Read e-book online Advances in Imaging and Electron Physics, Vol. 111 PDF

By Peter W. Hawkes

Advances in Imaging & Electron Physics merges long-running serials--Advances in Electronics & Electron Physics and Advances in Optical & Electron Microscopy . The sequence beneficial properties prolonged articles at the physics of electron units (especially semiconductor devices), particle optics at low and high energies, microlithography, picture technological know-how and electronic snapshot processing, electromagnetic wave propagation, electron microscopy, and the computing tools utilized in most of these domain names.

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3 B k, l D nl ˛mk 1 ˛2 mod F 64 mD0 nD0 3k 3l 1 C ˛12 C ˛2l B k, l D 1 C ˛k1 C ˛2k 1 C ˛1 2 C ˛2 D 0 3k 1 C ˛k1 C ˛2k 1 C ˛1 D 0 for 3l 1 C ˛l2 C ˛2l 2 C ˛2 D 0 for 65 k D M 2i C 1 /2 and k D M 2i C 1 /4 and mod F 66 l D N 2j C 1 /2 and l D N 2j C 1 /4 67 where i and j are integers such that k and l are less than M and N, respectively. For N D M D 16, the solutions are k, l D 4, 8, 12. Hence, the pattern of a 28 S. BOUSSAKTA AND A. G. J. HOLT square image with side L D 4 divides the NTT image into 16 parts, as shown in Figure 3(f).

38 S. BOUSSAKTA AND A. G. J. HOLT 9. Summary Although the number domain generated by the 2-D NTTs is not always simple to interpret, 2-D NTTs are meaningful. The study of some of the patterns of zeros that appear in the number domain for 2-D NTTs shows that, even though the patterns may be similar for some features, they might be used effectively in pattern-recognition problems where there is a need only for classifying a closed set of objects, such as those that occur in character recognition.

BOUSSAKTA AND A. G. J. HOLT B. Number Domain Analysis in Two Dimensions with Possible Applications NTTs have been mainly applied to the calculation of convolutions (filtering) and correlations. Until recently no other applications were thought to exist, because of the residue number system, where the same quantities are congruent rather than equal. Hence the concept of magnitude, as in normal fields, does not hold. NTTs are calculated by retaining the residues only, which has led to difficulty in trying to relate the information content in the number domain generated by NTTs to the time representation of signals and images, such as that of the Fourier transform correspondence between frequency and time domain.

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