Complex Functional Maps: A Conformal Link Between Tangent Bundles
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Date
2022
Journal Title
Journal ISSN
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Publisher
© 2022 Eurographics ‐ The European Association for Computer Graphics and John Wiley & Sons Ltd
Abstract
In this paper, we introduce complex functional maps, which extend the functional map framework to conformal maps between tangent vector fields on surfaces. A key property of these maps is their . More specifically, we demonstrate that unlike regular functional maps that link of two manifolds, our complex functional maps establish a link between , thus permitting robust and efficient transfer of tangent vector fields. By first endowing and then exploiting the tangent bundle of each shape with a complex structure, the resulting operations become naturally orientation‐aware, thus favouring across shapes, without relying on descriptors or extra regularization. Finally, and perhaps more importantly, we demonstrate how these objects enable several practical applications within the functional map framework. We show that functional maps and their complex counterparts can be estimated jointly to promote orientation preservation, regularizing pipelines that previously suffered from orientation‐reversing symmetry errors.
Description
@article{10.1111:cgf.14437,
journal = {Computer Graphics Forum},
title = {{Complex Functional Maps: A Conformal Link Between Tangent Bundles}},
author = {Donati, Nicolas and Corman, Etienne and Melzi, Simone and Ovsjanikov, Maks},
year = {2022},
publisher = {© 2022 Eurographics ‐ The European Association for Computer Graphics and John Wiley & Sons Ltd},
ISSN = {1467-8659},
DOI = {10.1111/cgf.14437}
}