Geometry and Statistics (20h) Implementation and projects on PYTHON

(using the Anaconda distribution )

Reda Chhaibi and Laurent Risser

• Practice 0 (2  hours)  Introduction to Python and Standard libraries (NUMPY, PANDAS,…)
• Practice 1 (4  hours)  Statistical inference in image processing using Wasserstein metric. Optimal transport; Segmentation of images.
• Practice 2 (4 hours) Riemannian techniques for brain images (2D or 3D).  Deformation of images; Groups of diffeomorphisms; Euler-Lagrande equations; Geodesic shooting.
• Practice 3 and 4 (6 hours) Geometry of Toeplitz covariance matrices in signal processing. Orthogonal polynomials on the circle ; Reflection coefficients ; Riemannian p-means of probability distributions.
• Defence of projects by the students (4 hours)