Surface reconstruction is an essential step in most processing pipelines involving point clouds. By constructing a surfacic or volumetric model of the cloud, it is possible to infer large-scale semantic and geometric information required for most applications in computer graphics, simulation and virtual reality. Among the different types of point cloud and the variety of possible problems, we are interested in airborne Lidar data and the problem of building reconstruction for urban planning ranging from flood and light exposure simulation to virtual touristic visits.

While most existing reconstruction methods are based on characteristic features extraction in point clouds such as planes, ridges, contours and their combination into a more complex model, we instead adopt a template-based approach relying on a library of complex primitives developed in an industrial context.

This is formulated as a global fitting problem between a constrained triangulated mesh (our template) and the point cloud. More precisely, we design an energy function that takes into account the distance between both objects while integrating outliers rejection directly in our numerical optimization through the use of an M-estimator. This energy function being smooth everywhere, it can be efficiently minimized by quasi-Newtonian methods like the L-BFGS algorithm.

We demonstrate the reliability of our approach on a collection of diverse roof models and several publicly available Lidar datasets, as well as its robustness and limits in function of initialization, point cloud quality and presence of outliers. By only fitting onto relevant points, this method allows a precise fitting as well as a correct outlier segmentation in a unique step, providing a reasonable initialization close to the barycenter of the cloud.

在大多数涉及点云的处理流程中，表面重建是必不可少的步骤。通过构建云的表面或体积模型，可以推断出计算机图形学、模拟和虚拟现实中的大多数应用所需的大规模语义和几何信息。在不同类型的点云和各种可能的问题中，我们对机载激光雷达数据和城市规划的建筑重建问题感兴趣，从洪水和光照模拟到虚拟旅游访问。

虽然大多数现有的重建方法都是​​基于点云中的特征提取，如平面、脊、轮廓以及将它们组合成更复杂的模型，但我们采用基于模板的方法，依赖于在工业环境中开发的复杂基元库.

这被表述为约束三角网格（我们的模板）和点云之间的全局拟合问题。更准确地说，我们设计了一个能量函数，它考虑了两个对象之间的距离，同时通过使用 M 估计器在我们的数值优化中直接集成了异常值拒绝。这个能量函数在任何地方都是平滑的，它可以通过像 L-BFGS 算法这样的拟牛顿方法有效地最小化。

我们在一系列不同的屋顶模型和几个公开可用的激光雷达数据集上证明了我们的方法的可靠性，以及它在初始化、点云质量和异常值存在方面的鲁棒性和限制。通过仅拟合相关点，该方法允许在独特的步骤中进行精确拟合以及正确的异常值分割，提供接近云重心的合理初始化。