# A metric for distributions with applications to image databases

@article{Rubner1998AMF, title={A metric for distributions with applications to image databases}, author={Yossi Rubner and Carlo Tomasi and Leonidas J. Guibas}, journal={Sixth International Conference on Computer Vision (IEEE Cat. No.98CH36271)}, year={1998}, pages={59-66} }

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…

## 1,801 Citations

Perceptual metrics for image database navigation

- Computer Science
- 1999

A novel approach to the problem of navigating through a collection of images for the purpose of image retrieval is presented, which leads to a new paradigm for image database search and a metric between any two such distributions is defined.

The Earth Mover''s Distance: Lower Bounds and Invariance under Translation

- Computer Science
- 1997

This report presents some fast to compute lower bounds on the EMD which may allow a system to avoid exact, more expensive EMD computations during query processing.

Finding color and shape patterns in images

- Computer Science
- 1999

This thesis gives a couple of modifications which make the EMD more amenable to partial matching, including the partial EMD in which only a given fraction of the weight in one distribution is forced to match weight in the other, and presents algorithms that are guaranteed to find a globally optimal transformation when matching equal-weight distributions under translation.

Adaptive Color-Image Embeddings for Database Navigation

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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…

Using the KL-center for efficient and accurate retrieval of distributions arising from texture images

- Computer Science2005 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR'05)
- 2005

A novel approach to search such collections of distributions efficiently by using an "average" to represent a large set of objects, thus allowing the search to disregard an unpromising subset with only one comparison to its average.

The Earth Mover's Distance under transformation sets

- Computer Science, MathematicsProceedings of the Seventh IEEE International Conference on Computer Vision
- 1999

This work considers the problem of computing a transformation of one distribution which minimizes its EMD to another, and presents a monotonically convergent iteration which can be applied to a large class of EMD under transformation problems, although the iteration may converge to only a locally optimal transformation.

Intensity-based image registration using Earth Mover's Distance

- Computer ScienceSPIE Medical Imaging
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Two image alignment measures using Earth Mover's Distance as a metric on the space of joint intensity distributions are introduced and it is shown that EMD-based measures can be efficiently applied to rigid registration tasks.

Earth Mover's Distance based Similarity Search at Scale

- Computer ScienceProc. VLDB Endow.
- 2013

This paper focuses on optimizing the refinement phase of EMD-based similarity search by adapting an efficient min-cost flow algorithm (SIA) for EMD computation, proposing a dynamic distance bound, and proposed a dynamic refinement order for the candidates which, paired with a concurrent EMD refinement strategy, reduces the amount of needless computations.

Color matching by using tuple matching

- Computer Science12th International Conference on Image Analysis and Processing, 2003.Proceedings.
- 2003

A new matching method called tuple matching (TM) is presented, which is an algorithm for matching image signatures that are generated from color histograms by using graph theoretical clustering (GT-clustering), which is better than EMD.

Color-Spatial Image Indexing and Applications

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The color correlogram is proposed as a generic color-spatial indexing tool to tackle various problems that arise in content-based image retrieval and video browsing and a method for hierarchical classification of images via supervised learning is proposed.

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