Total Generalized Variation of the Normal Vector Field and Applications to Mesh Denoising
This work addresses mesh denoising for computer graphics and geometry processing, presenting an incremental extension of TGV models to manifold settings.
The authors tackled the problem of mesh denoising by proposing a novel formulation for the second-order total generalized variation (TGV) of the normal vector on triangular meshes, extending discrete TGV models to manifold-valued functions and constructing a tangential Raviart-Thomas type finite element space, with results compared to existing methods in experiments.
We propose a novel formulation for the second-order total generalized variation (TGV) of the normal vector on an oriented, triangular mesh embedded in $\R^3$. The normal vector is considered as a manifold-valued function, taking values on the unit sphere. Our formulation extends previous discrete TGV models for piecewise constant scalar data that utilize a Raviart-Thomas function space. To extend this formulation to the manifold setting, a tailor-made tangential Raviart-Thomas type finite element space is constructed in this work. The new regularizer is compared to existing methods in mesh denoising experiments.