## NURBS-based surfaces generation from MRI : spectral construction and data-centric model selection

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Vendredi 2 avril 2021
Antoine Perney
(Université of Luxembourg, Mines ParisTech)

Retrieving the geometrical features of objects from images or point cloud is a challenging problem of digital engineering.
In this context, we will investigate how a NURBS surface can be determined from images (MRI).
Hence, we will start by giving an overview about NURBS and observe that a quad mesh is required as a natural initial step.
A method to determine such a quad mesh from an initial triangle tessellation using Morse theory will be presented. This method leads to different choices of quad mesh, with varying levels of density/resolution.
This work will focus on the fitting of the surface to the data points, adjusted with a gradient descent method, and a statistical model selection to determine the best Morse-Smale complex quad surface resolution.