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Artificial geometry for spline model design
Host: Prof. Kai Hormann
USI Campus EST, room D1.13, Sector D
14:30 - 16:00
University of Florence
Abstract: 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.
Biography: 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.
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