Proceedings ArticleDOI
Accurate and fast discrete polar Fourier transform
Amir Averbuch,Ronald R. Coifman,David L. Donoho,Michael Elad,Moshe Israeli +4 more
- Vol. 2, pp 1933-1937
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TLDR
The pseudopolar FFT plays the role of a halfway point-a nearly-polar system from which conversion to polar coordinates uses processes relying purely on interpolation operations, and the conversion process is described.Abstract:
In this article we develop a fast high accuracy polar FFT. For a given two-dimensional signal of size N/spl times/N, the proposed algorithm's complexity is O(N/sup 2/ log N), just like in a Cartesian 2D-FFT. A special feature of our approach is that it involves only 1-D equispaced FFT's and 1D interpolations. A central tool in our approach is the pseudopolar FFT, an FFT where the evaluation frequencies lie in an over-sampled set of nonangularly equispaced points. The pseudopolar FFT plays the role of a halfway point-a nearly-polar system from which conversion to polar coordinates uses processes relying purely on interpolation operations. We describe the conversion process, and compare accuracy results obtained by unequally-sampled FFT methods to ours and show marked advantage to our approach.read more
Citations
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Journal ArticleDOI
Radon transform orientation estimation for rotation invariant texture analysis
TL;DR: In the proposed approach, the Radon transform is first employed to detect the principal direction of the texture and a wavelet transform is applied to the rotated image to extract texture features, providing a features space with small intraclass variability and, therefore, good separation between different classes.
Journal ArticleDOI
Fast and accurate Polar Fourier transform
TL;DR: A fast high accuracy Polar FFT based on the pseudo-Polar domain, an FFT where the evaluation frequencies lie in an oversampled set of nonangularly equispaced points, including fast forward and inverse transforms.
Journal ArticleDOI
Rotational Invariance Based on Fourier Analysis in Polar and Spherical Coordinates
TL;DR: The proposed transforms provide effective decompositions of an image into basic patterns with simple radial and angular structures and the theory is compactly presented with an emphasis on the analogy to the normal Fourier transform.
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Pseudo-log-polar Fourier transform for image registration
TL;DR: A new registration algorithm based on pseudo-log-polar Fourier transform (PLPFT) for estimating large translations, rotations, and scalings in images is developed and the robustness and high accuracy of this algorithm is verified.
Journal ArticleDOI
On the computation of the polar FFT
TL;DR: In this paper, the polar and pseudo-polar FFT can be computed very accurately and efficiently by the well-known nonequispaced FFT, and the reconstruction of a 2D signal from its Fourier transform samples on a (pseudo)polar grid by means of the inverse nonequispecific FFT is discussed.
References
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Journal ArticleDOI
Nonuniform fast Fourier transforms using min-max interpolation
TL;DR: This paper presents an interpolation method for the nonuniform FT that is optimal in the min-max sense of minimizing the worst-case approximation error over all signals of unit norm and indicates that the proposed method easily generalizes to multidimensional signals.
Journal ArticleDOI
Fast Fourier transforms for nonequispaced data
A. Dutt,Vladimir Rokhlin +1 more
TL;DR: In this paper, a group of algorithms is presented generalizing the fast Fourier transform to the case of noninteger frequencies and nonequispaced nodes on the interval $[ - \pi,\pi ].
Journal ArticleDOI
Digital reconstruction of multidimensional signals from their projections
TL;DR: A tutorial review of the reconstruction problem and some of the algorithms which have been proposed for its solution, and a number of new algorithms that appear to have some advantages over previous algorithms are presented.
Journal ArticleDOI
On the Fast Fourier Transform of Functions with Singularities
TL;DR: An explicit approximation of the Fourier Transform of generalized functions of functions with singularities based on projecting such functions on a subspace of Multiresolution Analysis is obtained and a fast algorithm based on its evaluation is developed.