Face Recognition Using Contourlet Transform and Multidirectional Illumination from a Computer Screen - Advanced Concepts for Intelligent Vision Systems - page 337

where are the subspace Contourlet coecients of the target and query

faces and n is the subspace dimension. The query image was assigned the iden-
tity of the one with the highest correlation. In the second approach, we used
the feature to subspace distance for classification and assigned the identity of
the nearest subspace to the query face. More specifically, we define face specific
subspaces comprising the subspace Contourlet coecients (i.e. columns of

t and q

F

)of
the face as the basis vectors. This is similar to Lee et al. [13] who defined face
specific subspaces using the images as basis vectors. The difference in our case is
that the face specific subspace is defined by features rather than the images. In
the third classification approach, we train a Support Vector Machine (SVM) [11]
using Radial Basis Function (RBF) kernel whose parameters are optimized using
the k-fold cross validation approach on the training data. All three classification
techniques gave similar identification rates however, the first technique consis-
tently gave much better verification results on all three databases. Therefore, we
will report results for classification based on correlation coecient.

4R su s

Three experiments were performed using our database (4347 images of 106 sub-
jects), the extended Yale B database (1710 images of 38 subjects) and the CMU-
PIE database (1344 images of 68 subjects). The number of different illumination
conditions for these databases are 23, 45 and 21 respectively. All images were
with frontal pose. Details of each experiment are given below.

4.1 Experiment 1

This experiment studies the recognition rate versus the number of subspace Con-
tourlet coecients. This experiment was first performed using the first session
(23 images of 106 subjects) of our database where five images per person were
used for training and the rest for testing. The experiment was then repeated by

100 100

90

95

80

90

70

85

60

80

50

75

40

Horizontal stripe
illumination

Vertical stripe illumination

70

0 50 100 150 200 250 300 350 2 4 6 8 10 12 14 16 18 20 22

Number of coefficients Image number

(a) (b)
Fig. 4. (a) Recognition rate vs. the number of subspace Contourlet coe cients. (b)
Recognition rates for individual images/illumination conditions (x-axis).