On the Euclidean distance of images

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 r...

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Bibliographic Details
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
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Summary: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.
ISSN:0162-8828
1939-3539
DOI:10.1109/TPAMI.2005.165