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Two-dimensional images in frequency-time representation: direction images and resolution map

[+] Author Affiliations
Artyom M. Grigoryan

University of Texas at San Antonio, Department of Electrical and Computer Engineering, One UTSA Circle, San Antonio, Texas 78249-0669

Nan Du

University of Texas at San Antonio, Department of Electrical and Computer Engineering, One UTSA Circle, San Antonio, Texas 78249-0669

J. Electron. Imaging. 19(3), 033012 (August 31, 2010). doi:10.1117/1.3483906
History: Received December 16, 2009; Revised July 07, 2010; Accepted July 12, 2010; Published August 31, 2010; Online August 31, 2010
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We discuss the concept of the direction image multiresolution, which is derived as a property of the 2-D discrete Fourier transform, when it splits by 1-D transforms. The N×N image, where N is a power of 2, is considered as a unique set of splitting-signals in paired representation, which is the unitary 2-D frequency and 1-D time representation. The number of splitting-signals is 3N2, and they have different durations, carry the spectral information of the image in disjoint subsets of frequency points, and can be calculated from the projection data along one of 3N2 angles. The paired representation leads to the image composition by a set of 3N2 direction images, which defines the directed multiresolution and contains periodic components of the image. We also introduce the concept of the resolution map, as a result of uniting all direction images into log2N series. In the resolution map, all different periodic components (or structures) of the image are packed into a N×N matrix, which can be used for image processing in enhancement, filtration, and compression.

© 2010 SPIE and IS&T

Citation

Artyom M. Grigoryan and Nan Du
"Two-dimensional images in frequency-time representation: direction images and resolution map", J. Electron. Imaging. 19(3), 033012 (August 31, 2010). ; http://dx.doi.org/10.1117/1.3483906


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