Master Thesis - Department of Computer Science

4.3.3 Algorithm for Feature Fusion
In this section, we describe the overall algorithm of our proposed method of feature
fusion from both range space and null space of within-class scatter. All null space
based methods try to extract discriminative directions present in the null space and
ignore range space with the view that it holds the complete intra-class variations. The
performance of null space based methods is highly sensitive to the size of null space
which in term depends on the original image size and also number of training samples.
For large databases, huge number of training samples creates a negative effect on the
performance of null space based methods. So, in the cases where 1) image size is
small and 2) total number of training samples is large, most of the discriminative
information goes to range space of within-class scatter. Our observation says that
there is a nice performance balance between range space and null space. While
image size is constant, total number of training samples controls the performance
of both spaces. When number of training samples is less, null space performs far
better than range space whereas increment in number of training samples enhances
the performance of range space noticeably. So one way of capturing and utilizing the
discriminative information present in entire face space is to merge the discriminative
information present in both spaces. We have attempted to do the merging with the
help of feature fusion. The steps of our algorithm is given below:
1. Compute Sw from training set X = [x 1 1, x 1 2, ..., x 1 N, x 2 1, ..., x C N], using Eqn. 4.1.
2. Perform eigen-analysis on Sw and select first r eigenvectors to form the basis
vector set Q for range space V .
3. Project all class means onto null space and range space using the basis vectors
for range space only (see Eqn. 4.12-4.13). The sets of class means, projected
on null space and range space, are denoted by XNull and XRange respectively.
4. Compute the scatter matrices SNull and SRange of XNull and XRange.
5. Perform eigen-analysis of SNull and SRange to obtain discriminative directions
W Null
opt
and W Range
opt
in null space and range space separately.
6. Perform feature fusion by applying either
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