# The Earth Mover's Distance as a Metric for Image Retrieval

@article{Rubner2004TheEM, title={The Earth Mover's Distance as a Metric for Image Retrieval}, author={Yossi Rubner and Carlo Tomasi and Leonidas J. Guibas}, journal={International Journal of Computer Vision}, year={2004}, volume={40}, pages={99-121} }

We investigate the properties of a metric between two distributions, the Earth Mover's Distance (EMD), for content-based image retrieval. [... ] Key Method 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. Expand

## 4,152 Citations

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.

Intensity-based image registration using Earth Mover's Distance

- Computer ScienceSPIE Medical Imaging
- 2007

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.

A Linear Approximate Algorithm for Earth Mover's Distance with Thresholded Ground Distance

- Computer Science
- 2014

A new image distance metric, , is presented, which applies a threshold to the ground distance and a novel linear approximation algorithm, which achieves complexity with the benefit of qualified bins.

Supervised Earth Mover's Distance Learning and Its Computer Vision Applications

- Computer ScienceECCV
- 2012

This work proposes to jointly optimize the ground distance matrix and the EMD flow-network based on a partial ordering of histogram distances in an optimization framework to produce more accurate EMD values and flow-networks.

A linear-time approximation of the earth mover's distance

- Computer ScienceCIKM '11
- 2011

A new distance function that calculates an approximate earth mover's distance in linear time and employs the space-filling curve for multidimensional color space to achieve order-of-magnitude time improvement but incurs small errors.

Earth Mover Distance on superpixels

- Computer Science2010 IEEE International Conference on Image Processing
- 2010

This construction approximates the EMD between two images, by computing a pixel-wise transport at the complexity cost of computing an E MD between 1-D Histograms and preserves the geometrical and topological structure of the image.

Localized Earth Mover's Distance for Robust Histogram Comparison

- Computer ScienceACCV
- 2010

The localized Earth Mover's Distance (LEMD) is proposed and it is shown that LEMD is more stable than EMD-hat for noise-added or shape-deformed data, and is faster than FastEMD that is the state of the art among EMD variants.

Accurate Approximation of the Earth Moverâ€™s Distance in Linear Time

- Computer ScienceJournal of Computer Science and Technology
- 2014

A new distance function is proposed that calculates an approximate earth moverâ€™s distance in linear time and employs the space-filling curve for multidimensional color space to calculate the dissimilarity between two images.

On the Earth Mover's Distance as a histogram similarity metric for image retrieval

- Computer Science2005 IEEE International Conference on Multimedia and Expo
- 2005

The performance of the Earth Mover's Distance vs /spl chi//sup 2/ distance as histogram similarity metrics for image retrieval is evaluated experimentally and may constitute guidelines in adopting the EMD.

On Efficient Query Processing with the Earth Mover's Distance

- Computer SciencePIKM '14
- 2014

The ongoing experimental evaluation on real data points out the high efficiency of the proposed lower bound Independent Minimization for Signatures (IM-Sig) to the Earth Mover's Distance on feature signatures as an efficient filter approximation approach, contributing to a promising start in the research field of efficient query processing with the Earth mover's distance.

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