12-10-2012, 01:14 PM
On the Euclidean Distance of Images
[attachment=36177]
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.
Introduction
A central problem in image recognition and computer vision is determining the distance
between images. Considerable efforts have been made to define image distances that provide
intuitively reasonable results [4], [16], [1], [10]. Among others, two representative measures
are the tangent distance [16] and the generalized Hausdorff distance [4]. Tangent distance is
locally invariant with respect to some chosen transformations, and has been widely used in
handwritten digit recognition. The generalized Hausdorff distance is not only robust to noise
but also allows portions of one image to be compared with another, and has become a
standard tool for comparing shapes.
Embedding IMED in Image Recognition Algorithms
Although image metrics may be utilized for image recognition in a direct matching (nearest
neighbor) algorithm, a key issue of an image distance is whether it can be embedded in other
powerful image recognition techniques. Because experimental results have demonstrated that
the state-of-the-art recognition techniques outperform direct matching in various applications.
The major significance of IMED is that one can easily embed it in most of the existing
recognition algorithms, because these algorithms are based on Euclidean distance
Embedding IMED in Recognition Techniques for Face Identification
The primary goal of the experiments in this section is to test a more important ability of
IMED. That is, whether embedding IMED in an image recognition algorithm can improve
that algorithm’s performance. Note that it is difficult to combine those intelligent metrics that
are good at direct matching with the recognition techniques described below.
Embedding IMED in an algorithm is simple: first transform all images by ST (see (9)),
and then run the algorithm with the transformed images as inputs.
The recognition task is human face identification, which has become an active area of
research over the last decade. The facial images are all from the FERET database [13].
FERET database contains four probe categories, named FB, duplicate I, duplicate II, and fc
respectively, and they all share a common gallery. A probe set consists of images of unknown
faces, while the gallery contains images of known individuals. For details about the FERET
database and the terminologies, please see [13]. We choose a training set of 1068 frontal
images from 554 classes to train the models.
Conclusion
It is desirable to define an image metric that can be efficiently embedded in the existing
image recognition methods. Euclidean distance is consequently a candidate because,
representing images as points in a high dimensional Euclidean space, the so-called image
space, is a common starting point of most recognition algorithms. Although there are
infinitely many Euclidean distances for images (for every symmetric and positive definite
matrix G defines a Euclidean distance, see Section 2), they often provide counter intuitive
results. For example, the traditional Euclidean distance is sensitive to deformation and
translation due to the lack of consideration of the spatial relationship of pixels. IMED, to a
certain extent, overcomes this defect. Experiments on FERET datasets demonstrated a
consistent performance improvement of two state-of-the-art algorithms when embedded with
IMED.
[attachment=36177]
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.
Introduction
A central problem in image recognition and computer vision is determining the distance
between images. Considerable efforts have been made to define image distances that provide
intuitively reasonable results [4], [16], [1], [10]. Among others, two representative measures
are the tangent distance [16] and the generalized Hausdorff distance [4]. Tangent distance is
locally invariant with respect to some chosen transformations, and has been widely used in
handwritten digit recognition. The generalized Hausdorff distance is not only robust to noise
but also allows portions of one image to be compared with another, and has become a
standard tool for comparing shapes.
Embedding IMED in Image Recognition Algorithms
Although image metrics may be utilized for image recognition in a direct matching (nearest
neighbor) algorithm, a key issue of an image distance is whether it can be embedded in other
powerful image recognition techniques. Because experimental results have demonstrated that
the state-of-the-art recognition techniques outperform direct matching in various applications.
The major significance of IMED is that one can easily embed it in most of the existing
recognition algorithms, because these algorithms are based on Euclidean distance
Embedding IMED in Recognition Techniques for Face Identification
The primary goal of the experiments in this section is to test a more important ability of
IMED. That is, whether embedding IMED in an image recognition algorithm can improve
that algorithm’s performance. Note that it is difficult to combine those intelligent metrics that
are good at direct matching with the recognition techniques described below.
Embedding IMED in an algorithm is simple: first transform all images by ST (see (9)),
and then run the algorithm with the transformed images as inputs.
The recognition task is human face identification, which has become an active area of
research over the last decade. The facial images are all from the FERET database [13].
FERET database contains four probe categories, named FB, duplicate I, duplicate II, and fc
respectively, and they all share a common gallery. A probe set consists of images of unknown
faces, while the gallery contains images of known individuals. For details about the FERET
database and the terminologies, please see [13]. We choose a training set of 1068 frontal
images from 554 classes to train the models.
Conclusion
It is desirable to define an image metric that can be efficiently embedded in the existing
image recognition methods. Euclidean distance is consequently a candidate because,
representing images as points in a high dimensional Euclidean space, the so-called image
space, is a common starting point of most recognition algorithms. Although there are
infinitely many Euclidean distances for images (for every symmetric and positive definite
matrix G defines a Euclidean distance, see Section 2), they often provide counter intuitive
results. For example, the traditional Euclidean distance is sensitive to deformation and
translation due to the lack of consideration of the spatial relationship of pixels. IMED, to a
certain extent, overcomes this defect. Experiments on FERET datasets demonstrated a
consistent performance improvement of two state-of-the-art algorithms when embedded with
IMED.