An Efficient Hybrid Optimization Strategy for Surface Reconstruction,Computer Graphics Forum

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An Efficient Hybrid Optimization Strategy for Surface Reconstruction
Computer Graphics Forum ( IF 2.7 ) Pub Date : 2021-04-22 , DOI: 10.1111/cgf.14269
Giulia Bertolino ₁ , Marco Montemurro ₁ , Nicolas Perry ₁ , Franck Pourroy ₂

Affiliation

An efficient surface reconstruction strategy is presented in this study, which is able to approximate non-convex sets of target points (TPs). The approach is split in two phases: (a) the mapping phase, making use of the shape preserving method (SPM) to get a proper parametrization of each sub-domain composing the TPs set; (b) the fitting phase, where each patch is fitted by means of a suitable non-uniform rational basis spline (NURBS) surface by considering, as design variables, all parameters involved in its definition. To this purpose, the surface fitting problem is formulated as a constrained non-linear programming problem (CNLPP) defined over a domain having changing dimension, wherein both the number and the value of the design variables are optimized. To deal with this CNLPP, the optimization process is split in two steps. Firstly, a special genetic algorithm (GA) optimizes both the value and the number of design variables by means of a two-level evolution strategy (species and individuals). Secondly, the solution provided by the GA constitutes the initial guess for the deterministic optimization, which aims at improving the accuracy of the fitting surfaces. The effectiveness of the proposed methodology is proven through some meaningful benchmarks taken from the literature.

中文翻译：

一种高效的表面重建混合优化策略

本研究提出了一种有效的表面重建策略，该策略能够逼近非凸集的目标点 (TP)。该方法分为两个阶段：(a) 映射阶段，利用形状保留方法 (SPM) 对组成 TP 集的每个子域进行适当的参数化；(b) 拟合阶段，其中每个面片通过合适的非均匀有理基样条 (NURBS) 曲面进行拟合，将其定义中涉及的所有参数视为设计变量。为此，表面拟合问题被表述为在具有变化维度的域上定义的约束非线性规划问题 (CNLPP)，其中优化设计变量的数量和值。为了处理这个 CNLPP，优化过程分为两个步骤。首先，一种特殊的遗传算法 (GA) 通过两级进化策略（物种和个体）优化设计变量的值和数量。其次，遗传算法提供的解构成了确定性优化的初始猜测，旨在提高拟合曲面的精度。通过从文献中提取的一些有意义的基准，证明了所提出方法的有效性。

更新日期：2021-04-22

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