A Fast Algorithm for Image Euclidean Distance

Determining, or selecting a distance measure over the input feature space is a fundamental problem in pattern recognition. A notable metric, called the image euclidean distance (IMED) was proposed by Wang et al. [5], which is demonstrated consistent performance improvements in many real-world problems. In this paper, we present a fast implementation of IMED, which is referred as the convolution standardizing transform (CST). It can reduce the space complexity from O(n
₁

²
n
₂

²
) to O(1) , and the time complexity from O(n
₁

²
n
₂

²
) to O(n
₁
n
₂
), for n
₁
X n
₂
images. Both theoretical analysis and experimental results show the efficiency of our algorithm.