better angular resolution by virtue of having more nearest neighbours, and.uniform connectivity of points (pixels) in the lattice,.
The strengths offered by hexagonal lattices over square lattices are considerable: Hexagonal Image Processing provides an introduction to the processing of hexagonally sampled images, includes a survey of the work done in the field, and presents a novel framework for hexagonal image processing (HIP) based on hierarchical aggregates.ĭigital image processing is currently dominated by the use of square sampling lattices, however, hexagonal sampling lattices can also be used to define digital images. It is also shown that the triangular grid shows better performance in some cases than the square grid regarding the number of lost pixels in the neighborhood motion map. Angles of all locally bijective and non-bijective rotations are described in details. In particular, different rotation centers are considered with respect to the corresponding main pixel, e.g.
In this paper we show digitized rotations of a pixel and its 12-neighbors on the triangular grid. Neighborhood motion maps are tools to analyze digital transformations, e.g., rotations by local bijectivity point of view. Since these transformations play an important role in image processing and in image manipulation, it is important to discover their properties. Rotations are bijective on the Euclidean plane, but in many cases they are not injective and not surjective on digital grids. Usually, these digital versions of the transformations have different properties than the original continuous variants have. Their digital counterpart, i.e., their digitized variants are defined on discrete grids, since most of our pictures are digital nowadays. There are various geometric transformations, e.g., translations, rotations, which are always bijections in the Euclidean space.
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