Fast Feature-Preserving Approach to Carpal Bone Surface Denoising

Area of Science:

• Computer Vision
• Geometric Deep Learning
• Medical Imaging

Background:

• Surface denoising is crucial for accurate 3D data analysis.
• Existing methods often struggle with complex noise patterns or geometric details.
• Graph signal processing (GSP) offers a powerful new paradigm for data structured as graphs.

Purpose of the Study:

• To develop a robust geometric framework for surface denoising.
• To leverage graph signal processing (GSP) for enhanced noise reduction on 3D surfaces.
• To compare the proposed method against existing surface denoising techniques.

Main Methods:

• A constrained optimization problem formulation for surface denoising.
• Utilizing a normalized mesh Laplacian weighted by a data-adaptive kernel similarity matrix.
• Iterative solution of sparse linear systems via the conjugate gradient method.

Main Results:

• Demonstrated effectiveness of the proposed geometric framework on noisy carpal bone surfaces.
• Qualitative and quantitative comparisons show superior performance against existing denoising methods.
• The approach successfully preserves surface details while reducing noise.

Conclusions:

• The presented geometric framework provides an effective solution for surface denoising.
• Graph signal processing (GSP) is a promising tool for advanced surface processing tasks.
• The method shows potential for applications in medical imaging and computer graphics.