Question: Write a program that inputs a 3  3 matrix consisting of orientation field values and de-termines if the matrix corresponds to a singular point or not. If it corresponds to a singular point, determine if it is a core (loop) or a delta point.

2. [25 points] The ridge pattern in a local area of a finger can be approximated by a cosine wave:

w(x, y) = Acos[2f0(x cos + y sin)].

Here, w(x, y) denotes the pixel intensity at location (x, y). Generate and display ridge patterns, each of size 600600, at the following orientation () values: 0, 45, 90, 135. You may set A= 80 and f0 = 0.01.

Now repeat the exercise, with A = 160 and f0 = 0.01; A = 80 and f0 = 1; and A = 80 and f0 = 10. What are your observations?

3. [25points]Basedonthegradientmapmethod(basedonedgefilters)discussedinclass,writeaprogram to compute the orientation field of a fingerprint image. The orientation should be computed for each pixel location. (So the number of rows and columns in the orientation field matrix should be the same as that of the image). Use the Sobel Operator to compute the x and y gradient value at each pixel location. Use a window size of 9  9 when computing the orientation field value associated with a pixel location (so value of k is 4). Run your program on the set of 10 fingerprint images available here.

Use the drawOrientation.m program (which is in Matlab) to display the orientation field as an overlay on the original fingerprint image. Include these overlay images in your submission.

Note: [1] You may not be able to compute the gradient values and the orientation field values on the border pixels. You may set those values to 0 or some other constant number in the orientation field matrix. [2] You can use any programming language to compute the orientation field. You can then use Matlab to display the orientation field based on the drawOrientation.m program.

4. [30 points] Recall that a minutiae set, M, is a set of 3-tupled values M = f(xi, yi,i)g, i = 1,2...NM, where (xi, yi) is the location of minutiae i, i is its orientation, and NM is the total number of minutiae in M. Implement the minutiae matching method discussed in class (RANSAC method) that compares two minutiae sets M1 and M2, and outputs the transformation parameters tx, ty and t relating M2 with M1, along with the number of matching minutiae pairs (you can use a tolerance value of 10 when determining matching minutiae pairs).

You are given a set of 10 minutiae files pertaining to 5 different fingers (the orientation value is denoted in “degrees"). Run your program on all possible pairings of the minutiae files and present a table listing the results in the following format: First File Name (M1), Second File Name (M2), tx, ty, t, Number of Matching Minutiae Pairs (s). There will be 10 genuine pairings and 80 impostor pairings. For example, the first line of the table will be:

user001_1.minpoints user001_2.minpoints -65 -6 0.052360 19