Master Thesis - Department of Computer Science
Master Thesis - Department of Computer Science
Master Thesis - Department of Computer Science
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Image<br />
Rows<br />
h(.)<br />
g(.)<br />
2<br />
2<br />
Columns<br />
Figure 3.2: Two dimensional discrete wavelet transform (DWT) for an image: The<br />
low pass filter h(.) and the high pass filter g(.) are applied along the rows initially<br />
followed by downsampling by a factor <strong>of</strong> two. This is followed by filtering using h(.)<br />
and g(.) along the columns and downsampled by factor <strong>of</strong> two.<br />
<strong>of</strong> the wavelet decomposition can be further decomposed using the DWT, giving a<br />
multi-level dyadic subband decomposition <strong>of</strong> the face. In the following subsection,<br />
the method <strong>of</strong> reconstructing a subband face using selective wavelet-decomposed sub-<br />
bands is discussed.<br />
3.2.2 Subband Face Reconstruction<br />
A face image <strong>of</strong> a person contains common (approximations) as well as discriminatory<br />
(details) information with respect to faces <strong>of</strong> all other persons. The discriminatory<br />
information is due to structural variations <strong>of</strong> the face which are acquired as intensity<br />
variations at different locations <strong>of</strong> the face. The location and degree <strong>of</strong> intensity vari-<br />
ations in a face <strong>of</strong> an individual are unique features which discriminate one from the<br />
rest <strong>of</strong> the population. The similarity <strong>of</strong> a face with respect to another is in the global<br />
appearance and structure <strong>of</strong> the face. These information (similar and discriminatory)<br />
are segregated at different subbands using different levels <strong>of</strong> decomposition <strong>of</strong> the<br />
face image. Wavelet decomposition helps to split the features <strong>of</strong> a face in different<br />
subbands with “approximations” containing the common (smooth) parts <strong>of</strong> the face<br />
and “details”, at certain levels <strong>of</strong> decomposition, containing the discriminatory (vari-<br />
49<br />
h(.)<br />
g(.)<br />
h(.)<br />
g(.)<br />
2<br />
2<br />
2<br />
2<br />
LL<br />
LH<br />
HL<br />
HH