Commend I used in order to generate eigenfaces and the userbase.

main --eigenface 10 25 25 faceImages\nonsmiling_cropped\facelist.txt faces\eigenface_10.face
main --constructuserbase faces\eigenface_10.face faceImages\nonsmiling_cropped\facelist.txt userbase\userbase_10.user

Average Face :

10 Eigenfaces :

1. Describe the trends you see in your plots. Discuss the tradeoffs; how many eigenfaces should one use? Is there a clear answer?
- As the number of eigenfaces used is increasing, the number of correct matches is increasing, too. Between 6 and 11, there is a bump. I think matches luckly occured with the small number of the eigenfaces. From 12, the trend is pretty stable, and the matches don't increase dramatically. I believe that about 15 eigenfaces are good enough for face detection since less-than-10 eigenfaces can make a unexpected result. However, this is not the perfect answer because more eigenfaces are used, more acccute result we can gain.

2. You likely saw some recognition errors in step 3; show images of a couple. How reasonable were the mistakes? Did the correct answer at least appear highly in the sorted results?
- Faces below are major recognition errors. They can be made pretty reasonably.

: Their skin color is pretty similar, and this make the sturation of their grayscale images similar. Also, both are wearing glasses.
0: faceImages\nonsmiling_cropped\neutral-17; MSE: 86396.7
1: faceImages\nonsmiling_cropped\neutral-13; MSE: 106253
2: faceImages\nonsmiling_cropped\neutral-19; MSE: 119248
3: faceImages\nonsmiling_cropped\neutral-25; MSE: 127003
4: faceImages\nonsmiling_cropped\neutral-4; MSE: 146594

: The size of the left person's eyes with his glasses and the right person's eyes are almost same. And, They both have mustache. I think the two things the reason why they are matched.
0: faceImages\nonsmiling_cropped\neutral-1; MSE: 86398.2
1: faceImages\nonsmiling_cropped\neutral-24; MSE: 99739.4
2: faceImages\nonsmiling_cropped\neutral-27; MSE: 119183
3: faceImages\nonsmiling_cropped\neutral-4; MSE: 122385
4: faceImages\nonsmiling_cropped\neutral-11; MSE: 131394
5: faceImages\nonsmiling_cropped\neutral-22; MSE: 131687
6: faceImages\nonsmiling_cropped\neutral-16; MSE: 135354
7: faceImages\nonsmiling_cropped\neutral-7; MSE: 136283
8: faceImages\nonsmiling_cropped\neutral-12; MSE: 141507
9: faceImages\nonsmiling_cropped\neutral-8; MSE: 152878
10: faceImages\nonsmiling_cropped\neutral-17; MSE: 157397
11: faceImages\nonsmiling_cropped\neutral-3; MSE: 158157
12: faceImages\nonsmiling_cropped\neutral-23; MSE: 161850
13: faceImages\nonsmiling_cropped\neutral-15; MSE: 164026

: Somehow, my face and his face on the right look similar in the pictures. The location of the eyeblows is pretty close.
0: faceImages\nonsmiling_cropped\neutral-27; MSE: 14947.6
1: faceImages\nonsmiling_cropped\neutral-20; MSE: 36609.8
2: faceImages\nonsmiling_cropped\neutral-24; MSE: 55243.2
3: faceImages\nonsmiling_cropped\neutral-12; MSE: 69795.9
4: faceImages\nonsmiling_cropped\neutral-26; MSE: 71657.8

The number of the correct matches is 23 out of 33, which is about 70%. This is less than 79%, which is your expectation. However, I believe this result is not too bad.

main --findface test_img/elf.tga faces/eigenface_10.face 0.45 0.55 0.01 crop 1 test_img/elf_output.tga

main --findface test_img/mypic.tga faces/eigenface_10.face 0.01 0.2 0.02 crop 1 test_img/mypic_output.tga

main --findface test_img/group.tga faces/eigenface_10.face 0.7 0.9 0.02 mark 3 test_img/group_output.tga

main --findface test_img/group_ms.tga faces/eigenface_10.face 0.3 0.5 0.02 mark 11 test_img/group_ms_output.tga

1. What min_scale, max_scale, and scale step did you use for each image?
- Elf Image - min:0.45, max:0.55, step:0.01
- My Picture - min:0.01, max:0.2, step:0.02
- Group Image - min:0.7, max:0.9, step:0.02
- Another Group Image - min:0.3, max:0.5, step:0.02

2. Did your attempt to find faces result in any false positives and/or false negatives? Discuss each mistake, and why you think they might have occurred.
- At the last image, there are some false negatives. Most false Negatives happened on faces of people who are wearing sun glasses or glasses, or having mustache above upper lip. That is because the average face is generated from our faces, and nobody is wearing sunglasses and has mustache above upper lip.

1. What MSE thresholds did you try? Which one worked best? What search method did you use to find it?
- I tried many numbers between 10000 and 100000. The best number is 40000; the number of correct matches is 10. The search method is as follows.
First, I computed all mse of correct face and the best mse of someone else's face.
Secondly, I inserted the data into Excel and made a simple script to check false positive and false nagative with the given threshold.
Third, I tried many times and found that 40000 is the best threshold.

2. Using the best MSE threshold, what was the false negative rate? What was the false positive rate?
With 40000, the number of false positive is 10, and the number of false negative is 17.