text: Gabor filters (GFs) play an important role in many application areas for the enhancement of various types of images and the extraction of Gabor features. For the purpose of enhancing curved structures in noisy images, we introduce curved GFs that locally adapt their shape to the direction of flow. These curved GFs enable the choice of filter parameters that increase the smoothing power without creating artifacts in the enhanced image. In this paper, curved GFs are applied to the curved ridge and valley structures of low-quality fingerprint images. First, we combine two orientation-field estimation methods in order to obtain a more robust estimation for very noisy images. Next, curved regions are constructed by following the respective local orientation. Subsequently, these curved regions are used for estimating the local ridge frequency. Finally, curved GFs are defined based on curved regions, and they apply the previously estimated orientations and ridge frequencies for the enhancement of low-quality fingerprint images. Experimental results on the FVC2004 databases show improvements of this approach in comparison with state-of-the-art enhancement methods.
  @cite_61: It is suggested that it may be possible to transmit speech and music in much narrower wavebands than was hitherto thought necessary, not by clipping the ends of the waveband, but by condensing the information. Two possibilities of more economical transmission are discussed. Both have in common that the original waveband is compressed in transmission and re-expanded to the original width in reception. In the first or ?kinematical? method a temporary or permanent record is scanned by moving slits or their equivalents, which replace one another in continuous succession before a ?window.? Mathematical analysis is simplest if the transmission of the window is graded according to a probability function. A simple harmonic oscillation is reproduced as a group of spectral lines with frequencies which have an approximately constant ratio to the original frequency. The average departure from the law of proportional conversion is in inverse ratio to the time interval in which the record passes before the window. Experiments carried out with simple apparatus indicate that speech can be compressed into a frequency band of 800 or even 500 c s without losing much of its intelligibility. There are various possibilities for utilizing frequency compression in telephony by means of the ?kinematical? method. In a second method the compression and expansion are carried out electrically, without mechanical motion. This method consists essentially in using non-sinusoidal carriers, such as repeated probability pulses, and local oscillators producing waves of the same type. It is shown that one variety of the electrical method is mathematically equivalent to the kinematical method of frequency conversion.
  @cite_32: 
  @cite_0: 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 parametrization 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.
  @cite_24: Abstract Dennis Gabor is mainly known for the invention of optical holography and the introduction of the so-called Gabor functions in communications. A few people know that he was also interested in image processing. In a paper entitled “Information theory in electron microscopy” ( Laboratory Investigation 14 (6), 801–807 (1965)), written in 1965, he examined the problem of image deblurring and was the first to suggest a method for edge enhancement based on principles widely accepted today and implemented in advanced image processing systems. In this paper his ideas are reviewed, their relation to contemporary methods is shown, and some simulations he could not do in 1965 are performed.
  @cite_45: The relative efficiency of any particular image-coding scheme should be defined only in relation to the class of images that the code is likely to encounter. To understand the representation of images by the mammalian visual system, it might therefore be useful to consider the statistics of images from the natural environment (i.e., images with trees, rocks, bushes, etc). In this study, various coding schemes are compared in relation to how they represent the information in such natural images. The coefficients of such codes are represented by arrays of mechanisms that respond to local regions of space, spatial frequency, and orientation (Gabor-like transforms). For many classes of image, such codes will not be an efficient means of representing information. However, the results obtained with six natural images suggest that the orientation and the spatial-frequency tuning of mammalian simple cells are well suited for coding the information in such images if the goal of the code is to convert higher-order redundancy (e.g., correlation between the intensities of neighboring pixels) into first-order redundancy (i.e., the response distribution of the coefficients). Such coding produces a relatively high signal-to-noise ratio and permits information to be transmitted with only a subset of the total number of cells. These results support Barlow’s theory that the goal of natural vision is to represent the information in the natural environment with minimal redundancy.
summary: Gabor functions @cite_61 , in the form of Gabor filters (GFs) @cite_32 and Gabor wavelets @cite_0 , are applied for a multitude of purposes in many areas of image processing and pattern recognition. Basically, the intentions for using GF and log-GF @cite_45 can be grouped into two categories: first, GF aim at enhancing images @cite_24 and the second common goal is to extract Gabor features obtained from responses of filterbanks. Typical fields of application include: