Gabor滤波器:Gabor Filters
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Let x=[x1 x2]T be the image coordinates. The impulse response of a Gabor filter g(x) is then given by:
The transfer function G(k) of a Gabor filter (Fourier transform of the impulse response) is given by:
In the figure shown above the transfer functions of the filters are choosen to overlap at a value of 0.5. Under this condition the DC component in the images and the frequency components lying above the frequency twice as large as the modulation freqency are damped by at least -54dB. Thus the filter results can be sub-sampled by a factor
The responses of the filters lying in the lower frequency half-plane need not to be calculated explicitely, because they can be generated by the complex-conjugation of the filter response lying on the other side of the origin. The following images show the original Lenna picture and Gabor filter results for different sampling factors. The size of the input image is choosen such that the filter results have always the same size after subsampling. This strategy leads to a multy resolution architecture which is also called Gabor pyramid. In the best resolution channel it is possible to extract fine image structures of a small image region whereas in the lower resolution levels coarse image structures can be extracted over large regions. This can be exploited in coarse-to-fine strategies [4,5]. On the left side of the following pictures the original input (sub) images and the superposed filter results for all orientations are shown. On the right side the subsampled filter result is shown for each orientation.
We use a set of Gabor filters as a preprocessing step for estimation of stereo disparity and extraction of oriented image features in the DEMONproject
from: http://homepages.inf.ed.ac.uk/rbf/CVonline/LOCAL_COPIES/TRAPP1/filter.html
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