By J M Blackledge

This authoritative textual content (the moment a part of a whole MSc path) offers mathematical equipment required to explain photographs, photo formation and diversified imaging platforms, coupled with the primary strategies used for processing electronic photographs. it truly is in keeping with a path for postgraduates interpreting physics, digital engineering, telecommunications engineering, info know-how and machine technology. This ebook relates the equipment of processing and studying electronic pictures to the ‘physics’ of imaging platforms. Case experiences make stronger the tools mentioned, with examples of present learn themes.

  • Provides mathematical equipment required to explain pictures, picture formation and diverse imaging systems
  • Outlines the main concepts used for processing electronic images
  • Relates the tools of processing and studying electronic photographs to the ‘physics’ of imaging systems

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Extra resources for Digital image processing : mathematical and computational methods

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Texture characterisation using cooccurrence matrices have also been studied on the hexagonal lattice [88]. It was found that there were benefits for textures which have information at multiples of 60◦ . Additionally, texture synthesis using Markov random fields has been proposed which permit classes of texture which are not simple to generate using square images [89]. A family of compactly supported hexagonal splines are proposed in [23]. It has an increased number of symmetry compared to the B-splines used on square lattices.

The conditions are based on the relationship between the sampled spectra and the original signal’s spectra. Given a continuous signal f (x) its Fourier transform F (Ω), the relationships between the two are defined as follows: ∞ F (Ω) = −∞ f (x) = 1 4π 2 f (x)e−jΩ ∞ −∞ T x dx F (Ω)ejΩ T x dΩ 32 The Proposed HIP Framework Here, Ω ∈ R2 is a frequency domain vector and x ∈ R2 is a vector in the spatial domain. Using the above relationship, it is possible to determine the effect of sampling the signal on its spectrum as follows: fs (n) = ∞ 1 4π 2 F (Ω)ejΩ T (Vn) dΩ −∞ Using a simple substitution ω = VT Ω yields: fs (n) = 1 4π 2 ∞ −∞ F ((VT )−1 ω)ejω T n dω |det V| Instead of integrating this over the entire plane it is possible to split it into a series of smaller sub integrals with area 4π 2 .

Stevenson [42] proposed the use of a hexagonal layout of dots. The dots, being squirts of ink, are circular and hence a hexagonal lattice was more robust to errors and compensated the characteristics of the non-ideal printing device. His method was analogous to that of Rosenfeld except that individual dots were used to indicate the hexagonal pixels instead of entire characters. These dots had a controllable radius and were slightly bigger than an individual print element. In this way, alternate rows could be offset to produce the required hexagonal lattice arrangement.

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