A linear optimal transportation framework for quantifying and visualizing variations in sets of images.

Area of Science:

• Computer Vision
• Image Analysis
• Computational Mathematics

Background:

• Transportation-based metrics are established for image comparison, treating pixel intensities as distributions.
• Existing methods like Earth Mover's Distance (EMD) are computationally intensive for large datasets.

Purpose of the Study:

• Introduce a novel transportation-based framework for analyzing sets of images.
• Develop an efficient distance metric for image comparison suitable for large databases.
• Enable effective pattern recognition and visualization in image datasets.

Main Methods:

• Linear Optimal Transportation (LOT): A new distance metric based on a linearized Kantorovich-Wasserstein metric.
• Direct application to pixel intensities for pairwise image comparisons.
• Isometric linear embedding for visualizing discriminant information.

Main Results:

• LOT provides an efficient method for computing all pairwise distances in large image databases.
• The framework successfully demonstrates pattern recognition capabilities.
• Facilitates visualization of discriminative features across different image classes.

Conclusions:

• The LOT framework offers an efficient and versatile tool for image set analysis and pattern recognition.
• Its ability to handle large datasets and provide visual insights makes it valuable for scientific discovery.
• Demonstrated success across diverse applications including biomedical imaging, facial recognition, and astronomy.