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Many natural shapes have most of their characterizing features concentratedover a few regions in space. For example, humans and animals have distinctivehead shapes, while inorganic objects like chairs and airplanes are made ofwell-localized functional parts with specific geometric features. Often, thesefeatures are strongly correlated -- a modification of facial traits in aquadruped should induce changes to the body structure. However, in shapemodelling applications, these types of edits are among the hardest ones; theyrequire high precision, but also a global awareness of the entire shape. Evenin the deep learning era, obtaining manipulable representations that satisfysuch requirements is an open problem posing significant constraints. In thiswork, we address this problem by defining a data-driven model upon a family oflinear operators (variants of the mesh Laplacian), whose spectra capture globaland local geometric properties of the shape at hand. Modifications to thesespectra are translated to semantically valid deformations of the correspondingsurface. By explicitly decoupling the global from the local surface features,our pipeline allows to perform local edits while simultaneously maintaining aglobal stylistic coherence. We empirically demonstrate how our learning-basedmodel generalizes to shape representations not seen at training time, and wesystematically analyze different choices of local operators over diverse shapecategories.

Localized Shape Modelling with Global Coherence: An Inverse Spectral Approach