Gabor Filtering

Filters are incorporated to get the ridge map used for removal of spurious pore that are not located on the fingerprint ridge. Gabor filters have been used in applications like texture segmentation, edge detection, retina identification and image coding and image representation. Gabor filter can be obtained by modulating a sinusoid of particular frequency and orientation with a Gaussian envelope. Gabor filter is a band bass filter which has both frequency selective and orientation selective properties. Thus by tuning the band pass filter to the corresponding frequency and orientation of sinusoidal wave of ridge and valley, the undesired noise can be removed resulting in a pure ridge valley structure. Gabor filter is used to extract the ridge valley structure.  The even-symmetric Gabor filter is the real part of the Gabor function, which is given by a cosine wave modulated by a Gaussian. The odd-symmetric Gabor filter is the imaginary part of the Gabor function, which is given by a sine wave modulated by a Gaussian. Even-symmetric Gabor filter for the image enhancement  has the general form:

Where delx and dely  are the constants of the Gaussian envelope along x and y axes respectively. F is the frequency of the of sinusoidal plane wave and  is the orientation of the Gabor filter. The standard deviations of the Gaussian envelope and  has to be chosen carefully. For larger values of standard deviations filter will be robust to noise and will create more spurious ridge valley. On the other hand for smaller values filter will be less effective in removing noise and will create less spurious ridge valley. 

The wavelength is reciprocal of the frequency. Thus the wavelength of the cosine factor of the Gabor filter kernel and herewith is the preferred wavelength of this filter. Its value is specified in pixels. Valid values are real numbers equal to or greater than 2. The value lambda = 2 should not be used in combination with phase offset because in these cases the Gabor function is sampled in its zero crossings. In order to prevent the occurrence of undesired effects at the image borders, the wavelength value should be smaller than one fifth of the input image size. The parameter theta specifies the orientation of the normal to the parallel stripes of a Gabor function. Its value is specified in degrees. Valid values are real numbers between 0 and 360. 

Two other parameters i.e. phase offset and aspect ratio can also be employed. The phase offset of the cosine factor is specified in degrees. Values 0 and 180 degree corresponds to ‘center on’ and ‘center off ’ function. The spatial aspect ratio specifies the ellipticity of the support of Gabor function. For vale 1 support is circular and for values less than 1 support is elongated in orientation. The values of delx and dely were set to 2 and 4 respectively. The enhanced image is obtained as follows:

 

Fig: Gabor Filtering; (a) Input image; b) Binary Gabor filtered image