A Linear-Time Approximation of the Earth Mover's Distance

TL;DR

This paper introduces a linear-time approximation method for the Earth Mover's Distance (EMD) using space-filling curves, enabling efficient image retrieval based on color descriptors with minimal accuracy loss.

Contribution

The paper presents a novel linear-time approximation of EMD for color-based image retrieval, employing space-filling curves and multiple adjustments to improve accuracy.

Findings

Achieves order-of-magnitude speedup over traditional EMD methods.

Maintains nearly the same retrieval accuracy as exact EMD.

Demonstrates effectiveness through extensive experiments.

Abstract

Color descriptors are one of the important features used in content-based image retrieval. The Dominant Color Descriptor (DCD) represents a few perceptually dominant colors in an image through color quantization. For image retrieval based on DCD, the earth mover's distance and the optimal color composition distance are proposed to measure the dissimilarity between two images. Although providing good retrieval results, both methods are too time-consuming to be used in a large image database. To solve the problem, we propose a new distance function that calculates an approximate earth mover's distance in linear time. To calculate the dissimilarity in linear time, the proposed approach employs the space-filling curve for multidimensional color space. To improve the accuracy, the proposed approach uses multiple curves and adjusts the color positions. As a result, our approach achieves order-of-magnitude time improvement but incurs small errors. We have performed extensive experiments to show the effectiveness and efficiency of the proposed approach. The results reveal that our approach achieves almost the same results with the EMD in linear time.