On the Euclidean distance of images

• Published in: IEEE transactions on pattern analysis and machine intelligence 2005-08, Vol.27 (8), p.1334-1339
• Main Authors: Wang, Liwei, Zhang, Yan, Feng, Jufu
• Format: Article
• Language: English
• Subjects: Algorithms; Applied sciences; Artificial Intelligence; Biometry - methods; Cluster Analysis; Computer science; control theory; systems; Computer Simulation; Euclidean distance; Exact sciences and technology; Face - anatomy & histology; Face recognition; Humans; Image classification; Image Enhancement - methods; Image Interpretation, Computer-Assisted - methods; Image recognition; Index Terms- Image metric; Information Storage and Retrieval - methods; Linear discriminant analysis; Models, Biological; Models, Statistical; Pattern Recognition, Automated - methods; Pattern recognition. Digital image processing. Computational geometry; Perturbation methods; positive definite function; Principal component analysis; Robustness; Smoothing methods; Subtraction Technique; Support vector machine classification; Support vector machines; Transformations; Transforms
• ISSN: 0162-8828; 1939-3539
• DOI: 10.1109/TPAMI.2005.165

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.