Learning IMED via shift-invariant transformation

The IMage Euclidean Distance (IMED) is a class of image metrics, in which the spatial relationship between pixels is taken into consideration. It was shown that calculating the IMED of two images is equivalent to performing a linear transformation called Standardizing Transform (ST) and then followed by the traditional Euclidean distance. However, while the IMED is invariant to image shift, the ST is not a Shift-Invariant (SI) filter. This left as an open problem whether IMED is equivalent to SI transformation plus traditional Euclidean distance. In this paper, we give a positive answer to this open problem. Specifically, for a wider class of metrics, including IMED, we construct closed-form SI transforms. Based on the SI metric-transform connection, we next develop an image metric learning algorithm by learning a metric filter in the transform domain. This is different from all previous metric approaches. Experimental results on benchmark datasets demonstrate that the learned image metric has promising performances.