The generalized Gabor scheme of image representation in biological and machine vision

Porat, Moshe; Zeevi, Yehoshua Y.

doi:10.1109/34.3910

Cited by 407 publications

(166 citation statements)

References 32 publications

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“…In 1946, Gabor [10] has extended this idea to signal and information theory, and has shown that there exists a trade off between time resolution and frequency resolution for one-dimensional signals, and that there is a lower bound on their joint product. These results were later extended to 2D signals [3,19].…”

Section: Background and Related Workmentioning

confidence: 99%

“…with respect to Gabor-functions which sample the joint spatial-frequency space via constantvalue translations. Gabor-wavelets can be generated by a logarithmic distortion of Gabor functions (the minimizers of the Weyl-Heisenberg group) [19] or alternatively by using multi-windows, so that a collection of the functions generated by both the Weyl-Heisenberg group and the affine group are considered [32]. As these Gabor-wavelets are generated using the affine group, the joint spatialfrequency space is sampled in an octave-like manner.…”

Section: Introductionmentioning

confidence: 99%

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The Uncertainty Principle: Group Theoretic Approach, Possible Minimizers and Scale-Space Properties

2006

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Abstract. The uncertainty principle is a fundamental concept in the context of signal and image processing, just as much as it has been in the framework of physics and more recently in harmonic analysis. Uncertainty principles can be derived by using a group theoretic approach. This approach yields also a formalism for finding functions which are the minimizers of the uncertainty principles. A general theorem which associates an uncertainty principle with a pair of self-adjoint operators is used in finding the minimizers of the uncertainty related to various groups. This study is concerned with the uncertainty principle in the context of the Weyl-Heisenberg, the SIM(2), the Affine and the Affine-WeylHeisenberg groups. We explore the relationship between the two-dimensional affine group and the SIM(2) group in terms of the uncertainty minimizers. The uncertainty principle is also extended to the Affine-Weyl-Heisenberg group in one dimension. Possible minimizers related to these groups are also presented and the scale-space properties of some of the minimizers are explored.

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Section: Background and Related Workmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

The Uncertainty Principle: Group Theoretic Approach, Possible Minimizers and Scale-Space Properties

2006

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“…This scheme incorporates scaling characteristics of wavelets and of the Gabor scheme with the logarithmically-distorted frequency axis [21]. However, in contrast with wavelets, this scheme has a finite number of window functions, i.e., resolution levels, and each of the windows is modulated by the infinite set of functions defined by the kernel.…”

Section: A Wavelet-type Gabor Schemementioning

confidence: 99%

“…Thus, it is desirable to incorporate scaling into the Gabor-type representation. This is accomplished by the generalized Gabor scheme [21], [35]. In this paper we focus on signal and image representation by multi-window Gabor-type schemes, where by proper choice of the set of windows we incorporate scaling [35].…”

Section: ì´ µ ì´ µmentioning

confidence: 99%

Multiwindow Gabor-type Representations and Signal Representation by Partial Information

Zeevi

2001

Twentieth Century Harmonic Analysis — A Celebration

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ABSTRACT. Harmonic analysis has been the longest lasting and most powerful tool for dealing with signals and systems which involve both periodic and transient phenomena. Further impact on signal processing was facilitated by what we refer to as representations in combined spaces. These representations, motivated by Gabor's concept of time-frequency information, cells have evolved in recent years into a rich repertoire of Gabor-type windowed Fourier transforms, relating Fourier analysis to the Heisenberg group. Such localized bases or frames are useful in the representation, processing, compression and transmission of speech, images and other natural signals that, by their very nature, are nonstationary. To incorporate scale that lends itself to multiresolution analysis as is the case with wavelets, the Gabor scheme is generalized to multiwindow Gabor frames. The properties of such sequences of functions are characterized by an approach that combines the concept of frames and the Zak Transform. Results on signal representation and reconstruction from partial information in the frequency domain are related to and derived, using relevant results obtained

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“…In the context of image representation schemes recently reported Porat & Zeevi, 1988), these data may be used to generate efficient imagery that consists of only those spectral components to which each region of the visual field is sensitive (cf. Zeevi et al, 1990).…”

mentioning

confidence: 99%

Variable-Resolution Imagery for Flight Simulation

Geri¹,

Zeevi²,

Vrana³

1994

PsycEXTRA Dataset

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The generalized Gabor scheme of image representation in biological and machine vision

Cited by 407 publications

References 32 publications

The Uncertainty Principle: Group Theoretic Approach, Possible Minimizers and Scale-Space Properties

The Uncertainty Principle: Group Theoretic Approach, Possible Minimizers and Scale-Space Properties

Multiwindow Gabor-type Representations and Signal Representation by Partial Information

Variable-Resolution Imagery for Flight Simulation

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