Progressive mesh simplification (PM) algorithm aims to generate simplified mesh at any resolution for the input high-precision mesh, and only needs to be optimized or fitted once. Most of the existing PM algorithms are obtained based on heuristic mesh simplification algorithms, which leads to redundant storage space and poor practice-ability of the algorithm. In this article, a progressive mesh simplification algorithm based on neural implicit representation (NePM) is proposed, and NePM transforms algorithm process into an implicit continuous optimization problem through neural network and probabilistic model. NePM uses Gaussian mixture model to model high-precision mesh and samples the probabilistic model to obtain simplified meshes at different resolutions. In addition, the simplified mesh is optimized through multi-level neural network, preserving characteristics of the input high-precision mesh. Thus, the algorithm in this work lowers the memory usage of the PM and improves the practicability of the algorithm while ensuring the accuracy.

中文翻译：

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基于神经隐式表示的渐进网格简化算法

渐进式网格简化（PM）算法旨在对输入的高精度网格生成任意分辨率的简化网格，并且只需要优化或拟合一次。现有的PM算法大多是基于启发式网格简化算法获得的，导致存储空间冗余，算法的实用性较差。本文提出了一种基于神经隐式表示（NePM）的渐进式网格简化算法，NePM通过神经网络和概率模型将算法过程转化为隐式连续优化问题。 NePM使用高斯混合模型对高精度网格进行建模，并对概率模型进行采样以获得不同分辨率下的简化网格。此外，简化的网格通过多级神经网络进行优化，保留了输入高精度网格的特征。因此，本文算法在保证精度的同时，降低了PM的内存占用，提高了算法的实用性。