Master Thesis - Department of Computer Science

Fig. 3.1 shows the block diagram of the proposed method. Fig. 3.1 (a) shows
the generation of the subband face. The face image is decomposed into several sub-
bands using the analysis filter of 2D Discrete Wavelet Transform (2D-DWT). The
2D-DWT is successively applied to the approximations to obtain a dyadic decom-
position [38]. The subbands thus obtained can be used to reconstruct the original
face using the inverse DWT (by synthesis filters). The subband face is obtained from
selected subbands by partial reconstruction of the original face. Fig. 3.1 (b) shows
that the subband face is transformed from image-space to feature-space by applying
subspace methods (PCA , LDA, 2D-PCA, 2D-LDA and DCV). The details of the
subspace methods used for integrating with subband face representation are provided
in section 2.1.1.1. The features thus obtained are matched using the nearest neighbor
strategy.
3.2 Subband Face Representation
A set of suitable wavelet subbands are selected to generate the subband face using
IDWT, for recognition using PCA, LDA, 2D-PCA, 2D-LDA and DCV. The method
of reconstructing a subband face is described in the following.
3.2.1 Wavelet Decomposition
The wavelet transform [38] is expressed as a decomposition of a signal f(x) ∈ L 2 (R)
into a family of functions which are translations and dilations of a mother wavelet
function ψ(x). The 2D wavelet transform uses a family of wavelet functions and
its associated scaling function to decompose the original image into different sub-
bands, namely the low-low (LL), low-high (LH), high-low (HL) and high-high (HH)
subbands, which are also known as A (approximations), H (horizontal details), V
(vertical details), D (diagonal details), respectively. Fig. 3.2 shows the 2D-DWT
performed using low pass h(.) and high pass g(.) filters [83]. The decomposition pro-
cess can be recursively applied to the low frequency channel (LL) to generate dyadic
decomposition at the next level.
Fig. 3.3 shows a face image, and its level-1 and level-3 dyadic decompositions
using the 4-tap Daubechies [30] wavelet filter. Lowest level approximation subband
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