# The Generalized Gabor Scheme of Image Representation in Biological and Machine Vision

@article{Porat1988TheGG, title={The Generalized Gabor Scheme of Image Representation in Biological and Machine Vision}, author={Moshe Porat and Yehoshua Y. Zeevi}, journal={IEEE Trans. Pattern Anal. Mach. Intell.}, year={1988}, volume={10}, pages={452-468} }

A scheme suitable for visual information representation in a combined frequency-position space is investigated through image decomposition into a finite set of two-dimensional Gabor elementary functions (GEF). The scheme is generalized to account for the position-dependent Gabor-sampling rate, oversampling, logarithmic frequency scaling and phase-quantization characteristic of the visual system. Comparison of reconstructed signal highlights the advantages of the generalized Gabor scheme in…

## 498 Citations

### Pattern analysis and texture discrimination in the Gabor space

- Computer Science[1988 Proceedings] 9th International Conference on Pattern Recognition
- 1988

A scheme of image decomposition into optimal localized frequency operators, the so-called Gabor elementary functions which minimize the uncertainty inherent in image representation, are proposed and applications to size-invariance and object-separable pattern analysis, localized texture discrimination, and representation by partial information are discussed.

### Pyramidal Image Representation In Nonuniform Systems

- Computer ScienceOther Conferences
- 1988

A formalism for representation and processing of images which are not band-limited is presented and an example of a sampling scheme wherein the sampling rate decreases as a function of the distance from the center of the visual field is elaborated.

### Incorporating Orientation Selectivity in Wavelet Transforms: For Multi--Resolution Fourier Analysis of Images

- Mathematics
- 1991

The problem of incorporating orientation selectivity into transforms which provide local frequency representation of image regions over a range of spatial scales is investigated. It is shown that…

### Realization of the Zak-Gabor representation of images

- Computer Science, MathematicsOther Conferences
- 1991

It is shown that the absolute value of the minimum of the ZT of the Gaussian is a function of the sub-pixel distance of translation and that the optimum value of such translation is 1/2 pixel.

### Structure of the Gabor matrix and efficient numerical algorithms for discrete Gabor expansions

- Computer ScienceOther Conferences
- 1994

An explicit description of the sparsity, the block and banded structure of the Gabor frame matrix G is presented and a fast Gabor reconstruction algorithm with very low computational complexity is proposed.

### Signal- and image-component separation by a multi-window Gabor-type scheme

- Computer ScienceProceedings of 13th International Conference on Pattern Recognition
- 1996

Two approaches are presented for the analysis of the generalized Gabor scheme: the signal domain approach and Zak transform domain approach, based on representing the frame operator as a matrix-valued function, and far less demanding from a computational complexity viewpoint.

### Adaptive Gabor transformation for image processing

- Engineering, Computer ScienceIEEE Trans. Image Process.
- 1993

An algorithm that computes the Gabor coefficients of an image is presented. An adaptive filter that uses the complex least mean-square algorithm for their computation is proposed, and its numerical…

### Generating complementary gray-level images for object recognition experiments using Gabor wavelet decomposition

- Computer Science
- 2010

A software image processing methodology is presented that is able to selectively mask or unmask specific resolutions, positions, and/or orientations of an input gray-level image using Gabor wavelet decomposition.

### Image representation by level crossings of the wavelet transform

- Computer Science, MathematicsProceedings of 3rd IEEE International Conference on Image Processing
- 1996

This study is devoted to multiresolution representation by partial information of the wavelet transform, and a theorem defining the conditions necessary for the zero crossing representation to be stable and complete is presented.

### Relaxation network for Gabor image decomposition

- BiologyBiological Cybernetics
- 2004

A cortical relaxation model is proposed which performs this minimisation of error between the original image and that reconstructed from the coefficients of Gabor function coefficients implicitly, and is used to examine the biological relevance and feasibility of reconstruction error minimisation.

## References

SHOWING 1-10 OF 50 REFERENCES

### Computer Image Generation Using Elementary Functions Matched to Human Vision

- Computer Science
- 1988

Visual representation in biological visual systems appears to be accomplished by a scheme of image decomposition into a finite set of localized operators which resemble the form of Gabor Elementary…

### Visual sensitivity to two-dimensional spatial phase.

- PhysicsJournal of the Optical Society of America
- 1982

We investigate some limits to phase processing in the human visual system with two-dimensional textured images. Results indicate that, although phase sensitivity increases with contrast and energy…

### Uncertainty relation for resolution in space, spatial frequency, and orientation optimized by two-dimensional visual cortical filters.

- PhysicsJournal of the Optical Society of America. A, Optics and image science
- 1985

Evidence is presented that the 2D receptive-field profiles of simple cells in mammalian visual cortex are well described by members of this optimal 2D filter family, and thus such visual neurons could be said to optimize the general uncertainty relations for joint 2D-spatial-2D-spectral information resolution.

### Visual cortical neurons as localized spatial frequency filters

- BiologyIEEE Transactions on Systems, Man, and Cybernetics
- 1983

The receptive field properties of neurons in the primary visual cortex, i.e. the striate cortex, are related to current issues in spatial visual information processing to consider two adjacent simple cell pairs as operating like paired Gaussian-attenuated sine and cosine filters of Gabor filters for restricted regions of visual space.

### Two-dimensional spectral analysis of cortical receptive field profiles

- BiologyVision Research
- 1980

### Sampling theorem for the complex spectrogram, and Gabor's expansion in Gaussian elementary signals

- Mathematics
- 1981

The complex spectrogram of a signal is defined as the Fourier transform of the product of the signal and the shifted and complex conjugated version of a so-called window function; it is thus a…

### The Laplacian Pyramid as a Compact Image Code

- Computer ScienceIEEE Trans. Commun.
- 1983

A technique for image encoding in which local operators of many scales but identical shape serve as the basis functions, which tends to enhance salient image features and is well suited for many image analysis tasks as well as for image compression.

### Encoding of spatial frequency, orientation, and contrast in striate cortex

- BiologyAnnual Meeting Optical Society of America
- 1985

Electrophysiological and anatomical evidence from monkeys indicates that the striate cortex is broken up into some 1500 modules, each containing cells which process information from a limited part of the visual field which overlaps to a varying extent with the cells in neighboring modules.

### Reorganization and diversification of signals in vision

- BiologyIEEE Transactions on Systems, Man, and Cybernetics
- 1985

It is concluded that the striate cortex performs many simultaneous functional mappings, or nonuniform processing, in the retino-cortical mapping.

### A Theory for Invariant Object Recognition in the Frontoparallel Plane

- Computer ScienceIEEE Transactions on Pattern Analysis and Machine Intelligence
- 1984

We suggest a new computational theory for position, size, and orientation invariant recognition of planar gray-scale forms in frontoparallel view. The theory employs a spatial-frequency…