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A continuous linear optimal transport approach for pattern analysis in image datasets.

Soheil Kolouri1, Akif B Tosun1, John A Ozolek2

  • 1Biomedical Engineering Department, Carnegie Mellon University, C120 Hamerschlag Hall, Pittsburgh, PA 15213, USA.

Pattern Recognition
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Summary
This summary is machine-generated.

This study introduces a linearized optimal transport metric for image pattern recognition. The method enables efficient shape and appearance modeling, improving classification accuracy across diverse image datasets.

Keywords:
Generative image modelingLinear embeddingOptimal transportPattern visualization

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Area of Science:

  • Computer Vision
  • Pattern Recognition
  • Geometric Analysis

Background:

  • Optimal transport (OT) metrics are powerful for comparing probability distributions, but computationally intensive for large image datasets.
  • Existing OT applications in image analysis often face challenges with computational speed and scalability.
  • Linearizing OT offers a potential solution to overcome these computational hurdles.

Purpose of the Study:

  • To develop a computationally efficient method for applying the optimal transport metric to image pattern recognition.
  • To enable robust shape and appearance modeling of images using linear techniques.
  • To demonstrate the method's effectiveness on diverse image datasets for variation analysis and classification.

Main Methods:

  • A linearized version of the optimal transport metric is proposed, providing a linear embedding for images.
  • Monge's formulation of the optimal transport problem is utilized for faster computation of the linearized embedding.
  • The method is applied to supervised learning tasks on image databases, including cell nuclei, galaxies, faces, and birds.

Main Results:

  • The linearized optimal transport embedding allows for efficient shape and appearance modeling in the embedded space.
  • The approach enables high-resolution visualization and construction of modes of variation.
  • Demonstrated enhanced classification accuracy in various image discrimination problems.

Conclusions:

  • The proposed linearized optimal transport approach offers a computationally feasible and effective tool for image pattern recognition.
  • This method facilitates advanced shape and appearance modeling, leading to improved discrimination capabilities.
  • The technique shows broad applicability across different scientific and visual domains for image analysis.