In this paper, we study the regularization of quadratic energies that are integrated over discrete domains. This is a fairly general setting, which is often found in but not limited to geometry processing. The standard Tikhonov regularization is widely used such that, e.g., a low-pass filter enforces smoothness of the solution. This approach, however, is independent of the energy and the concrete problem, which leads to artifacts in various applications. Instead, we propose a regularization that enforces a low variation of the energy and is problem-specific by construction. Essentially, this approach corresponds to minimization w.r.t. a different norm. Our construction is generic and can be plugged into any quadratic energy minimization, is simple to implement, and has no significant runtime overhead. We demonstrate this for a number of typical problems and discuss the expected benefits.



  title = {Smoothed Quadratic Energies on Meshes},
  author = { {Martinez~Esturo}, J. and R{\"o}ssl, C. and Theisel, H.},
  journal = {ACM Trans. Graph.},
  number = {1},
  pages = {2:1--2:12},
  volume = {34},
  year = {2014}