CWF: Consolidating Weak Features in High-quality Mesh Simplification

TL;DR

This paper introduces a novel mesh simplification method that combines accuracy, feature preservation, and triangle quality by using a smooth functional with decaying weights, outperforming existing algorithms.

Contribution

A new mesh simplification approach that simultaneously optimizes for accuracy, feature alignment, and triangle quality using a combined functional with adaptive weighting.

Findings

Decaying weight improves weak feature preservation.

The method outperforms existing algorithms on CAD and organic models.

Enhanced shape understanding demonstrated through experimental results.

Abstract

In mesh simplification, common requirements like accuracy, triangle quality, and feature alignment are often considered as a trade-off. Existing algorithms concentrate on just one or a few specific aspects of these requirements. For example, the well-known Quadric Error Metrics (QEM) approach prioritizes accuracy and can preserve strong feature lines/points as well but falls short in ensuring high triangle quality and may degrade weak features that are not as distinctive as strong ones. In this paper, we propose a smooth functional that simultaneously considers all of these requirements. The functional comprises a normal anisotropy term and a Centroidal Voronoi Tessellation (CVT) energy term, with the variables being a set of movable points lying on the surface. The former inherits the spirit of QEM but operates in a continuous setting, while the latter encourages even point distribution, allowing various surface metrics. We further introduce a decaying weight to automatically balance the two terms. We selected 100 CAD models from the ABC dataset, along with 21 organic models, to compare the existing mesh simplification algorithms with ours. Experimental results reveal an important observation: the introduction of a decaying weight effectively reduces the conflict between the two terms and enables the alignment of weak features. This distinctive feature sets our approach apart from most existing mesh simplification methods and demonstrates significant potential in shape understanding.