Fundamentals of Digital Optics

Yaroslavsky, Leonid P.; Eden, Murray

doi:10.1007/978-1-4612-0845-7

Cited by 119 publications

(85 citation statements)

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“…One may see now that the correspondence between CFT and DFT given in references (Collier et al, 1971;Yaroslavsky & Eden, 1996) is of a different kind than that shown above. In those references the output function G is not discrete.…”

Section: The Discrete Fourier Transformmentioning

confidence: 72%

The Fourier Transform in Optics: Analogous Experiment and Digital Calculus

Logofătu¹,

Nascov²,

Apostol³

2011

Holography, Research and Technologies

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Section: The Discrete Fourier Transformmentioning

confidence: 72%

The Fourier Transform in Optics: Analogous Experiment and Digital Calculus

Logofătu¹,

Nascov²,

Apostol³

2011

Holography, Research and Technologies

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“…In fact, E 0 corresponds to the celebrated ROF filter originally introduced by Rudin, Osher, and Fatemi in [83]. While, E δ (with ϕ as in Example 2) is reminiscent of a Yaroslavsky filter (see [36,88,89]), once it has been expressed in the variational framework, as explained in the paper by Kindermann, Osher, and Jones [84]. Theorem 8.3 says that the Yaroslavsky filter converges to the ROF filter-a fact which seems to be new to the experts in Image Processing.…”

Section: Further Results and Their Applications In Image Processingmentioning

confidence: 99%

Estimates for the topological degree and related topics

Nguyên

2014

J. Fixed Point Theory Appl.

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Abstract. This is a survey paper on estimates for the topological degree and related topics which range from the characterizations of Sobolev spaces and BV functions to the Jacobian determinant and nonlocal filter problems in Image Processing. These results are obtained jointly with Bourgain and Brezis. Several open questions are mentioned.Mathematics Subject Classification. 55M25, 49J99, 46E35, 46B50.

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“…Periodic noise has a periodic pattern in the spatial domain. In the Fourier amplitude spectrum, it is revealed as conjugate peaks having very clear spectral appearance at conjugate frequencies [2][3][4][5]. Gonzalez and Wintz stressed that filtering in the amplitude spectrum with a notch filter could be an effective removal method [5].…”

Section: Introductionmentioning

confidence: 99%

Automatic reduction of periodic noise in images using adaptive Gaussian star filter

Ketenci¹,

Gangal²

2017

Turk J Elec Eng & Comp Sci

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Abstract:The reduction of noise in images is a crucial issue and an inevitable preprocessing step in image analysis.Many diverse noise sources, which disrupt source images, exist in nature and through manmade devices. Periodic noise is one such disruption that has a periodic pattern in the spatial domain, causing hills in the image spectrum. In practice, quasiperiodic noise is commonly encountered instead of periodic noise. It has a more complex frequency spectrum, such as a star shape, in place of a pure delta shape in the frequency amplitude spectrum. In this study, we consider designing a star shape Gaussian filter that is a more appropriate adaptive filter of (quasi-) periodic noise. We called this filter the adaptive Gaussian star filter (AGSF), regarding the extension of the standard Gaussian filter. The proposed method is fully automatic and consists of three steps. Firstly, the low-frequency region in the image spectrum is detected via region-growing in the frequency domain. Next, the noise coordinates are estimated, and each noise spread area is determined and labeled using region-growing in the spectrum. Finally, AGSF shape and parameters are adjusted adaptively according to estimated noise characteristics. The performance of the method is discussed in the context of different sizes and contrasts for noisy images. The results are compared with previous work in the literature and they show that the developed algorithm is quite robust in reducing both periodic and quasiperiodic noise.

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Fundamentals of Digital Optics

Cited by 119 publications

References 0 publications

The Fourier Transform in Optics: Analogous Experiment and Digital Calculus

The Fourier Transform in Optics: Analogous Experiment and Digital Calculus

Estimates for the topological degree and related topics

Automatic reduction of periodic noise in images using adaptive Gaussian star filter

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