Hexagonal Image Processing: A Practical Approach by Lee Middleton PhD, Jayanthi Sivaswamy PhD (auth.)

By Lee Middleton PhD, Jayanthi Sivaswamy PhD (auth.)

Hexagonal snapshot Processing presents an advent to the processing of hexagonally sampled photographs, contains a survey of the paintings performed within the box, and provides a singular framework for hexagonal photo processing (HIP) in response to hierarchical aggregates.
Digital photo processing is at the moment ruled via sq. sampling lattices, in spite of the fact that, hexagonal sampling lattices is usually used to outline electronic pictures. The strengths provided by means of hexagonal lattices over sq. lattices are considerable:
• larger packing density,
• uniform connectivity of issues (pixels) within the lattice,
• higher angular answer by way of advantage of getting extra nearest neighbours, and
• superlative illustration of curves.
The software of the HIP framework is confirmed by means of enforcing numerous easy photo processing options (for the spatial and frequency area) and a few purposes. 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. the speculation and algorithms lined are supplemented through cognizance to sensible info akin to accommodating that aid in simple terms pictures sampled on a sq. lattice.
Including a Foreword written through Professor Narendra Ahuja, an eminent researcher within the box of photograph Processing and desktop imaginative and prescient, the book’s clean method of the topic bargains perception and practicable information to either researchers and postgraduates.

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2 Hexagonal image processing in computer vision nearest integer grid points in a hexagonal lattice, which are useful in geometric transformations. Kimuro [87] used a spherical hexagonal pyramid to analyse the output from an omni-directional camera. The results were promising and were better than such systems designed using square images. Surface area estimates of scanned images, have been computed using hexagonal and other tilings by Miller [44]. Hexagonal tiles were found to perform with less error than the other tiles.

Both these works use a pyramidal decomposition of the image with three sub-band orientations namely at 30◦ , 90◦ and 120◦ . The hexagonal, orthogonal, oriented pyramid of Watson [16] was used for an image coding scheme. The main motivation was to be comparable to the receptive fields of the human visual system. It was built upon an earlier work called the cortex transform. The levels of compression achieved in this scheme were greater than the equivalent schemes for square images. The orientation selectivity afforded by hexagonal lattice and multiscale representations have been used a bit differently to define a set of ranklets for feature detection [86].

Consider a continuous function, f (x1 , x2 ), that is defined in R2 . In order to uniformly sample this function, the domain of the function must be divided up in a regular fashion and samples taken. An intuitive way to perform this is to use rectangular sampling and derive a sampled version of the function fs (n1 , n2 ) = f (n1 T1 , n2 T2 ) = f (Vn). T1 and T2 are real numbered constants that provide the horizontal and vertical sampling intervals respectively. There is no reason why rectangular sampling must be used and in fact, any valid basis of R2 can be used.

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