Master Thesis - Department of Computer Science

F
DIFS
DFFS
F
(a) (b)
F
1 L
Figure 2.4: (a) Decomposition of R M into the principal subspace F and its orthogonal
component ¯ F for a Gaussian density. (b) A typical eigenvalue spectrum and its
division into the two orthogonal subspaces.
estimated in a similar way in extra-personal subspace computed from SE.
Fig. 2.4(a) shows the decomposition of ∆ into DIFS and DFFS. An alter-
native maximum likelihood (ML) measure, using the intra-personal likelihood
S ′ (∆) = P (∆|ΩI) is as effective as MAP measure. In face recognition, all pa-
rameters in Equation 2.11 are same except dF (∆) and ε 2 (∆). So, it is equivalent
to evaluate the distance,
F
DI = dF (∆) + ε 2 (∆)/ρ. (2.12)
• 2D-PCA (Two Dimensional Principal Component Analysis): The 2D-
PCA technique [141] is based on 2D image matrices instead of 1D vectors. The
image covariance matrix is constructed directly from the original image. Let A
denote the image with m rows and n columns. The image matrix is projected
on to n-dimension column vector x as,
y = Ax. (2.13)
where y is an m dimensional column vector called the projected feature vector
of the image A. Let Gt is the image covariance matrix and is represented as,
Gt = E[(A − Ā)T (A − Ā)] (2.14)
17
M