Regularization

1. Total Variation (TV) Regularization

   • A classic smoothness prior that penalizes the sum of absolute image gradients, encouraging piece-wise constant regions.
   • Wikipedia: https://en.wikipedia.org/wiki/Total_variation_denoising
   • Original paper: Rudin, Osher & Fatemi (1992), “Nonlinear total variation based noise removal algorithms.”

2. Edge-Aware Total Variation Regularization

   • A variant of TV that weights the gradient penalty by an edge strength term, so that true geometric or color edges are preserved while suppressing noise elsewhere.
   • Example method: “Weighted TV” or “Anisotropic TV” with per-pixel weights derived from guide images.
   • Tutorial/discussion: https://dsp.stackexchange.com/questions/12227/what-is-edge-aware-total-variation-smoothing

3. Laplacian (Mesh) Regularization

   • Penalizes the discrete Laplace operator on either vertex positions (geometry) or texture values, encouraging each value to be close to the average of its neighbors.
   • Wikipedia: https://en.wikipedia.org/wiki/Laplacian_smoothing
   • Often called “Laplacian smoothing” or “umbrella operator” in geometry processing.

4. Visibility / Occlusion Regularization

   • A data-driven term that penalizes textures in regions rarely seen or always occluded, to avoid fitting noise in those unseen areas.
   • Not a standard name, but generally just an “Occlusion-based Smoothness” term.