Efficient Mesh Smoothing Algorithm via Iterative Least Squares

As the use of geometric scanners for 3D model creation continues to grow, there arises an increasing requirement for efficient mesh smoothing algorithms. Balancing the quality of smoothing and processing speed involves a tradeoff. Achieving high-quality results typically requires a substantial investment in computational resources, which can have an impact on processing speed. Motivated by recent progress in image smoothing techniques, we present a novel global optimization-based approach designed to concurrently deliver high-quality smoothing and expedited processing speed. The proposed method relies on a non-convex optimization, enforcing mesh smoothness through generalized Charbonnier penalty. To address the non-convex optimization problem, we introduce an efficient algorithm termed iterative least squares, which is based on additive half-quadratic minimization and variable-splitting. Initially, this optimization can be applied to the normal field, and subsequently, the vertex positions are reconstructed from the updated normal field. This process is essential for preserving mesh geometry features during smoothing. The experimental results illustrate the flexibility, effectiveness and efficiency of the proposed approach.