Maths and algorithms

The internal workings of GeomLoss are fully described in Jean Feydy’s PhD thesis, Geometric data analysis, beyond convolutions:

  • Chapter 1 provides context on our first motivations;

  • Chapter 2 covers numerical foundations;

  • Chapter 3 presents the main properties and implementations of the GeomLoss functions;

  • Chapter 4 discusses applications to geometric data analysis;

  • Chapter 5 highlights the limitations of optimal transport theory in computational anatomy and discusses open problems in the field.

The most relevant parts of this work will soon be uploaded on this website.