A faster strongly polynomial minimum cost flow algorithm
Operations Research
The Earth Mover's Distance as a Metric for Image Retrieval
International Journal of Computer Vision
Optimal Mass Transport for Registration and Warping
International Journal of Computer Vision
Computing Large Deformation Metric Mappings via Geodesic Flows of Diffeomorphisms
International Journal of Computer Vision
Pattern Recognition and Machine Learning (Information Science and Statistics)
Pattern Recognition and Machine Learning (Information Science and Statistics)
An Efficient Earth Mover's Distance Algorithm for Robust Histogram Comparison
IEEE Transactions on Pattern Analysis and Machine Intelligence
A Linear Time Histogram Metric for Improved SIFT Matching
ECCV '08 Proceedings of the 10th European Conference on Computer Vision: Part III
IEEE Transactions on Information Technology in Biomedicine - Special section on biomedical informatics
An Efficient Numerical Method for the Solution of the $L_2$ Optimal Mass Transfer Problem
SIAM Journal on Scientific Computing
An Efficient Numerical Method for the Solution of the $L_2$ Optimal Mass Transfer Problem
SIAM Journal on Scientific Computing
Penalized Fisher discriminant analysis and its application to image-based morphometry
Pattern Recognition Letters
Generalized Monge-Kantorovich Optimization for Grid Generation and Adaptation in $L_{p}$
SIAM Journal on Scientific Computing
Least squares quantization in PCM
IEEE Transactions on Information Theory
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Transportation-based metrics for comparing images have long been applied to analyze images, especially where one can interpret the pixel intensities (or derived quantities) as a distribution of `mass' that can be transported without strict geometric constraints. Here we describe a new transportation-based framework for analyzing sets of images. More specifically, we describe a new transportation-related distance between pairs of images, which we denote as linear optimal transportation (LOT). The LOT can be used directly on pixel intensities, and is based on a linearized version of the Kantorovich-Wasserstein metric (an optimal transportation distance, as is the earth mover's distance). The new framework is especially well suited for computing all pairwise distances for a large database of images efficiently, and thus it can be used for pattern recognition in sets of images. In addition, the new LOT framework also allows for an isometric linear embedding, greatly facilitating the ability to visualize discriminant information in different classes of images. We demonstrate the application of the framework to several tasks such as discriminating nuclear chromatin patterns in cancer cells, decoding differences in facial expressions, galaxy morphologies, as well as sub cellular protein distributions.