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When an object's velocity changes over time, the total distance traveled can be determined by summing small displacement intervals over short increments. This approach approximates the true distance through numerical summation and the use of integral calculus. An estimate of the total displacement can be obtained by measuring velocity at regular intervals and multiplying each value by the corresponding time step.If a runner accelerates over the first three seconds of a race, speed measurements...
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On Markov Earth Mover's Distance.

Jie Wei1

  • 1Department of Computer Science, City College of New York, New York, New York 10031, USA.

International Journal of Image and Graphics
|May 19, 2015
PubMed
Summary
This summary is machine-generated.

A new Markov Earth Mover's Distance (MEMD) offers efficient similarity measurement for small datasets. This localized approach improves upon existing methods for pattern recognition and signal processing tasks.

Keywords:
Goodness-of-fitcontent-based image retrievalearth mover’s distancegreedy algorithmlinear programmingpattern matching

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Area of Science:

  • Statistics
  • Pattern Recognition
  • Signal Processing

Background:

  • Effective distance metrics are crucial for comparing distributions and sequences in statistics, pattern recognition, and signal processing.
  • Traditional methods like chi-square and Kolmogorov-Smirnov distances have limitations with small sample sizes due to their localized nature.
  • Earth Mover's Distance (EMD) and its variants (EMD-L1, EMD-hat) were developed to address these limitations by allowing flexible distance calculations.

Purpose of the Study:

  • To introduce a novel Markov Earth Mover's Distance (MEMD) for enhanced similarity measurement.
  • To develop an efficient algorithm for evaluating MEMD, particularly for localized pattern and signal analysis.

Main Methods:

  • Introduced MEMD by symmetrically treating source and destination nodes, enabling localized earth movement based on a neighborhood system's degree (d).
  • Handled unmatched nodes using dummy source and destination nodes within the localized network structure.
  • Developed a greedy algorithm with linear complexity relative to the degree (d) and number of nodes for MEMD evaluation.

Main Results:

  • MEMD demonstrated encouraging performance in empirical studies.
  • Evaluations were conducted on deterministic and statistical synthetic sequences.
  • Effectiveness was also shown in SIFT-based image retrieval tasks.

Conclusions:

  • MEMD provides an effective and efficient localized distance measure for similarity assessment.
  • The developed greedy algorithm offers computational efficiency for MEMD evaluation.
  • MEMD shows promise for applications in pattern recognition, signal processing, and image retrieval, especially with limited data.