings may be described and compared.Of the 11 topologically distinct types of isohedral tiling, three ([36], [44] and [63]) are composed of regular polygons, and two of these ([36] and[44]) satisfy the condition that all tiles have the same ‘orientation’. In general, although each level in a hierarchy is topologically equivalent, the tiles may differ in shape at different levels and only [63], [44], [4.82] and [4.6.12] are capable of giving rise to hierarchies in which the tiles at all levels are the same shape. The possible apertures of hierarchies obeying this condition are n2 (for any n > 1)in the cases of [63] and [44]; n2 or 2n2 in the case of [4.82]; and n2 or 3n2 in the case of [4.6.12].In contrast the only tiling exhibiting the uniform ‘adjacency’ criterion is[36]. However, hierarchies based on this atomic tiling generate molecular tiles with different shapes at every level. If these disadvantages are accepted, hierarchies based on first-level molecular tiles referred to as the 4-shape, 4′-shape, 7-shape and 9-shape are generated. Of these the 4-shape and the 9-shape appear to satisfy many of the cartographically desirable properties in addition to having an atomic tiling which exhibits uniform adjacency.In recent years the generalized balanced ternary addressing system has been developed to exploit the image processing power of the 7-shape. The authors have generalized and extended this system as ‘tesseral addressing and arithmetic’, showing how it can be used to render a 4-shape into a spatially correct linear quadtree.