Computer Vision Pattern Recognition

Hexagonal Image Processing. A Practical Approach by Lee Middleton

By Lee Middleton

Hexagonal picture Processing develops and offers a singular framework for hexagonal photo processing via taking cues from human visible approach and tiling idea. This body paintings is termed the HIP framework and offers an answer for conversion among sq. sampled pictures and hexagonally sampled photographs, and processing in either the spatial and frequency domain names. This framework is proven by way of imposing a number of easy snapshot processing strategies and a few novel purposes are carried out similar to discovering attractions and shapes utilizing saccadic exploration. The HIP framework serves as a device for evaluating processing of pictures outlined on a sq. vs hexagonal grid, to figure out their relative advantages and demerits. Comparisons and case reviews are utilized in the evaluate. Hexagonal sampling lattices were thought of through researchers in photo processing for a very long time as a good substitute to the normal sq. sampling. This e-book addresses the advantages over the traditional technique.

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The length of time for which hexagonal sampling has held interest among researchers and the wide range of areas covered, we believe, points to the fact that there is not only significant interest but also merit in processing hexagonally sampled images. However, the second point to note from the figure is that the level of activity is low in general, notwithstanding the upward trend that is apparent in the last 15 years. This is true both in terms of the number of researchers and in the number of publications that has come out in this area over 40 odd years.

An isometry is a mapping of the Euclidean plane onto itself which preserves all distances [104]. The mapping is denoted by σ : R2 → R2 . There are only four types of isometries [105]: 1. 2. 3. 4. 1(d)) Isometries of types 1 and 2 are called direct because they preserve the sense of the points. This means that if the points are labelled in an anti-clockwise sense then they will remain so after the isometry has been performed. Isometries of types 3 and 4 are called indirect. For a particular isometry, σ, being performed on a set S the symmetries of the set are the isometries which map onto the original set, or σ(S) = S.

The GBT consists of hierarchical aggregation of cells, with the cells at each level constructed from those at a previous level using an aggregation rule. For the 2-D case, the aggregation rule is the same as that of Burt’s sept-tree. Each level consists of clusters of seven cells, and any GBT-based structure can be represented by unique, base-seven indices. The work of Sheridan [58] studies the effect of modulo operations on these addresses. Independent of the work on GBT-based data structures, Hartman and Tanimoto [15] also investigated generating hexagonal pyramid structures, for the purpose of modelling the behaviour of the orientation- and locationspecific cells in the primary visual cortex.

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