Orthogonal projection technique for resolution enhancement of the Fourier transform fringe analysis method

2006 ◽  
Vol 266 (2) ◽  
pp. 465-468 ◽  
Author(s):  
Paulo J. Tavares ◽  
Mário A. Vaz
Keyword(s):  
Fourier Transform ◽  
Orthogonal Projection ◽  
Resolution Enhancement ◽  
Analysis Method ◽  
Projection Technique ◽  
Fringe Analysis ◽  
The Fourier Transform

Coordinate-transform technique for closed-fringe analysis by the Fourier-transform method

2001 ◽  
Vol 40 (10) ◽  
pp. 1649 ◽  
Author(s):  
Zongtao Ge ◽  
Fumio Kobayashi ◽  
Shinichi Matsuda ◽  
Mitsuo Takeda
Keyword(s):  
Fourier Transform ◽  
Fringe Analysis ◽  
Transform Method ◽  
Fourier Transform Method ◽  
The Fourier Transform ◽  
Coordinate Transform

Study on Woven Fabric Texture Based on Fourier Transform and Gabor Transform

2015 ◽  
Vol 671 ◽  
pp. 369-377 ◽  
Author(s):  
Li Qing Li ◽  
Ting Ting Shan ◽  
Le Xue ◽  
Jun Wang ◽  
Xia Chen
Keyword(s):  
Fourier Transform ◽  
Texture Analysis ◽  
Gabor Filter ◽  
Image Resolution ◽  
Woven Fabric ◽  
Gabor Transform ◽  
Analysis Method ◽  
Transform Method ◽  
Enhancement Method ◽  
The Fourier Transform

Woven fabric texture was periodic and complex, the woven fabric texture analysis method was based on Fourier transform and Gabor transform. Firstly the frequency range of woven fabric texture was obtained by using the Fourier Transform method, and the influence on fabric frequency of image resolution and fabric density was analyzed. Then the main parameters of Gabor filter was confirmed by the woven fabric texture frequency, and the sub-images which contain different texture information were obtained after the woven fabric images were decomposed and fused in different scales and directions using the Gabor filters. Finally the main texture enhancement method, the main texture elimination method, the direntional texture analysis method and extraessential texture enhancement method were discussed. The experiment proved that this method would be a powerful tool in the application of texture analysis.

scholarly journals Decomposable projections related to the Fourier and flip automorphisms

2010 ◽  
Vol 107 (2) ◽  
pp. 174 ◽  
Author(s):  
S. Walters
Keyword(s):  
Fourier Transform ◽  
Orthogonal Projection ◽  
Analogous Result ◽  
Irrational Rotation ◽  
Topological Invariants ◽  
Orthogonal Projections ◽  
C Algebra ◽  
Orthogonal Decompositions ◽  
The Fourier Transform

In this paper we classify Fourier invariant projections $g$ in the irrational rotation $C^*$-algebra that can be decomposed in the form 26741 g = f + \sigma(f) + \sigma^2(f) + \sigma^3(f) 26741 for some Fourier orthogonal projection $f$, where $\sigma$ is the Fourier transform automorphism. The analogous result is shown for the flip automorphism as well as the existence of flip-orthogonal projections. Both classifications are achieved by means of topological invariants (given by unbounded traces) and the canonical trace. We also show (in both the flip and Fourier cases) that invariant projections $h$ are subprojections of orthogonal decompositions $g$ for some projection $f$ such that $\tau(f) = \tau(h)$ (where $\tau$ is the canonical trace).

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