Smooth Signed Distance Surface Reconstruction and Applications
Smooth Signed Distance Surface Reconstruction and Applications
复制标题
光滑符号距离曲面重构及应用
DOI：
--
复制
发表时间：
2012
期刊：
影响因子：
--
通讯作者：
G. Taubin
中科院分区：
文献类型：
--
作者：
G. Taubin
我们描述了一个新的和简单的变分公式重建表面的几何形状，拓扑结构和彩色地图的三维场景从一组有限的彩色定向点。点云现在使用各种技术获得，包括结构化照明系统，被动多视图立体算法和3D激光扫描。在我们的公式中，隐式函数被迫是表面的符号距离函数的光滑近似。该配方允许一些不同的有效的离散化，减少到一个有限维的最小二乘问题的所有线性参数化的家庭的功能，不需要规范的边界条件，它是特别好的外推丢失和/或不规则的采样数据。由此产生的算法是显着更简单，更容易实现比替代方法。特别是，我们的实现基于原始图八叉树的混合有限元-有限差分离散化，和Dual Marching Cubes等值面提取算法是非常有效的，并产生高质量的无裂纹自适应流形多边形网格。几何和拓扑结构重建后，从点的颜色信息被顺利地外推到表面通过解决第二变分问题，这也减少到一个有限维最小二乘问题。由此产生的方法产生高质量的多边形网格与光滑的颜色映射，准确地近似源着色定向点。该方法的开源实现可供下载。我们描述了数字考古，3D取证和3D广播的应用。
We describe a new and simple variational formulation to reconstruct the surface geometry, topology, and color map of a 3D scene from a finite set of colored oriented points. Point clouds are nowadays obtained using a variety of techniques, including structured lighting systems, pasive multi-view stereo algorithms, and 3D laser scanning. In our formulation the implicit function is forced to be a smooth approximation of the signed distance function to the surface. The formulation allows for a number of different efficient discretizations, reduces to a finite dimensional least squares problem for all linearly parameterized families of functions, does not require the specification of boundary conditions, and it is particularly good at extrapolating missing and/or irregularly sampled data. The resulting algorithms are significantly simpler and easier to implement than alternative methods. In particular, our implementation based on a primal-graph octree-based hybrid finite element-finite difference discretization, and the Dual Marching Cubes isosurface extraction algorithm is very efficient, and produces high quality crack-free adaptive manifold polygon meshes. After the geometry and topology are reconstructed, the color information from the points is smoothly extrapolated to the surface by solving a second variational problem which also reduces to a finite dimensional least squares problem. The resulting method produces high quality polygon meshes with smooth color maps, which accurately approximate the source colored oriented points. An open source implementation of this method is available for download. We describe applications to digital archaeology, 3D forensics, and 3D broadcasting.