Simplifying Textured Triangle Meshes in the Wild

TL;DR

The paper tackles textured mesh simplification for wild, non-manifold, multi-component meshes, reproaching the limitations of classic quadrics when inputs deviate from manifold topology. It introduces a topology-varying decimation framework that operates on a simplicial 2-complex $M=(V,E,F)$ by collapsing $1$-simplices, using a memory edge quadric augmented by a memoryless area quadric and a Čech-inspired construction of virtual edges to connect components. To manage textures, it abandons UV-boundary preservation in favor of a successive mapping $T: ext{M}^c ightarrow ext{M}^0$ that bakes textures through successive closest-point projections, effectively reducing texture bleeding. The result is a robust textured mesh simplification system that offers high visual fidelity on wild inputs while preserving strong performance on manifold inputs, as demonstrated by qualitative, quantitative, and user-study evaluations. The approach advances practical geometry processing by enabling fast, texture-safe simplification of arbitrary triangle meshes suitable for real-time rendering and interactive applications.

Abstract

This paper introduces a method for simplifying textured surface triangle meshes in the wild while maintaining high visual quality. While previous methods achieve excellent results on manifold meshes by using the quadric error metric, they struggle to produce high-quality outputs for meshes in the wild, which typically contain non-manifold elements and multiple connected components. In this work, we propose a method for simplifying these wild textured triangle meshes. We formulate mesh simplification as a problem of decimating simplicial 2-complexes to handle multiple non-manifold mesh components collectively. Building on the success of quadric error simplification, we iteratively collapse 1-simplices (vertex pairs). Our approach employs a modified quadric error that converges to the original quadric error metric for watertight manifold meshes, while significantly improving the results on wild meshes. For textures, instead of following existing strategies to preserve UVs, we adopt a novel perspective which focuses on computing mesh correspondences throughout the decimation, independent of the UV layout. This combination yields a textured mesh simplification system that is capable of handling arbitrary triangle meshes, achieving to high-quality results on wild inputs without sacrificing the excellent performance on clean inputs. Our method guarantees to avoid common problems in textured mesh simplification, including the prevalent problem of texture bleeding. We extensively evaluate our method on multiple datasets, showing improvements over prior techniques through qualitative, quantitative, and user study evaluations.

Figures (34)

• Figure 1: Comparison between our textured mesh simplification method and a representative prior technique QEMWithTexture (using the implementation from meshlab). On single component and manifold inputs, both methods produce excellent results (compare baseline, top center, vs. ours, top right). However, for challenging "wild" inputs, often characterized by non-manifold and multiple components geometry, the baseline approach frequently yields unsatisfactory results (bottom center). In contrast, our method preserves visual fidelity and geometric structure more effectively on these wild meshes (bottom right).
• Figure 2: Many meshes available in online repositories are non-manifold. For instance, Thingi10k Thingi10K (a dataset consisting of 3D-printable shapes) includes 22.5% non-manifold shapes, ModelNet WuSKYZTX15 (a dataset of CAD models) contains 54.3% non-manifold objects, and more severely 98.9% of the meshes in the ShapeNet dataset shapenet2015 (a widely used dataset for machine learning) are non-manifold.
• Figure 3: We stress test our method by simplifying a variety of challenging cases encountered in the wild, including noisy 3D scans (left), low-quality triangles from CAD models (middle), and meshes with defects (right).
• Figure 4: Repairing a triangle mesh with HuSWZP20 (third) and then simplifying the repaired model (fourth) depends on having a high quality repaired model, which is not always the case. Our method simplifies the input mesh directly and leads to a better result (first).
• Figure 5: Running mesh repairing HuSWZP20 (second column) and then simplifying the mesh with GarlandH97 (third column) leads to losses on surface attributes, such as textures, and may suffer from suboptimal results due to inperfect repairing. In contrast, our method directly simplifies the input, leading to better results (fourth column).