Gabor filters are cool

A picture worth more than a thousand words, so I am going to explain briefly what I did, and then show the results.

- I tryed SVD on the covariance matrix of the gradient versus averaging the gradient, and SVD gives better results. It provides an estimation of the reliability of the orientation (using the ratio of the two eigenvalues). The ridge orientation is given by the orientation of the vector having the smallest eigenvalue (which is positive because the covariance matrix is symetric).

- I change the color legend used to plot the orientation. HSV color space is used: Hue for the orientation (0°=red, 120°=green and so on), Saturation is maximum (full color), and Value is the max eigenvalue normalised in the overall image (I notice writting this post that it needs to be the ratio of the eigenvalues instead). Orientation directions are the same length on the picture.

- In order to get the orientation for each pixel in the image, orientation is bilinearly interplolated using the orientation computed on the small windows.

- Finally, I applied Gabor filters to enhance the fingerprint. For each pixel, given the orientation, I compute the Gabor filter having that direction (it is really expensive, but I was lazy to precompute a bank of filters). This gives a pretty neat nearly black and white image, where ridges are clearly visible. As the authors of "the handbook of fingerprint recognition" advised, I fixed the standard deviation of the gaussian in x and y to 4. I used a sine wave instead of a cosine (against what is used in the book), so that the average value of the filter is 0. The frequency of the sine wave can be set, but I did not estimate the local ridge frequency. I will do that later on.

Here is the picture summing up the results: