Global Mesh Denoising with Fairness

We propose a novel global 3D mesh denoising method that is carried out in two steps, i.e. mollification of normals followed by vertex correction. Both steps involve minimising sparse, quadratic cost functions that yield efficient non-iterative solutions. In the mollification step, we use adaptive weights that allows for appropriate diffusion while preserving features. While many existing methods only correct for the vertex position along the normal direction, we argue that this is inadequate in many scenarios. Instead, we allow for vertex correction in all directions while enforcing a novel face fairness penalty that preserves face shapes in the denoised mesh. We present a number of tests and examples that demonstrate the efficacy of our method in denoising while preserving face fairness. We demonstrate the superiority of our approach over some relevant methods in the literature