Operator-based representations of discrete tangent vector fields

Ben‐Chen, Mirela; Azencot, Omri

doi:10.1016/bs.hna.2019.07.007

Cited by 1 publication

(1 citation statement)

References 26 publications

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“…These operator representations enable tasks such as computing vector field flow efficiently, which has been used both for matching functions on surfaces [AVBC16] and even for recovering continuous maps between shapes [COC15]. Furthermore, functional representations have been also proposed for extrinsic ‘deformation fields’ [CO19] and for capturing the intrinsic shape metric [ROA*13, CSBC*17], among others (see also Chapter 6 in [OCB*17] and [BCA19] for an overview of some recent approaches).…”

Section: Related Workmentioning

confidence: 99%

Complex Functional Maps: A Conformal Link Between Tangent Bundles

Donati

Corman

Melzi

et al. 2022

Computer Graphics Forum

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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 orientation awareness. More specifically, we demonstrate that unlike regular functional maps that link functional spaces of two manifolds, our complex functional maps establish a link between oriented tangent bundles, 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 orientation and angle preserving correspondence 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.

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