By Lee Middleton
ISBN-10: 1846282039
ISBN-13: 9781846282034
ISBN-10: 1852339144
ISBN-13: 9781852339142
This booklet offers an creation to the processing of hexagonally sampled photographs, contains a survey of the paintings performed within the box, and offers a unique framework for hexagonal picture processing (HIP) in response to hierarchical aggregates. The strengths provided by means of hexagonal lattices over sq. lattices to outline electronic photographs are significant: better packing density uniform connectivity of issues (pixels) within the lattice higher angular answer by means of advantage of getting extra nearest neighbours superlative illustration of curves The application of the HIP framework is proven by means of imposing a number of easy photo processing recommendations (for the spatial and frequency area) and a few purposes. idea and algorithms are lined in addition to info corresponding to accommodating that help in basic terms photographs sampled on a sq. lattice. A CD-ROM offers code permitting the reader to advance and try out algorithms for processing hexagonal photos. This clean technique bargains perception and practicable knowledge to either researchers and postgraduates.
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Additional info for Hexagonal Image Processing: A Practical Approach (Advances in Pattern Recognition)
Example text
Hence, the indexing scheme can exploit this by using base seven numbering. A simple addressing scheme that does this is as follows: Assign a base seven number to each of the points labelled in the aggregate, starting at 0. 10. In this scheme, the address of each individual hexagon also encodes the spatial location within a tile of a given level of aggregation. Consider the cell labelled 42 (the number is in base 7). The fact that it has two digits reveals that the hexagonal cell has its position within a second level aggregate.
C, +) is a group. Any lattice is a subset of the set of complex numbers, and it is well known that the lattice is an additive subgroup of complex numbers. 46 The Proposed HIP Framework Since HIP addressing is just a particular form of representation of the points on a hexagonal lattice, the results obtained above are not surprising. The next fundamental operation to examine is that of multiplication. Again this can be derived using the vectorial nature of the HIP addressing scheme. In this case it is more convenient to convert the address into a polar equivalent: a ∈ G, a → (ra , θa ) b ∈ G, b → (rb , θb ) a ❝ b = ra rb ej(θ a +θb ) Thus, the effect of multiplication of an address by another is to rotate and scale the original address.
Let it be labelled as point (0, 0) relative to B. This is the zeroth level aggregate and the set containing all these points can be called A0 . The circular aggregate (or the first level aggregate), which is illustrated in the centre of the figure, can be considered as a set of seven points in this coordinate system. 3) Examination of these coordinates confirms the hierarchical nature of the tiling as A0 is a member of A1 . 9. It would be rotation translation reflection glide reflection Fig. 8. Symmetries of a circular hexagonal aggregate.