# Monge's Optimal Transport Distance for Image Classification Source: [Monge's Optimal Transport Distance for Image Classification]() Collection index: [llms.txt]() Data updated: 2026-06-05T05:01:08.426Z Authors: Michael Snow, Jan Van lent Published: 2016-12-01T09:05:30.000Z ## Abstract This paper focuses on a similarity measure, known as the Wasserstein distance, with which to compare images. The Wasserstein distance results from a partial differential equation (PDE) formulation of Monge's optimal transport problem. We present an efficient numerical solution method for solving Monge's problem. To demonstrate the measure's discriminatory power when comparing images, we use a $1$-Nearest Neighbour ($1$-NN) machine learning algorithm to illustrate the measure's potential benefits over other more traditional distance metrics and also the Tangent Space distance, designed to perform excellently on the well-known MNIST dataset. To our knowledge, the PDE formulation of the Wasserstein metric has not been presented for dealing with image comparison, nor has the Wasserstein distance been used within the $1$-nearest neighbour architecture. ## Recorded benchmark results A research result applies to its stated dataset, split, metric and evaluation configuration. Compare like-for-like settings, preserve the metric's unit and direction, and distinguish paper-reported results from independent reproduction. The best result recorded here is not a claim of exhaustive, current global coverage. - [Image Classification on MNIST (test) (Accuracy Only)](): Image Classification; MNIST (test); Accuracy: 87.1. ## Original sources and implementation [Original paper]() [PDF]()