Mesh generation has become a critical topic in recent years, forming the foundation of all 3D objects used across various applications, such as virtual reality, gaming, and 3D printing. With advancements in computational resources and machine learning, neural networks have emerged as powerful tools for generating high-quality 3D object representations, enabling accurate scene and object reconstructions. Despite these advancements, many methods produce meshes that lack realism or exhibit geometric and textural flaws, necessitating additional processing to improve their quality. This research introduces a convex optimization programming called disciplined convex programming to enhance existing meshes by refining their texture and geometry with a conic solver. By focusing on a sparse set of point clouds from both the original and target meshes, this method demonstrates significant improvements in mesh quality with minimal data requirements. To evaluate the approach, the classical dolphin mesh dataset from Facebook AI was used as a case study, with optimization performed using the CVXPY library. The results reveal promising potential for streamlined and effective mesh refinement.

翻译：近年来，网格生成已成为一个关键课题，构成了虚拟现实、游戏和三维打印等各种应用中所有三维对象的基础。随着计算资源和机器学习的进步，神经网络已成为生成高质量三维对象表示的强大工具，能够实现精确的场景和物体重建。尽管取得了这些进展，但许多方法生成的网格缺乏真实感或存在几何与纹理缺陷，需要额外处理以提升其质量。本研究引入了一种称为规范凸规划的凸优化编程方法，通过圆锥求解器优化现有网格的纹理和几何结构，从而提升网格质量。该方法聚焦于原始网格和目标网格的稀疏点云集合，展示了在最小数据需求下显著改善网格质量的潜力。为评估该方法，本研究以Facebook AI的经典海豚网格数据集作为案例研究，并使用CVXPY库执行优化。结果表明，该方法在简化和有效的网格优化方面展现出广阔前景。