Ridge Frequency

The Fingerprint ridge frequency along with the ridge orientation serves as parameters for image filtering in the filtering section. Ridge frequency is the measure of number of pixels located between the two consecutive peaks, computed over a rotated block which is of larger dimension than the block of image.

The block rotation is specified by the ridge orientation angle theta.

The normalized fingerprint image is first divided into blocks of dimension w*w. An oriented window of dimension l*w is computed for each block centered at pixel (i,j). This oriented window is used for getting signature X[0],X[1],X[2]....X[l-1] of the ridge and valley, which is computed for each block centered at pixel (i,j) within an oriented window. Computation of  X signature is based on the following expression.

The frequency of the ridge and valley is estimated from the x-signature as the x-signature for each block forms a sinusoidal wave. Let the average number of pixel between the two consecutive peaks be T(i,j ).

Then the frequency is defined as the reciprocal of T(i,j) as F(i,j) = 1/T(i,j).

The blocks in which minutiae or singular points appear or ridge endings are corrupted do not form a well define sinusoidal shaped wave. Also for a given fingerprint image  scanned at fixed resolution, the value of the frequency of the ridge and valleys in a local neighborhood lies in a certain range. If no consecutive peaks can be detected then a value of -1 is assigned to the frequency. This is done to differentiate it with the other valid blocks. No peaks can be obtained from the singular points, minutia or corrupted region of fingerprint. Thus the frequencies of these blocks are interpolated from the neighboring blocks using neighboring interpolation.  For each block with the frequency value of -1 centered at (i, j) the interpolation is performed as follows:

 

 

Where Wg is the Gaussian kernel of size wg = 7 with mean and variance of zero and nine respectively. The resultant value is interchanged with the F and the step is repeated for all the blocks of image. In order to remove the noise in F` a low pass filter can be used.

 

Here Wl is a two dimensional low pass filter with filter size of wl = 7. Above equation is the convolution between the low pass filter and the frequency of fingerprint image.