In this project, we applied PCA to generage eigenfaces from the set of user faces and use Jacobi::jacobi() method for fiding the eignvector.
My problem of this project is how to find faces on the given image and given number of faces. It took me really long time to do it but turned out I couldn't find the correct faces and also I cannot find as many faces as the given number gave.
This project is interesting one. I have seen on the digital camera have this tool to figure out faces on the camera before to take the picture, but after did this project I have known how the camera figure out faces. Also, I found that the Jacobi::jacobi() method is useful since we use it for 2 projects in this class.
The project is structured as follows:
- Faces::eigenFaces - Applies PCA to generate eigenfaces from the set of user faces and use Jacobi::jacobi() method to find the eigenvector.
- EigFaces::projectFace - Projects a given face onto the face space to generate a vector of n eigenfaces.
- EignFaces::construcFace - Constructs a given face from a vector of coefficients.
- EignFaces::isFace - Decides whether a given image is a face by computing the Mean Square Error (MSE) between projection and original. Returns true if a given image is a face and falst otherwise.
- EignFaces::verifyFace - Decides if a face is a given user's given by coefficients computed from another face image of that user.
- EignFaces::recognizeFace - Finds the best match of the first user in the userbase by sorting the MSE of each user in the userbase.
- EignFaces::findFace - Searches on a given image and finds the first n best matched faces.
Average face:
main --eigenfaces 10 25 25 nonsmiling_cropped/list.txt nosmile_eig.face
Plot the number of faces correctly recognized versus the number of eigenfaces used:
See the plot, the number of faces recognized correctly is increasing from the number of eigenfaces are 1 to 5 and after that the number of faces recognized correctly stays almost the same between 22 & 24. It makes sense because if you have more samples, then we should the result more correct. We should use at least 5 eigenfaces but the best one should be 33 eigenfaces which is all the faces.
Yes, there is a clear answer.
Faces cannot recognized correctly:
The reason might be some of faces above have glasses and some are weird faces. Also, some faces have pixels color are almost the same for the whole face; it is hard to figure out whether it is a face or not.
Yes, the correct answer at least appear highly in the sorted results. Most of them are in the first 4 images appear in the sorted results.
Commands
main --eigenfaces 6 25 25 nonsmiling_cropped/list.txt nosmile_eig_6.face
main --constructuserbase nosmile_eig_6.face nonsmiling_cropped/list.txt nosmile_6.user
main --verifyface smiling_cropped/smiling-1.tga nosmile_6.user nonsmiling_cropped/neutral-1 nosmile_eig_6.face 60000.0
main --verifyface smiling_cropped/smiling-2.tga nosmile_6.user nonsmiling_cropped/neutral-1 nosmile_eig_6.face 60000.0
...
main --verifyface smiling_cropped/smiling-33.tga nosmile_6.user nonsmiling_cropped/neutral-1 nosmile_eig_6.face 60000.0
main --verifyface smiling_cropped/smiling-1.tga nosmile_6.user nonsmiling_cropped/neutral-2 nosmile_eig_6.face 60000.0
main --verifyface smiling_cropped/smiling-2.tga nosmile_6.user nonsmiling_cropped/neutral-2 nosmile_eig_6.face 60000.0
...
main --verifyface smiling_cropped/smiling-33.tga nosmile_6.user nonsmiling_cropped/neutral-2 nosmile_eig_6.face 60000.0
...
main --verifyface smiling_cropped/smiling-1.tga nosmile_6.user nonsmiling_cropped/neutral-6 nosmile_eig_6.face 60000.0
main --verifyface smiling_cropped/smiling-2.tga nosmile_6.user nonsmiling_cropped/neutral-6 nosmile_eig_6.face 60000.0
...
main --verifyface smiling_cropped/smiling-33.tga nosmile_6.user nonsmiling_cropped/neutral-6 nosmile_eig_6.face 60000.0
MSE thresholds that I tried: 60000, 35000, 40000
From all the thresholds above, 40000 is the one worked best even it cannot make all the smiling face with its neutral face correct but it removes most the smiling faces which are not the same with its neutral face.
Here is all the MSE values of all 6 smiling faces with its neutral face:
smiling-1.tga & neutral-1: 15,978
smiling-2.tga & neutral-2: 39,669.3
smiling-3.tga & neutral-3: 11,347.4
smiling-4.tga & neutral-4: 197,721
smiling-5.tga & neutral-5: 76,265.1
smiling-16.tga & neutral-6: 7189.94
I ran all the commands above and see all the MSE values to see which thresholds will work best.
Using the best MSE threshold, the false negative rate is: 1/198 and the false positive is: 1/99
Go through this process, I feel like no threshold makes the verifyFace method works for 100% correctly. I think it is possible to make it work 100% correctly because people can figure out it so I think computer can do it as well.
