On the Euclidean Distance of Images

Abstract We present a new Euclidean distance for images, which we call IMage Euclidean Distance (IMED). Unlike the traditional Euclidean distance, IMED takes into account the spatial relationships of pixels. Therefore it is robust to small perturbation of images. We argue that IMED is the only intuitively reasonable Euclidean distance for images. IMED is then applied to image recognition. The key advantage of this distance measure is that it can be embedded in most image classification techniques such as SVM, LDA and PCA. The embedding is rather efficient by involving a transformation referred to as Standardizing Transform (ST). We show that ST is a transform domain smoothing. Using the Face Recognition Technology (FERET) database and two state-of-the-art face identification algorithms, we demonstrate a consistent performance improvement of the algorithms embedded with the new metric over their original versions. Index Terms Image metric, Euclidean distance, face recognition, positive definite function 1