  In this paper a novel method called Extended Two-Dimensional PCA (E2DPCA) is
proposed which is an extension to the original 2DPCA. We state that the
covariance matrix of 2DPCA is equivalent to the average of the main diagonal of
the covariance matrix of PCA. This implies that 2DPCA eliminates some
covariance information that can be useful for recognition. E2DPCA instead of
just using the main diagonal considers a radius of r diagonals around it and
expands the averaging so as to include the covariance information within those
diagonals. The parameter r unifies PCA and 2DPCA. r = 1 produces the covariance
of 2DPCA, r = n that of PCA. Hence, by controlling r it is possible to control
the trade-offs between recognition accuracy and energy compression (fewer
coefficients), and between training and recognition complexity. Experiments on
ORL face database show improvement in both recognition accuracy and recognition
time over the original 2DPCA.
