Regression models for data distributed over non-planar domains

Regression models for data distributed over non-planar domains
Friday 11th May 2012
Ettinger, B.; Passerini, T.;Perotto, S.; Sangalli, L.M.
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We consider the problem of surface estimation and spatial smoothing over non-planar domains. In particular, we deal with the case where the data or signals occur on a domain that is a surface in a three-dimensional space. The application driving our research is the modeling of hemodynamic data, such as the shear stress and the pressure exerted by blood flow on the wall of a carotid artery. The regression model we propose consists of two key phases. First, we conformally map the surface domain to a region in the plane. Then, we apply existing regression methods for planar domains, suitably modified to respect the geometry of the original surface domain.
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Bree Ettinger, Tiziano Passerini, Simona Perotto, Laura M. Sangalli (2013), Spatial smoothing for data distributed over non-planar domains, in Complex Models and Computational Methods in Statistics, Springer, Series Contribution to Statistics, p. 123-136.