This repository contains the code for a face recognition system that combines three popular algorithms: PCA, LDA, and ICA.
New team members should look at CONTRIBUTING.md to learn about our work-flow, especially those who are unfamiliar with Github.
Usage for the face recognition system:
Usage: ./face-rec [options]
Options:
--train DIRECTORY create a database from a training set
--rec DIRECTORY test a set of images against a database
--lda run PCA, LDA
--ica run PCA, ICA2
--all run PCA, LDA, ICA2
To run an automated test (k-fold cross-validation) with the ORL face database:
# test once with 1.pgm removed from each class
./cross-validate.sh 1 1
# repeat with each index removed (takes much longer)
./cross-validate.sh 1 10
To test MATLAB code with ORL database:
./create-sets.sh 1 10
./convert-images.sh test_images orl_faces_ppm pgm ppm
# run MATLAB/LDA/example.m
# run MATLAB/PCA/example.m
This software currently supports a subset of the Netpbm format, particularly with PGM and PPM images.
Images should not be stored in this repository! Instead, images should be downloaded separately. Face databases are widely available on the Internet, such as here and here. I am currently using the ORL database.
To convert JPEG images to PGM with ImageMagick:
convert-images.sh [src-folder] [dst-folder] jpeg pgm
| Function Name | PCA | LDA | ICA | Verification Status |
|---|---|---|---|---|
| Constructors, Destructor | ||||
| m_initialize | x | x | x | Verified |
| m_identity | x | Verified | ||
| m_zeros | x | Verified | ||
| m_copy | x | Verified | ||
| m_free | x | x | x | Verified |
| Input/Output | ||||
| m_fprint | x | Verified | ||
| m_fwrite | x | Verified | ||
| m_fscan | Verified | |||
| m_fread | x | Verified | ||
| m_image_read | x | Verified | ||
| m_image_write | x | Verified | ||
| Getters | ||||
| m_covariance | x | Verified w/ BLAS | ||
| m_eigen | x | x | Verified w/ BLAS | |
| m_eigen2 | (x) | Not Verified | ||
| m_inverse | x | x | Verified w/ BLAS | |
| m_mean_column | x | x | x | Verified |
| m_product | x | x | x | Verified w/ BLAS |
| m_sqrtm | x | Verified w/ BLAS | ||
| m_transpose | x | x | x | Verified |
| Mutators | ||||
| m_add | x | x | Verified | |
| m_elem_mult | x | x | Verified | |
| m_shuffle_columns | x | Verified | ||
| m_subtract | x | x | Verified | |
| m_subtract_columns | x | Verified |
Much of the code in this project depends on BLAS and LAPACK. In order to run it properly, it is necessary to install the following libraries:
libblas-dev (1.2.20110419-5)
libblas3 (1.2.20110419-5)
libgfortran3 (4.8.1-10ubuntu9)
liblapack-dev (3.4.2+dfsg-2)
liblapack3 (3.4.2+dfsg-2)
liblapacke (3.4.2+dfsg-2)
liblapacke-dev (3.4.2+dfsg-2)
Documentation for BLAS and LAPACK consists mostly of the documentation for each function. For any given BLAS/LAPACK function, you will want to reference two documents:
- The Fortran source file http://www.netlib.org/lapack/double/
- The cblas/lapacke header http://www.netlib.org/blas/cblas.h http://www.netlib.org/lapack/lapacke.h
The Fortran source provides documentation for function parameters, and the C headers show how to order those arguments with the C interface.
sudo apt-get install libblas-dev liblapacke-dev
Confirmed to run on Mac OS 10.11.1
Download LAPACK 3.5.0 http://www.netlib.org/lapack/
Download BLAS 3.5.0 http://www.netlib.org/blas/
(10.10 - 10.11) Download gfortran 5.2 http://coudert.name/software/gfortran-5.2-Yosemite.dmg
(10.7 - 10.9) Download gfortran 4.8.2 http://coudert.name/software/gfortran-4.8.2-MountainLion.dmg
# in BLAS directory
make
sudo cp blas-LINUX.a /usr/local/lib/libblas.a
# in LAPACK directory
mv make.inc.example make.inc
# set BLASLIB in make.inc line 68 equal to ‘/usr/local/lib/libblas.a’
make
sudo cp liblapack.a /usr/local/lib
Here is the working flow graph for the combined algorithm:
m = number of dimensions per image
n = number of images
train: X -> (a, W', P)
X = [X_1 ... X_n] (image matrix) (m-by-n)
a = sum(X_i, 1:i:n) / n (mean face) (m-by-1)
X = [(X_1 - a) ... (X_n - a)] (mean-subtracted image matrix) (m-by-n)
W_pca' = PCA(X) (PCA projection matrix) (n-by-m)
P_pca = W_pca' * X (PCA projected image matrix) (n-by-n)
W_lda' = LDA(W_pca, P_pca) (LDA projection matrix) (n-by-m)
P_lda = W_lda' * X (LDA projected image matrix) (n-by-n)
W_ica' = ICA2(W_pca, P_pca) (ICA2 projection matrix) (n-by-m)
P_ica = W_ica' * X (ICA2 projected image matrix) (n-by-n)
recognize: X_test -> P_match
a = mean face (m-by-1)
(W_pca, W_lda, W_ica) = projection matrices (m-by-n)
(P_pca, P_lda, P_ica) = projected image matrices (n-by-n)
X_test = test image (m-by-1)
P_test_pca = W_pca' * (X_test - a) (n-by-1)
P_test_lda = W_lda' * (X_test - a) (n-by-1)
P_test_ica = W_ica' * (X_test - a) (n-by-1)
P_match_pca = nearest neighbor of P_test_pca (n-by-1)
P_match_lda = nearest neighbor of P_test_lda (n-by-1)
P_match_ica = nearest neighbor of P_test_ica (n-by-1)
PCA: X -> W_pca'
X = [X_1 ... X_n] (image matrix) (m-by-n)
L = X' * X (surrogate matrix) (n-by-n)
L_ev = eigenvectors of L (n-by-n)
W_pca = X * L_ev (eigenfaces) (m-by-n)
LDA: (W_pca, P_pca) -> W_lda'
X = P_pca (n-by-n)
c = number of classes
n_i = size of class i
U_i = sum(X_j, j in class i) / n_i (n-by-1)
u = sum(U_i, 1:i:c) / c (n-by-1)
S_b = sum((U_i - u) * (U_i - u)', 1:i:c) (n-by-n)
S_w = sum(sum((X_j - U_i) * (X_j - U_i)', j in class i), 1:i:c) (n-by-n)
W_fld = eigenvectors of (S_b, S_w) (n-by-n)
W_lda' = W_fld' * W_pca' (n-by-m)
ICA2: (W_pca, P_pca) -> W_ica'
X = P_pca (n-by-n)
W_z = 2 * Cov(X)^(-1/2) (n-by-n)
X_sph = W_z * X (n-by-n)
W = (train with sep96) (n-by-n)
W_I = W * W_z (n-by-n)
W_ica' = W_I * W_pca' (n-by-m)