The translation-invariant metric and its application

The image Euclidean distance (IMED) is a class of image metric that takes the spatial relationship between pixels into consideration. Sun et al. [9] showed that IMED is equivalent to a translation-invariant transform. In this paper, we extend the equivalency to the discrete frequency domain. Based on the connection, we show that GED and IMED can be implemented as low-pass filters, which reduce the space and time complexities significantly. The transform domain metric learning (TDML) proposed in [9] is also resembled as a translation-invariant counterpart of LDA. Experimental results demonstrate improvements in algorithm efficiency and performance boosts on the small sample size problems. ? 2013 Springer-Verlag Berlin Heidelberg.EI