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Journal of Electronic Imaging

Two-dimensional images in frequency-time representation: direction images and resolution map
Author(s): Artyom M. Grigoryan; Nan Du
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Paper Abstract

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 3N-2, 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 3N/2 angles. The paired representation leads to the image composition by a set of 3N-2 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 log2 N 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

Paper Details

Date Published: 1 July 2010
PDF: 14 pages
J. Electron. Imaging. 19(3) 033012 doi: 10.1117/1.3483906
Published in: Journal of Electronic Imaging Volume 19, Issue 3
Show Author Affiliations
Artyom M. Grigoryan, The Univ. of Texas at San Antonio (United States)
Nan Du, The Univ. of Texas at San Antonio (United States)


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