Ridge Orientation

Here I'll be discussing about ridge orientation. Ridge orientation is also used as a parameter for ridge frequency, Gabor filtering and many other algorithms. Thus it is considered as a vital parameter as far as fingerprint recognition is concerned.

Ridge orientation field describes overall ridge flow pattern in the fingerprint image. The ridge orientation image represents an intrinsic property of the fingerprint image and defines invariant coordinates for ridges and valley in a local neighborhood .Since the ridges are of key interest in fingerprint image, ridge orientation field estimation has been incorporated in most of the fingerprint recognition algorithm as an initial and important stage. The approach used here for extracting the ridge orientation field is based on the average squared gradient method. There are different methods used for ridge orientation estimation of which the gradient method is more reliable and mostly used.  

Ridges run nearly parallel with each other in a local region of fingerprint and pixel-wise computational will be quite time consuming. Thus using block-wise approach does not affect the result, rather reduces the computational time. For the estimation of orientation field following steps were employed. Fingerprint image is divided into non-overlapping blocks. Gradient magnitude in x and y direction are estimated within each block using simple gradients or sobel mask. Let x and y be the gradients within a block centered at pixel. The ridge orientation of the image is estimated using the following expression:

Here theta is the least square estimation of local ridge orientation at the block centered at (i , j). Here, Gxx (i, j), Gyy (I, j) and Gxy (i, j) are the different squared gradients obtained from the gradients in x and y direction. Smoothening using the Gaussian filter is performed in a local neighborhood of the orientation field. The orientation image is then converted into continuous vector field which is defined as:

Where phi_x and phi_y are the x and y component of vector field respectively. After vector filed has been computed then Gaussian smoothing is performed as follows:

Where G is a Gaussian low pass filter of size wg * wg. The final smooth orientation is obtained as:

The orientation filed obtained using the above method shown in the Fig. 1.2(b) and (d). The Block size could be of 8*8, 16*16 and 32*32.  Here we have used the block size of 20*20 and 40*40 depending upon the image size and requirement of the topic.

Fig 1:Ridge orientation output (a) and (c) input image;(b) and (d) ridge orientation image of (a) and (c)