Spectral Mesh Segmentation via l₀ Gradient Minimization.

Area of Science:

• Computer Graphics
• Computational Geometry
• Digital Geometry Processing

Background:

• Mesh segmentation is crucial for analyzing and manipulating 3D models across various fields.
• Existing methods often struggle with complex meshes and hierarchical structures.
• There is a need for robust and efficient mesh segmentation techniques.

Purpose of the Study:

• To introduce a novel mesh segmentation method inspired by sparsity pursuit.
• To address the limitations of current mesh segmentation approaches.
• To develop a method capable of extracting hierarchical structures from mesh models.

Main Methods:

• Utilizing local geometric and topological information to construct a Laplacian matrix.
• Employing the Fiedler vector to characterize segment uniformity.
• Reformulating segmentation as an l0 gradient minimization problem.
• Implementing a coarse-to-fine strategy with heuristic and ADMM-based optimization algorithms.
• Applying a recursive approach for hierarchical structure extraction.

Main Results:

• The proposed method demonstrates superior performance compared to state-of-the-art techniques.
• Effective segmentation of complex mesh models was achieved.
• The method successfully identified and extracted inherent hierarchical structures.
• Evaluations on the Princeton and LIFL/LIRIS Segmentation Benchmarks confirm its efficacy.

Conclusions:

• The novel sparsity pursuit-inspired mesh segmentation method offers significant improvements.
• The coarse-to-fine strategy and ADMM optimization provide efficient and accurate results.
• The recursive approach effectively captures the hierarchical nature of mesh data.
• This method represents a promising advancement in mesh segmentation technology.