# Automatic Target Recognition Using Discrimination Based on Optimal Transport

## TL;DR

This paper explores the application of optimal transport distances, specifically the Monge-Kantorovich distance, for automatic target recognition in SAR images, demonstrating its effectiveness over traditional l2 distance.

## Contribution

It introduces a novel use of Monge-Kantorovich distance for classifying targets with spectral data, including a formulation for spectra with different total mass.

## Key findings

- Monge-Kantorovich distance improves classification accuracy.
- Efficient algorithms enable practical computation of the distance.
- Spectral distances based on optimal transport are robust for target recognition.

## Abstract

The use of distances based on optimal transportation has recently shown promise for discrimination of power spectra. In particular, spectral estimation methods based on l1 regularization as well as covariance based methods can be shown to be robust with respect to such distances. These transportation distances provide a geometric framework where geodesics corresponds to smooth transition of spectral mass, and have been useful for tracking. In this paper, we investigate the use of these distances for automatic target recognition. We study the use of the Monge-Kantorovich distance compared to the standard l2 distance for classifying civilian vehicles based on SAR images. We use a version of the Monge-Kantorovich distance that applies also for the case where the spectra may have different total mass, and we formulate the optimization problem as a minimum flow problem that can be computed using efficient algorithms.