By Lee Middleton
This e-book presents an advent to the processing of hexagonally sampled photographs, incorporates a survey of the paintings performed within the box, and provides a unique framework for hexagonal photograph processing (HIP) according to hierarchical aggregates. The strengths provided through hexagonal lattices over sq. lattices to outline electronic photographs are significant: greater packing density uniform connectivity of issues (pixels) within the lattice higher angular solution via advantage of getting extra nearest neighbours superlative illustration of curves The application of the HIP framework is proven by means of enforcing a number of simple photograph processing ideas (for the spatial and frequency area) and a few purposes. conception and algorithms are lined in addition to information akin to accommodating that aid merely photographs sampled on a sq. lattice. A CD-ROM presents code permitting the reader to strengthen and try algorithms for processing hexagonal pictures. This clean technique bargains perception and manageable knowledge to either researchers and postgraduates.
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Additional info for Hexagonal Image Processing: A Practical Approach (Advances in Pattern Recognition)
However, such representations are cumbersome and do not fully exploit the hexagonal nature of the underlying lattice. Devising an eﬃcient representation scheme for hexagonal images is necessary as it can drastically aﬀect the overall performance of a system. Towards this purpose, we take a fresh look at the sampling process from the point of view of tiling theory. 1 Sampling as a tiling The notion put forward in this section is that trying to sample a 2-D spatial signal is similar to trying to tile the Euclidean plane.
Fig. 11. Rosenfeld’s method for displaying a hexagonally sampled image . and an oﬀ pixel was illustrated with a ‘ ’. Intensities and other information, however, could be conveyed by employing diﬀerent characters. The results were generated using a dot matrix printer. As the horizontal spacing is ﬁxed, the sole manipulation that could be performed was the vertical spacing. This approach generated hexagonal lattices that appeared very regular. In the 1980s there were several signiﬁcant advances in technology which directly impacted on the visualisation of hexagonal images.
A frequency domain sampling lattice. B, though certain shapes make the reconstruction simpler. It is possible to vary the spatial sampling matrix V so that there is no overlap among the periodically repeated versions of F (Ω). Consequently, there is no aliasing. The main point to draw from this discussion is that in terms of sampling, it is desirable that no aliasing is present for perfect reconstruction. In the language of tiling, this is equivalent to requiring the sampled signal’s spectrum to be a monohedral packing.