 Example of a two-dimensional Gabor filter A Gabor filter is a linear filter whose impulse response is defined by a harmonic function multiplied by a Gaussian function. Because of the multiplication-convolution property, the Fourier transform of a Gabor filter's impulse response is the convolution of the Fourier transform of the harmonic function and the Fourier transform of the Gaussian function. Image File history File links Gabor_filter. ...
Image File history File links Gabor_filter. ...
The word linear comes from the Latin word linearis, which means created by lines. ...
Television signal splitter consisting of a hi-pass and a low-pass filter. ...
In the language of mathematics, the impulse response of a linear transformation is the image of Diracs delta function under the transformation. ...
In mathematics, mathematical physics and the theory of stochastic processes, a harmonic function is a twice continuously differentiable function f : U → R (where U is an open subset of Rn) which satisfies Laplaces equation, i. ...
Gaussian curves parametrised by expected value and variance (see normal distribution) A Gaussian function (named after Carl Friedrich Gauss) is a function of the form: for some real constants a > 0, b, and c. ...
In mathematics, the Fourier transform is a certain linear operator that maps functions to other functions. ...
In mathematics and, in particular, functional analysis, convolution is a mathematical operator which takes two functions f and g and produces a third function that in a sense represents the amount of overlap between f and a reversed and translated version of g. ...
 where  and  In this equation, λ represents the wavelength of the cosine factor, θ represents the orientation of the normal ot the parallel stripes of a Gabor function in degrees, ψ is the phase offset in degrees, and γ is the spatial aspect ratio, and specifies the ellipticity of the support of the Gabor function.
Gabor filters are directly related to Gabor wavelets, since they can be designed for number of dilations and rotations. However, in general, expansion is not applied for Gabor wavelets, since this requires computation of biorthogonal wavelets, which may be very time-consuming. Therefore, usually, a filter bank consisting of Gabor filters with various scales and rotations is created. The filters are convolved with the signal, resulting in a so-called Gabor space. This process is closely related to processes in the primary visual cortex. The Gabor space is very useful in e.g., image processing applications such as iris recognition. Relations between activations for a specific spatial location are very distinctive between objects in an image. Furthermore, important activations can be extracted from the Gabor space in order to create a sparse object representation. In mathematics, wavelets, wavelet analysis, and the wavelet transform refers to the representation of a signal in terms of a finite length or fast decaying oscillating waveform (known as the mother wavelet). ...
In mathematics, wavelets, wavelet analysis, and the wavelet transform refers to the representation of a signal in terms of a finite length or fast decaying oscillating waveform (known as the mother wavelet). ...
UPIICSA IPN - Binary image In the broadest sense, image processing is any form of information processing for which both the input and output are images, such as photographs or frames of video. ...
Iris recognition is one of the most accurate methods of biometric identification. ...
To visualize a 2-dimensional Gabor filter and the resulting activations after convolving it with an image, the on-line Gabor application on http://matlabserver.cs.rug.nl can be useful.
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