Papers › Monge-Kantorovich quantiles and ranks for image data
Monge-Kantorovich quantiles and ranks for image data
Gauthier Thurin
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This paper defines quantiles, ranks and statistical depths for image data by leveraging ideas from measure transportation. The first step is to embed a distribution of images in a tangent space, with the framework of linear optimal transport. Therein, Monge-Kantorovich quantiles are shown to provide a meaningful ordering of image data, with outward images having unusual shapes. Numerical experiments showcase the relevance of the proposed procedure, for descriptive analysis, outlier detection or statistical testing.
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