Project 2
CSE 402 - Biometrics and Pattern Recognition
Instructor: Dr. Arun Ross
Due Date: November 11, 2022 (11:00pm ET)
Total Points: 100
Note:
1. You are permitted to discuss the following questions with others in the class. However, you must write up
your own solutions to these questions. Any indication to the contrary will be considered an act of academic
dishonesty. Copying from any source constitutes academic dishonesty.
2. A neatly typed report is expected (alternately, you can neatly handwrite the report and then scan it). The
report, in PDF format, must be uploaded in D2L by November 11, 11:00 pm. Late submissions will not be
graded. In your submission, please include the names of individuals you discussed this assignment with
and the list of external resources (e.g., websites, other books, articles, etc.) that you used to complete the
assignment (if any).
3. When solving equations or reducing expressions you must explicitly show every step in your computation
and/or include the code that was used to perform the computation. Missing steps or code will lead to a
deduction of points.
4. Code developed as part of this assignment must be (a) included as an appendix to your report or inline
with your solution (in the report), and also (b) archived in a single zip file and uploaded in D2L. Including
the code without the outputs or including the outputs without the code will result in deduction of points.
5. Please submit the report (PDF) and the code (Zip file) as two separate files in D2L.
1. [20 points] 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.
Input the following matrices to your program and report the output.
1.
10 15 -10
12 0 15
13 12 -5
2.
45 90 -50
50 0 -45
5 0 -5
3.
50 0 -50
75 0 -70
85 90 -85
1
4.
45 2 -50
90 0 90
-50 2 50
2. [25 points] The ridge pattern in a local area of a finger can be approximated by a cosine wave:
w(x , y) = Acos [2pi f0(x cosθ + y sinθ )] .
Here, w(x , y) denotes the pixel intensity at location (x , y). Generate and display ridge patterns, each
of size 600× 600, at the following orientation (θ) 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. [25 points] Using the gradient estimation method discussed in class (based on edge filters), write a
program 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] It
would be better to use the atan2 function rather than the atan function. [3] 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 = {(x i , yi ,θi)}, i = 1, 2 . . . NM ,
where (x i , yi) is the location of minutiae i, θi 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 t x , t y and tθ 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), t x , t y , tθ , 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