Spectral Processing for Denoising and Compression of 3D Meshes Using Dynamic Orthogonal Iterations

Area of Science:

• Computer Graphics
• Computational Geometry
• Digital Signal Processing

Background:

• Spectral methods leverage Laplacian matrix properties for 3D mesh processing.
• Existing spectral methods face computational complexity with increasing mesh vertex count.
• This limits their application in real-time scenarios like denoising and compression.

Purpose of the Study:

• To develop a fast and efficient spectral processing approach for dense static and dynamic 3D meshes.
• To enable real-time applications such as 3D model denoising and compression.
• To address the computational complexity limitations of traditional spectral methods.

Main Methods:

• Exploiting spectral coherence between adjacent mesh parts to enhance computational efficiency.
• Employing an orthogonal iteration approach for tracking graph Laplacian eigenspaces.
• Introducing a dynamic version that optimizes subspace size for desired reconstruction quality.

Main Results:

• The proposed method demonstrates significant speed improvements over Singular Value Decomposition (SVD) based spectral processing.
• Achieved reconstruction quality is comparable or superior to existing methods.
• The dynamic version effectively mitigates perceptual distortions by adapting subspace size.

Conclusions:

• The developed spectral processing approach offers a fast and efficient solution for 3D mesh manipulation.
• It is well-suited for real-time denoising and compression of dense 3D models.
• The method can serve as a valuable preprocessing step for other denoising techniques to improve results and reduce computational load.