The content of an image can be summarized by a set of homogeneous regions in an appropriate featu... more The content of an image can be summarized by a set of homogeneous regions in an appropriate feature space. When exact shape is not important, the regions can be represented by simple “blobs”. Even for similar images, the blobs in the two images might vary in shape, position, and the represented features. In addition, separate blobs in one image might get merged together in the other image. We present a novel method to compute the dissimilarity of two sets of blobs. Gaussian mixture modeling is used to represent the input images. The Earth Mover's Distance (EMD) is utilized to compute both the dissimilarity of the images and the flow matrix of the blobs between the images. The flow is used to merge blobs such that the dissimilarity between the images gets smaller. Examples are shown on synthetic and natural images
ABSTRACT In recent years super-resolution (S-R) methods are starting to emerge in the field of me... more ABSTRACT In recent years super-resolution (S-R) methods are starting to emerge in the field of medical imaging for the reconstruction of isotropic images with increased slice resolution. Use of the maximal likelihood S-R estimator is not advisable as the S-R reconstruction is an ill-posed problem. Regularizing the S-R algorithm using specific apriori knowledge may compensate for missing measurement information and improve the resolved result. In this work two novel regularization methods are proposed, utilizing domain-specific spatial and intensity constraints on brain MRI data. Experiments indicate that the proposed methods eliminate disadvantages of common regularization methods and outperform these methods with better edge definition and increased image quality.
The content of an image can be summarized by a set of homogeneous regions in an appropriate featu... more The content of an image can be summarized by a set of homogeneous regions in an appropriate feature space. When exact shape is not important, the regions can be represented by simple "blobs". Even for similar images, the blob representation of the two images might vary in shape, position, the number of blobs, and the represented features. In addition, separate blobs in one image might correspond to a single blob in the other image and vice versa. In this paper we present the BlobEMD framework as a novel method to compute the dissimilarity of two sets of blobs while allowing for context-based adaptation of the image representation. This results in representation that represent well the original images but at the same time are best aligned with respect to the representation of the context images.
In this work we address the task of adapting the model representation of a given image, in the co... more In this work we address the task of adapting the model representation of a given image, in the context of a second, target image model. We present the BlobEMD framework, in which the images are represented as sets of blobs and optimal correspondences are found between the representations of the images and are used to adapt the representation of the source image to that of the target image. The contextbased model adaptation results in models which represent well the original images but are more uniform, and best aligned with respect to the target images. This allows for similarity measures between images that are insensitive to the segmentation process and to different levels of details of the representation. We show applications of this method for matching models of heavily dithered images with models of full resolution images, and for content-based image segmentation where the transition from regions to representative silhouettes is shown.
We devise a statistical framework for edge detection by performing a statistical analysis of zero... more We devise a statistical framework for edge detection by performing a statistical analysis of zero crossings of the second derivative of an image. This analysis enables us to estimate at each pixel of an image the probability that an edge passes through the pixel. We present a statistical analysis of the Lindeberg operators that we use to compute image derivatives. We also introduce a confidence probability that tells us how reliable the edge probability is, given the image's noise level and the operator's scale. Combining the edge and confidence probabilities leads to a probabilistic scale selection algorithm. We present the results of experiments on natural images.
This paper empirically compares nine families of image dissimilarity measures that are based on d... more This paper empirically compares nine families of image dissimilarity measures that are based on distributions of color and texture features summarizing over 1000 CPU hours of computational experiments. Ground truth is collected via a novel random sampling scheme for color, and by an image partitioning method for texture. Quantitative performance evaluations are given for classification, image retrieval, and segmentation tasks, and for a wide variety of dissimilarity measure parameters. It is demonstrated how the selection of a measure, based on large scale evaluation, substantially improves the quality of classification, retrieval, and unsupervised segmentation of color and texture images. c 2001 Elsevier Science (USA) 25
This paper empirically compares nine image dissimilarity measures that are based on distributions... more This paper empirically compares nine image dissimilarity measures that are based on distributions of color and texture features summarizing over 1,000 CPU hours of computational experiments. Ground truth is collected via a novel random sampling scheme for color and via an image partitioning method for texture. Quantitative performance evaluations are given for classification, image retrieval, and segmentation tasks, and for a wide variety of dissimilarity measures. It is demonstrated how the selection of a measure, based on large scale evaluation, substantially improves the quality of classification, retrieval, and unsupervised segmentation of color and texture images
The increasing amount of information available in today's world raises the need to retrieve relev... more The increasing amount of information available in today's world raises the need to retrieve relevant data e ciently. Unlike text-based retrieval, where keywords are successfully used to index into documents, content-based image retrieval poses up front the fundamental questions how to extract useful image features and how to use them for intuitive retrieval. We present a n o vel approach to the problem of navigating through a collection of images for the purpose of image retrieval, which leads to a new paradigm for image database search. We summarize the appearance of images by distributions of color or texture features, and we de ne a metric between any two such distributions. This metric, which we call the "Earth Mover's Distance" EMD, represents the least amount of work that is needed to rearrange the mass is one distribution in order to obtain the other. We show that the EMD matches perceptual dissimilarity better than other dissimilarity measures, and argue that it has many desirable properties for image retrieval. Using this metric, we employ Multi-Dimensional Scaling techniques to embed a group of images as points in a two-or three-dimensional Euclidean space so that their distances re ect image dissimilarities as well as possible. Such geometric embeddings exhibit the structure in the image set at hand, allowing the user to understand better the result of a database query and to re ne the query in a perceptually intuitive w ay. By iterating this process, the user can quickly zoom in to the portion of the image space of interest. We also apply these techniques to other modalities such as mug-shot retrieval. iv Acknowledgements I w ould like to thank the many people who made my time at Stanford a period I will treasure.
We present a novel approach to the problem of navigating through a database of color images for t... more We present a novel approach to the problem of navigating through a database of color images for the purpose of image retrieval. We endow the database with a metric for the color distributions of the images. We then use multi-dimensional scaling techniques to embed a group of images as points in a two-dimensional Euclidean space so that their distances reflect image dissimilarities as well as possible. Such geometric embeddings allow the user to perceive the dominant axes of variation in the displayed image group, and form a mental picture of the database contents. Furthermore, since these embeddings group similar images together, away from dissimilar ones, the user can refine the query in a perceptually intuitive way. By iterating this process, the user can quickly navigate to the portion of the image space of interest.
This paper empirically compares nine families of image dissimilarity measures that are based on d... more This paper empirically compares nine families of image dissimilarity measures that are based on distributions of color and texture features summarizing over 1000 CPU hours of computational experiments. Ground truth is collected via a novel random sampling scheme for color, and by an image partitioning method for texture. Quantitative performance evaluations are given for classification, image retrieval, and segmentation tasks, and for a wide variety of dissimilarity measure parameters. It is demonstrated how the selection of a measure, based on large scale evaluation, substantially improves the quality of classification, retrieval, and unsupervised segmentation of color and texture images. c 2001 Elsevier Science (USA) 25
This paper empirically compares nine image dissimilarity measures that are based on distributions... more This paper empirically compares nine image dissimilarity measures that are based on distributions of color and texture features summarizing over 1,000 CPU hours of computational experiments. Ground truth is collected via a novel random sampling scheme for color, and via an image partitioning method for texture. Quantitative performance evaluations are given for classification, image retrieval, and segmentation tasks, and for a wide variety of dissimilarity measures. It is demonstrated how the selection of a measure, based on large scale evaluation, substantially improves the quality of classification, retrieval, and unsupervised segmentation of color and texture images. Computational complexity medium low medium medium medium medium high high Exploits ground distance no no yes no no no yes yes Individual binning no yes no no no no no yes Multiple dimensions yes yes no yes yes yes yes yes Partial matches see text no no no no no no yes Non-parametric
We investigate the properties of a metric between two distributions, the Earth Mover's Distance (... more We investigate the properties of a metric between two distributions, the Earth Mover's Distance (EMD), for content-based image retrieval. The EMD is based on the minimal cost that must be paid to transform one distribution into the other, in a precise sense, and was first proposed for certain vision problems by Peleg, Werman, and Rom. For image retrieval, we combine this idea with a representation scheme for distributions that is based on vector quantization. This combination leads to an image comparison framework that often accounts for perceptual similarity better than other previously proposed methods. The EMD is based on a solution to the transportation problem from linear optimization, for which efficient algorithms are available, and also allows naturally for partial matching. It is more robust than histogram matching techniques, in that it can operate on variable-length representations of the distributions that avoid quantization and other binning problems typical of histograms. When used to compare distributions with the same overall mass, the EMD is a true metric. In this paper we focus on applications to color and texture, and we compare the retrieval performance of the EMD with that of other distances.
We investigate the properties of a metric between two distributions, the Earth Mover's Distance (... more We investigate the properties of a metric between two distributions, the Earth Mover's Distance (EMD), for content-based image retrieval. The EMD is based on the minimal cost that must be paid to transform one distribution into the other, in a precise sense, and was first proposed for certain vision problems by Peleg, Werman, and Rom. For image retrieval, we combine this idea with a representation scheme for distributions that is based on vector quantization. This combination leads to an image comparison framework that often accounts for perceptual similarity better than other previously proposed methods. The EMD is based on a solution to the transportation problem from linear optimization, for which efficient algorithms are available, and also allows naturally for partial matching. It is more robust than histogram matching techniques, in that it can operate on variable-length representations of the distributions that avoid quantization and other binning problems typical of histograms. When used to compare distributions with the same overall mass, the EMD is a true metric. In this paper we focus on applications to color and texture, and we compare the retrieval performance of the EMD with that of other distances.
We introduce a class of metric perceptual distances between textures. The first metric is sensiti... more We introduce a class of metric perceptual distances between textures. The first metric is sensitive to both rotation and scale differences, and provides a basis for two other metrics, one invariant to rotation, and the other invariant to both rotation and scale. Our metrics are based on Earth Mover's Distance computations on log-polar distributions of spatial frequency computed from Gabor filters. We show consistency of our metrics with psychophysical findings on texture discrimination and classification.
We introduce a new distance between two distributions that we call the Earth Mover's Distance (EM... more We introduce a new distance between two distributions that we call the Earth Mover's Distance (EMD), which reflects the minimal amount of work that must be performed to transform one distribution into the other by moving "distribution mass" around. This is a special case of the transportation problem from linear optimization, for which efficient algorithms are available. The EMD also allows for partial matching. When used to compare distributions that have the same overall mass, the EMD is a true metric, and has easy-to-compute lower bounds. In this paper we focus on applications to image databases, especially color and texture. We use the EMD to exhibit the structure of color-distribution and texture spaces by means of Multi-Dimensional Scaling displays. We also propose a novel approach to the problem of navigating through a collection of color images, which leads to a new paradigm for image database search.
In this paper we present a n o vel approach t o t h e problem of navigating through a database of... more In this paper we present a n o vel approach t o t h e problem of navigating through a database of color images. We consider the images as points in a metric space in which w e wish to move around so as to locate image neighborhoods of interest, based on color information. The data base images are mapped to distributions in color space, these distributions are appropriately compressed, and then the distances between all pairs I;Jof images are computed based on the work needed to rearrange the mass in the compressed distribution representing I to that of J. We also propose the use of multi-dimensional scaling MDS techniques to embed a group of images as points in a two-or three-dimensional Euclidean space so that their distances are preserved as much as possible. Such geometric embeddings allow the user to perceive the dominant axes of variation in the displayed image group. In particular, displays of 2-d MDS embeddings can be used to organize and re ne the results of a nearest-neighbor query in a perceptually intuitive w ay. By iterating this process, the user is able to quickly navigate to the portion of the image space of interest.
The increasing amount of information available in today's world raises the need to retrieve relev... more The increasing amount of information available in today's world raises the need to retrieve relevant data e ciently. Unlike text-based retrieval, where keywords are successfully used to index into documents, content-based image retrieval poses up front the fundamental questions how to extract useful image features and how to use them for intuitive retrieval. We present a n o vel approach to the problem of navigating through a collection of images for the purpose of image retrieval, which leads to a new paradigm for image database search. We summarize the appearance of images by distributions of color or texture features, and we de ne a metric between any two such distributions. This metric, which we call the "Earth Mover's Distance" EMD, represents the least amount of work that is needed to rearrange the mass is one distribution in order to obtain the other. We show that the EMD matches perceptual dissimilarity better than other dissimilarity measures, and argue that it has many desirable properties for image retrieval. Using this metric, we employ Multi-Dimensional Scaling techniques to embed a group of images as points in a two-or three-dimensional Euclidean space so that their distances re ect image dissimilarities as well as possible. Such geometric embeddings exhibit the structure in the image set at hand, allowing the user to understand better the result of a database query and to re ne the query in a perceptually intuitive w ay. By iterating this process, the user can quickly zoom in to the portion of the image space of interest. We also apply these techniques to other modalities such as mug-shot retrieval. iv Acknowledgements I w ould like to thank the many people who made my time at Stanford a period I will treasure.
The content of an image can be summarized by a set of homogeneous regions in an appropriate featu... more The content of an image can be summarized by a set of homogeneous regions in an appropriate feature space. When exact shape is not important, the regions can be represented by simple “blobs”. Even for similar images, the blobs in the two images might vary in shape, position, and the represented features. In addition, separate blobs in one image might get merged together in the other image. We present a novel method to compute the dissimilarity of two sets of blobs. Gaussian mixture modeling is used to represent the input images. The Earth Mover's Distance (EMD) is utilized to compute both the dissimilarity of the images and the flow matrix of the blobs between the images. The flow is used to merge blobs such that the dissimilarity between the images gets smaller. Examples are shown on synthetic and natural images
ABSTRACT In recent years super-resolution (S-R) methods are starting to emerge in the field of me... more ABSTRACT In recent years super-resolution (S-R) methods are starting to emerge in the field of medical imaging for the reconstruction of isotropic images with increased slice resolution. Use of the maximal likelihood S-R estimator is not advisable as the S-R reconstruction is an ill-posed problem. Regularizing the S-R algorithm using specific apriori knowledge may compensate for missing measurement information and improve the resolved result. In this work two novel regularization methods are proposed, utilizing domain-specific spatial and intensity constraints on brain MRI data. Experiments indicate that the proposed methods eliminate disadvantages of common regularization methods and outperform these methods with better edge definition and increased image quality.
The content of an image can be summarized by a set of homogeneous regions in an appropriate featu... more The content of an image can be summarized by a set of homogeneous regions in an appropriate feature space. When exact shape is not important, the regions can be represented by simple "blobs". Even for similar images, the blob representation of the two images might vary in shape, position, the number of blobs, and the represented features. In addition, separate blobs in one image might correspond to a single blob in the other image and vice versa. In this paper we present the BlobEMD framework as a novel method to compute the dissimilarity of two sets of blobs while allowing for context-based adaptation of the image representation. This results in representation that represent well the original images but at the same time are best aligned with respect to the representation of the context images.
In this work we address the task of adapting the model representation of a given image, in the co... more In this work we address the task of adapting the model representation of a given image, in the context of a second, target image model. We present the BlobEMD framework, in which the images are represented as sets of blobs and optimal correspondences are found between the representations of the images and are used to adapt the representation of the source image to that of the target image. The contextbased model adaptation results in models which represent well the original images but are more uniform, and best aligned with respect to the target images. This allows for similarity measures between images that are insensitive to the segmentation process and to different levels of details of the representation. We show applications of this method for matching models of heavily dithered images with models of full resolution images, and for content-based image segmentation where the transition from regions to representative silhouettes is shown.
We devise a statistical framework for edge detection by performing a statistical analysis of zero... more We devise a statistical framework for edge detection by performing a statistical analysis of zero crossings of the second derivative of an image. This analysis enables us to estimate at each pixel of an image the probability that an edge passes through the pixel. We present a statistical analysis of the Lindeberg operators that we use to compute image derivatives. We also introduce a confidence probability that tells us how reliable the edge probability is, given the image's noise level and the operator's scale. Combining the edge and confidence probabilities leads to a probabilistic scale selection algorithm. We present the results of experiments on natural images.
This paper empirically compares nine families of image dissimilarity measures that are based on d... more This paper empirically compares nine families of image dissimilarity measures that are based on distributions of color and texture features summarizing over 1000 CPU hours of computational experiments. Ground truth is collected via a novel random sampling scheme for color, and by an image partitioning method for texture. Quantitative performance evaluations are given for classification, image retrieval, and segmentation tasks, and for a wide variety of dissimilarity measure parameters. It is demonstrated how the selection of a measure, based on large scale evaluation, substantially improves the quality of classification, retrieval, and unsupervised segmentation of color and texture images. c 2001 Elsevier Science (USA) 25
This paper empirically compares nine image dissimilarity measures that are based on distributions... more This paper empirically compares nine image dissimilarity measures that are based on distributions of color and texture features summarizing over 1,000 CPU hours of computational experiments. Ground truth is collected via a novel random sampling scheme for color and via an image partitioning method for texture. Quantitative performance evaluations are given for classification, image retrieval, and segmentation tasks, and for a wide variety of dissimilarity measures. It is demonstrated how the selection of a measure, based on large scale evaluation, substantially improves the quality of classification, retrieval, and unsupervised segmentation of color and texture images
The increasing amount of information available in today's world raises the need to retrieve relev... more The increasing amount of information available in today's world raises the need to retrieve relevant data e ciently. Unlike text-based retrieval, where keywords are successfully used to index into documents, content-based image retrieval poses up front the fundamental questions how to extract useful image features and how to use them for intuitive retrieval. We present a n o vel approach to the problem of navigating through a collection of images for the purpose of image retrieval, which leads to a new paradigm for image database search. We summarize the appearance of images by distributions of color or texture features, and we de ne a metric between any two such distributions. This metric, which we call the "Earth Mover's Distance" EMD, represents the least amount of work that is needed to rearrange the mass is one distribution in order to obtain the other. We show that the EMD matches perceptual dissimilarity better than other dissimilarity measures, and argue that it has many desirable properties for image retrieval. Using this metric, we employ Multi-Dimensional Scaling techniques to embed a group of images as points in a two-or three-dimensional Euclidean space so that their distances re ect image dissimilarities as well as possible. Such geometric embeddings exhibit the structure in the image set at hand, allowing the user to understand better the result of a database query and to re ne the query in a perceptually intuitive w ay. By iterating this process, the user can quickly zoom in to the portion of the image space of interest. We also apply these techniques to other modalities such as mug-shot retrieval. iv Acknowledgements I w ould like to thank the many people who made my time at Stanford a period I will treasure.
We present a novel approach to the problem of navigating through a database of color images for t... more We present a novel approach to the problem of navigating through a database of color images for the purpose of image retrieval. We endow the database with a metric for the color distributions of the images. We then use multi-dimensional scaling techniques to embed a group of images as points in a two-dimensional Euclidean space so that their distances reflect image dissimilarities as well as possible. Such geometric embeddings allow the user to perceive the dominant axes of variation in the displayed image group, and form a mental picture of the database contents. Furthermore, since these embeddings group similar images together, away from dissimilar ones, the user can refine the query in a perceptually intuitive way. By iterating this process, the user can quickly navigate to the portion of the image space of interest.
This paper empirically compares nine families of image dissimilarity measures that are based on d... more This paper empirically compares nine families of image dissimilarity measures that are based on distributions of color and texture features summarizing over 1000 CPU hours of computational experiments. Ground truth is collected via a novel random sampling scheme for color, and by an image partitioning method for texture. Quantitative performance evaluations are given for classification, image retrieval, and segmentation tasks, and for a wide variety of dissimilarity measure parameters. It is demonstrated how the selection of a measure, based on large scale evaluation, substantially improves the quality of classification, retrieval, and unsupervised segmentation of color and texture images. c 2001 Elsevier Science (USA) 25
This paper empirically compares nine image dissimilarity measures that are based on distributions... more This paper empirically compares nine image dissimilarity measures that are based on distributions of color and texture features summarizing over 1,000 CPU hours of computational experiments. Ground truth is collected via a novel random sampling scheme for color, and via an image partitioning method for texture. Quantitative performance evaluations are given for classification, image retrieval, and segmentation tasks, and for a wide variety of dissimilarity measures. It is demonstrated how the selection of a measure, based on large scale evaluation, substantially improves the quality of classification, retrieval, and unsupervised segmentation of color and texture images. Computational complexity medium low medium medium medium medium high high Exploits ground distance no no yes no no no yes yes Individual binning no yes no no no no no yes Multiple dimensions yes yes no yes yes yes yes yes Partial matches see text no no no no no no yes Non-parametric
We investigate the properties of a metric between two distributions, the Earth Mover's Distance (... more We investigate the properties of a metric between two distributions, the Earth Mover's Distance (EMD), for content-based image retrieval. The EMD is based on the minimal cost that must be paid to transform one distribution into the other, in a precise sense, and was first proposed for certain vision problems by Peleg, Werman, and Rom. For image retrieval, we combine this idea with a representation scheme for distributions that is based on vector quantization. This combination leads to an image comparison framework that often accounts for perceptual similarity better than other previously proposed methods. The EMD is based on a solution to the transportation problem from linear optimization, for which efficient algorithms are available, and also allows naturally for partial matching. It is more robust than histogram matching techniques, in that it can operate on variable-length representations of the distributions that avoid quantization and other binning problems typical of histograms. When used to compare distributions with the same overall mass, the EMD is a true metric. In this paper we focus on applications to color and texture, and we compare the retrieval performance of the EMD with that of other distances.
We investigate the properties of a metric between two distributions, the Earth Mover's Distance (... more We investigate the properties of a metric between two distributions, the Earth Mover's Distance (EMD), for content-based image retrieval. The EMD is based on the minimal cost that must be paid to transform one distribution into the other, in a precise sense, and was first proposed for certain vision problems by Peleg, Werman, and Rom. For image retrieval, we combine this idea with a representation scheme for distributions that is based on vector quantization. This combination leads to an image comparison framework that often accounts for perceptual similarity better than other previously proposed methods. The EMD is based on a solution to the transportation problem from linear optimization, for which efficient algorithms are available, and also allows naturally for partial matching. It is more robust than histogram matching techniques, in that it can operate on variable-length representations of the distributions that avoid quantization and other binning problems typical of histograms. When used to compare distributions with the same overall mass, the EMD is a true metric. In this paper we focus on applications to color and texture, and we compare the retrieval performance of the EMD with that of other distances.
We introduce a class of metric perceptual distances between textures. The first metric is sensiti... more We introduce a class of metric perceptual distances between textures. The first metric is sensitive to both rotation and scale differences, and provides a basis for two other metrics, one invariant to rotation, and the other invariant to both rotation and scale. Our metrics are based on Earth Mover's Distance computations on log-polar distributions of spatial frequency computed from Gabor filters. We show consistency of our metrics with psychophysical findings on texture discrimination and classification.
We introduce a new distance between two distributions that we call the Earth Mover's Distance (EM... more We introduce a new distance between two distributions that we call the Earth Mover's Distance (EMD), which reflects the minimal amount of work that must be performed to transform one distribution into the other by moving "distribution mass" around. This is a special case of the transportation problem from linear optimization, for which efficient algorithms are available. The EMD also allows for partial matching. When used to compare distributions that have the same overall mass, the EMD is a true metric, and has easy-to-compute lower bounds. In this paper we focus on applications to image databases, especially color and texture. We use the EMD to exhibit the structure of color-distribution and texture spaces by means of Multi-Dimensional Scaling displays. We also propose a novel approach to the problem of navigating through a collection of color images, which leads to a new paradigm for image database search.
In this paper we present a n o vel approach t o t h e problem of navigating through a database of... more In this paper we present a n o vel approach t o t h e problem of navigating through a database of color images. We consider the images as points in a metric space in which w e wish to move around so as to locate image neighborhoods of interest, based on color information. The data base images are mapped to distributions in color space, these distributions are appropriately compressed, and then the distances between all pairs I;Jof images are computed based on the work needed to rearrange the mass in the compressed distribution representing I to that of J. We also propose the use of multi-dimensional scaling MDS techniques to embed a group of images as points in a two-or three-dimensional Euclidean space so that their distances are preserved as much as possible. Such geometric embeddings allow the user to perceive the dominant axes of variation in the displayed image group. In particular, displays of 2-d MDS embeddings can be used to organize and re ne the results of a nearest-neighbor query in a perceptually intuitive w ay. By iterating this process, the user is able to quickly navigate to the portion of the image space of interest.
The increasing amount of information available in today's world raises the need to retrieve relev... more The increasing amount of information available in today's world raises the need to retrieve relevant data e ciently. Unlike text-based retrieval, where keywords are successfully used to index into documents, content-based image retrieval poses up front the fundamental questions how to extract useful image features and how to use them for intuitive retrieval. We present a n o vel approach to the problem of navigating through a collection of images for the purpose of image retrieval, which leads to a new paradigm for image database search. We summarize the appearance of images by distributions of color or texture features, and we de ne a metric between any two such distributions. This metric, which we call the "Earth Mover's Distance" EMD, represents the least amount of work that is needed to rearrange the mass is one distribution in order to obtain the other. We show that the EMD matches perceptual dissimilarity better than other dissimilarity measures, and argue that it has many desirable properties for image retrieval. Using this metric, we employ Multi-Dimensional Scaling techniques to embed a group of images as points in a two-or three-dimensional Euclidean space so that their distances re ect image dissimilarities as well as possible. Such geometric embeddings exhibit the structure in the image set at hand, allowing the user to understand better the result of a database query and to re ne the query in a perceptually intuitive w ay. By iterating this process, the user can quickly zoom in to the portion of the image space of interest. We also apply these techniques to other modalities such as mug-shot retrieval. iv Acknowledgements I w ould like to thank the many people who made my time at Stanford a period I will treasure.
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Papers by Yossi Rubner