Artificial geometry for spline model design
02 September 2022 - 02 September 2022
East Campus USI-SUPSI Room D1.13 14:30-16:00
For centuries mathematics has been an activity carried out by humans for
humans. In recent years, a new perspective has arisen, in which
mathematics is an activity that humans and machines perform for humans
and machines. In the seminar, we exploit this duality within Computer
Aided Geometric Design (CAGD) and deep learning frameworks.

We consider the problem of constructing spline models starting from data
observations and their necessary parameterization. This latter step,
namely computing the parametric values associated with each observation,
highly affects the shape and accuracy of the final spline model. In
particular, we propose a data-driven parameterization based on
convolutional neural networks which take in input the relative distances
of a variable number of data points and return a suitable
parameterization of randomly measured points. We show, with numerical
examples, that the proposed scheme leads to improve the spline model
accuracy, it is flexible with respect to the input data dimension and
can generalize with respect to different kinds of data.

The speaker

Sofia Imperatore is a PhD student in Applied Mathematics at the
University of Florence, Florence, Italy.

Since her master's studies in Applied Mathematics, geometric and shape modelling have been her main research interests. In particular, adaptive spline fitting techniques have been the focus of her master thesis and the related six months internship at MTU Aero Engines, Germany.

From the beginning of the PhD, she has been exploring both spline and artificial intelligence theories and applications. In particular, her research explores how this two frameworks can interact and benefit from each other. She is currently investigating how to suitably combine classes of smooth curves and surfaces with innovative learning models. The aim is to improve the performance of advanced adaptive spline approximation schemes.