Question: Consider an experiment involving the face images from N different individuals. Assume that each individual, Pi, provides mi face images, i = 1,2...N. Derive expressions for the number of genuine scores and number of impostor scores that will be generated by a symmetric face matcher.

1. [5 points] Consider an experiment in which you are provided the face images of 5 subjects. The number of images collected from each subject is tabulated below:

Based on these numbers, what is the number of genuine scores and the number of impostor scores that can be generated using an asymmetric face matcher? Explain your answer.

2. [10 points] Consider an experiment involving the face images from N different individuals. Assume that each individual, Pi, provides mi face images, i = 1,2...N. Derive expressions for the number of genuine scores and number of impostor scores that will be generated by a symmetric face matcher.

3. [15 points] Let B1, B2 and B3 denote 3 different fingerprint matchers that are used to generate genuine and impostor match scores on a fixed set of fingerprint images. The mean () and variance (2) of the

genuine and impostor score distributions resulting from the 3 different matchers are tabulated below.

Based on the score statistics, determine which one of the three matchers has performed well and which one has performed the worst. Provide adequate numerical justification.

4. [70 points] This exercise involves generating match score distributions and DET curves for two different modalities/matchers - fingerprint and hand. The fingerprint scores are similarity-based, while the hand scores are distance-based. The set of scores can be accessed here.

(a) [5 points] How many genuine and impostor scores are available for the fingerprint matcher and the hand matcher?

(b) [5 points] What are the maximum and minimum scores generated by each matcher?

(c) [5 points] Compute and report the mean and variance of the (a) genuine scores and (b) impostor scores for each matcher.

(d) [10 points] Compute and report the d-prime value for each matcher.

(e) [10points]Foreachmatcher, plotthehistogramofgenuineandimpostorscoresinthesamegraph. So there will be two graphs - one for the fingerprint matcher and the other for the hand matcher.

(f) [10 points] Write a program that inputs a threshold value, , for each matcher and outputs the False Match Rate (FMR) and False Non-match Rate (FNMR) at that threshold. Use this program to compute the FMR and FNMR for the following scenarios:

i. Fingerprint Matcher:  = 45 ii. Hand Matcher:  = 45

(g) [15 points] Based on the program designed in (4f), write another program that inputs a set of genuine scores and impostor scores and plots the Detection Error Tradeoff (DET) Curve. Use this program to plot the DET curve for both the matchers and report the Equal Error Rate (EER) and the Area Under the Curve (AUC).

(h) [5 points] For each of the two matchers determine what the FNMR is at (a) FMR = 10%; (b) FMR = 5%; (c) FMR = 1%. You can determine these values from the DET curve.

(i) [5 points] Which matcher, in your opinion, has performed well? Justify your answer.