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.Computer Science, Artificial IntelligenceCPCI-S(ISTP)