Ridge Orientation

First of all, since minutiae points detection has to be trainned using fingerprints, I separate evenly my database into the trainning set and the testing set (about 600 prints each). I then separate the trainning set into 2 subsets, which will allow me to do trainning-testing cycles without using the original testing set. The fingerprints were downloaded from the FVC (Fingerprint Verification Competition). Of course, I will not use the testing set until the end of the project.

Then, the first set in minutia detection is to estimate rigde field orientation. This allows to find the local orientation of the ridges. In the handbook of fingerprint recognition, several methods are presented. I programed the first one, which is directly inspired from CSE166.

Using Sobel filter, I compute the gradient in x and y of the image (Ix and Iy). Then, for each pixel in the image, I can compute the orientation and the norm of the gradient and plot it. The orientation is a number between 0° and 180° representing the angle from the x axis. Since it is influenced by noise and difficult to plot, we need to compute an average inside a small window (let's say 8x8). A trick is used to average the angles: because we don't want that the average of 10° and 170° be 90°, the angles are doubled. Averaging 20° and 340° gives 180°, which is the right direction angle (same direction as 0°).

One thing to notice is that the orientation given by the formula atan(Iy/Ix), is not the direction of the ridge. We need to add Pi/2 to it.

I had some problems to plot the direction of the minutiae points. I was first testing it on a circle image:



After I got it working right, I then tryed it on a fingerprint using a 4x4 window. Here are the original print, the direction field thresholded, and height map (the norm field).





Some issues to test:
- what is the right size of the small window?
- Using an other method, based on SVD on the covariance matrix of the gradient.