Total Generalized Variation of the Normal Vector Field and Applications to Mesh Denoising
Lukas Baumgärtner and Ronny Bergmann and Roland Herzog and Stephan Schmidt and Manuel Weiß
我们提出了一个新颖的公式,用于在嵌入 ^3 的定向三角形网格上对正常矢量的第二顺序总广义变异 (TGV)。 正常的向量被认为是多形值函数,在单位球体上取值。 我们的配方扩展了以前的离散TGV模型,用于利用Raviart-Thomas功能空间的分段恒定标量数据。 为了将这个公式扩展到流形设置,在这项工作中构建了一个定制的切线Raviart-Thomas类型有限元空间。 新的正则器与网格去角质实验中的现有方法进行了比较。
We propose a novel formulation for the second-order total generalized variation (TGV) of the normal vector on an oriented, triangular mesh embedded in ^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 sp...