Robust Mesh Denoising via Triple Sparsity.

Area of Science:

• Computer Graphics
• Computational Geometry
• Image Processing

Background:

• Mesh denoising is essential for real-world scanned data in geometry processing and computer vision.
• Current methods struggle with preserving sharp features and fine details, often causing artifacts in smooth regions.
• Robustness against diverse noise types (Gaussian, impulsive, mixed) remains a challenge for state-of-the-art techniques.

Purpose of the Study:

• To develop a robust mesh denoising method capable of handling complex features and various noise corruptions.
• To introduce a novel optimization framework leveraging a triple sparsity prior for enhanced mesh quality.
• To provide a computationally efficient algorithm for practical application.

Main Methods:

• A novel optimization method based on a triple sparsity prior is proposed.
• The prior incorporates sparsity on first and second-order variations of face normals and the residual field.
• An efficient algorithm using variable-splitting and augmented Lagrange methods is developed for solving the optimization problem.

Main Results:

• The proposed method effectively recovers sharp features, fine details, and smooth regions without staircase artifacts.
• Demonstrated robustness against Gaussian, impulsive, and mixed Gaussian-impulsive noise.
• Outperformed state-of-the-art methods qualitatively and quantitatively on synthetic and real-world scanned data (laser scanner, Kinect v1/v2, Kinect-fusion).

Conclusions:

• The novel triple sparsity prior offers a robust and effective solution for mesh denoising.
• The developed algorithm provides an efficient means to achieve high-quality mesh reconstruction.
• This method advances the state-of-the-art in handling challenging mesh denoising scenarios.