Exercise 4. The Eigenfaces method training 1. Aim: acquire skills ...

Exercise 4. The Eigenfaces method training
1. Aim: acquire skills concerning PCA training (creating of covariance matrix,
calculating its eigenvalues and eigenvectors using OpenCV library, acquiring
eigenfaces).
2. Function to be modified: TrainEigenfaces in Lab component. The following
arguments are passed to the function:
• pImgs – normalised images from the training set.
• nImgCount and nImgSize – number of images and their size (number of
pixels).
• pfEigenVectors – a two dimensional array, in which the eigenvectors
should be saved (they should be orthonormal and sorted in descending
order by the corresponding eigenvalues). The memory is allocated for
nEigenCount eigenvectors (each has length of nImgSize elements).
• pfEigenValues – an array to which the eigenvalues sorted in the descending
order should be saved. The memory is allocated for nEigenCount values.
• pEF – an array similar to pfEigenVectors, but its elements have BYTE
type. The eigenvectors should be written not in orthonormal form, but their
elements should be scaled to the 0-255 value range (so that they may be
saved as images).
• nEigenCount – number of eigenvectors which should be calculated.
3. The testing consists of two stages:
• PCA training is performed by the TrainEF.sf script. The training set is
specified by image directory and list. The MaxEigenCount variable is the
number of eigenvectors to be calculated (training is performed by the
TrainEigenfaces function). It is possible to set less dimensions of the face
space (utilise less eigenvectors for feature extraction) by the CutEigen
function – the dimensionality is set to EigenCount dimensions (it cannot be
larger than MaxEigenCount).
Attention: If the training is not performed correctly, the feature extraction
may result in application crash (it is not checked whether the eigenvectors
have sensible values). It is possible to overwrite the data files (acltw.dat
and aclww.dat) with their original versions. They are located in
c:\RT\install\data (the original are in lab5.zip).
• Tests of recognition effectiveness. When the training has been performed, a
recognition test may be performed (in the same way as in previous
exercises – using the recognition_test.sf script).
4. Tasks:
• calculate the average face and subtract it from every image in the training
set.
• calculate the covariance matrix of the training set.
• find the eigenvalues and eigenvectors of the covariance matrix. It is
recommended to use the cvmEigenVV function from OpenCV library. The
eigenvectors and eigenvalues calculated by this function are already sorted.

• scale the calculated eigenvectors to the pixel value range and save them to
pEF array. When the training is finished, the images from the array are
saved automatically to c:\RT\test\eigenfaces\Eigen. The conclusions drawn
from these images should be listed in the report.
• perform the recognition tests for various numbers of dimensions of the face
space. It is necessary to perform the training once (e.g. for 500 dimensions)
and then set the dimensionality using the CutEigen function in the
TrainEF.sf script. An optimal number of dimensions should be found.
Perform the training for the FeretB database and the recognition tests for
the FeretA database for 10, 20, ..., 200 dimensions. Draw the conclusions.
5. Remarks concerning OpenCV:
• there is a CvMat object which represents a matrix. It must be created using
the cvCreateMat function (it returns a pointer to the new object) and
deleted using the cvReleaseMat function. It is recommended to use cvmSet
and cvmGet functions to access the matrix data.
• the calculations should be performed for float data type (CV_MAT32F
matrix type).
• the precision coefficient eps should be set to 10 -3 .
• some examples are presented in Lab.cpp.
• more details can be found in the documentation (chapter 23, opencv.pdf
file).