The orientation field of a fingerprint image defines the local orientation of the
ridges contained in the fingerprint (see Figure 2.1). The orientation estimation is
a fundamental step in the enhancement process as the subsequent Gabor filtering
stage relies on the local orientation in order to effectively enhance the fingerprint
image. The least mean square estimation method employed by Hong et al. is used
to compute the orientation image. However, instead of estimating the orientation
block-wise, I have chosen to extend their method into a pixel-wise scheme, which
produces a finer and more accurate estimation of the orientation field. The steps
for calculating the orientation at pixel (i; j) are as follows: