  Mesh denoising is a fundamental problem in digital geometry processing. It
seeks to remove surface noise, while preserving surface intrinsic signals as
accurately as possible. While the traditional wisdom has been built upon
specialized priors to smooth surfaces, learning-based approaches are making
their debut with great success in generalization and automation. In this work,
we provide a comprehensive review of the advances in mesh denoising, containing
both traditional geometric approaches and recent learning-based methods. First,
to familiarize readers with the denoising tasks, we summarize four common
issues in mesh denoising. We then provide two categorizations of the existing
denoising methods. Furthermore, three important categories, including
optimization-, filter-, and data-driven-based techniques, are introduced and
analyzed in detail, respectively. Both qualitative and quantitative comparisons
are illustrated, to demonstrate the effectiveness of the state-of-the-art
denoising methods. Finally, potential directions of future work are pointed out
to solve the common problems of these approaches. A mesh denoising benchmark is
also built in this work, and future researchers will easily and conveniently
evaluate their methods with the state-of-the-art approaches.
