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