## Image Representation Using 2D Gabor Wavelets (1996)

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Venue: | IEEE Trans. Pattern Analysis and Machine Intelligence |

Citations: | 284 - 4 self |

### BibTeX

@ARTICLE{Lee96imagerepresentation,

author = {Tai Sing Lee},

title = {Image Representation Using 2D Gabor Wavelets},

journal = {IEEE Trans. Pattern Analysis and Machine Intelligence},

year = {1996},

volume = {18},

pages = {959--971}

}

### Years of Citing Articles

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### Abstract

This paper extends to two dimensions the frame criterion developed by Daubechies for one-dimensional wavelets, and it computes the frame bounds for the particular case of 2D Gabor wavelets. Completeness criteria for 2D Gabor image representations are important because of their increasing role in many computer vision applications and also in modeling biological vision, since recent neurophysiological evidence from the visual cortex of mammalian brains suggests that the filter response profiles of the main class of linearly-responding cortical neurons (called simple cells) are best modeled as a family of self-similar 2D Gabor wavelets. We therefore derive the conditions under which a set of continuous 2D Gabor wavelets will provide a complete representation of any image, and we also find self-similar wavelet parameterizations which allow stable reconstruction by summation as though the wavelets formed an orthonormal basis. Approximating a "tight frame" generates redundancy which allows low-resolution neural responses to represent high-resolution images, as we illustrate by image reconstructions with severely quantized 2D Gabor coefficients. Index Terms---Gabor wavelets, coarse coding, image representation, visual cortex, image reconstruction.

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Citation Context ...hysiological findings [7]. The spatial frequency bandwidths of the simple and complex cells have been found to range from 0.5 to 2.5 octaves, clustering around 1.2 octaves [10], [18], and 1.5 octaves =-=[38]. -=-The Gaussian envelope is usually elliptical, with an aspect ratio of 1.5-2.0 [38], [7] and with the plane wave’s propagating direction along the short axis of the elliptical Gaussian (Fig. 2). CONST... |

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Citation Context .... Simple cells are often not strictly even or odd symmetric, but the quadrature-phase relationship between a pair of simple cells is generally preserved, whatever the absolute phase may be [33], [7], =-=[9]. -=-Since only the power-modulus enters into our later calculation, we can simplify the Gabor filter by setting the spatial location of the filter’s center (x o = 0, y o = 0) and the absolute phase U of... |

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Citation Context ...], [20]. Recent neurophysiological evidence [11] suggests that the spatial structure of the receptive fields of simple cells having different sizes is virtually invariant. Daugman [8] and others [3], =-=[34]-=- have proposed that an ensemble of simple cells is best modeled as a family of 2D Gabor wavelets sampling the frequency domain in a log-polar manner. This class is equivalent to a family of affine coh... |

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