结合插值细分和径向基函数的3维扫描数据孔洞修补

目的 逆向工程中3维扫描数据通常产生孔洞影响逆向造型精度.针对已有算法补洞会导致的边界突变问题,提出基于插值细分和基于径向基函数的孔洞修复算法。方法 首先,对有噪声孔洞边界进行拉普拉斯平滑预处理;其次,通过快速重心插值细分孔洞;然后,结合孔洞周围曲率信息,利用边界和法线约束点进行隐式曲面求解;最后,利用求得的隐式曲面方程,利用梯度下降法调整孔洞插值点,获得平滑修补孔洞结果。结果 对3维经典造型以及实际机械工件等两类不同的数据进行扫描并进行孔洞修补实验。由于算法针对有噪声孔洞结合了孔洞周围曲率信息并通过插值细分进行约束求解,保证了补洞效果的平滑性。实验结果表明,本文算法使得基于径向基函数隐式曲面对有噪声孔洞的适应性更强,其修补结果更加平滑,符合周围曲率变化,改进了已有孔洞修补的边缘突变和修补痕迹明显问题。结论 本文算法针对基于径向基函数的隐式曲面求解对噪声敏感的局限性,进行平滑预处理,结合孔洞周围曲率,提高了孔洞修补效果。由于基于径向基函数的隐式曲面对光顺的流形曲面模拟较好,所以算法对特征孔洞的修补存在一定的不足,快速重心插值法针对不规则孔洞也有一定的局限性。     

针对密集点云的快速曲面重建算法

为了能够快速地从高密度散乱点云生成三角形网格曲面,提出一种针对散乱点云的曲面重建算法.首先通过逐层外扩建立原始点云的近似网格曲面,然后对近似网格曲面进行二次剖分生成最终的精确曲面;为了能够处理噪声点云,在剖分过程中所有网格曲面顶点都通过层次B样条进行了优化.相比于其他曲面重建方法,该算法剖分速度快,且能够保证点云到所生成的三角网格曲面的距离小于预先设定容限.实验结果表明,文中算法能够有效地实现高密度散乱点云的三角剖分,且其剖分速度较已有算法有大幅提高.     

散乱点云数据的高阶平滑隐式曲面重建

针对三维扫描或三维重建获取的散乱点云数据曲面重建问题, 提出基于拉普拉斯规则化的高阶平滑算法。首先, 计算点云数据的包围盒并离散化得到体素空间; 其次, 在体素空间根据隐式曲面的梯度和点云位置、法向信息建立目标函数, 并通过对目标函数的拉普拉斯规则化达到控制重建曲面光顺效果的目的; 再次, 根据最优化原理将重建问题转换为一个稀疏线性方程组求解问题; 最后, 通过步进立方体算法得到重建曲面的三角网格表示。定性和定量的实验结果表明, 该方法重建曲面绘制效果和精确度优于常用的Poisson方法。     

基于Delaunay三角化的噪声点云非均匀采样

针对基于Delaunay三角化曲面重建方法要求点云密度满足ε-sample条件,提出了一种基于Delaunay三角化的噪声点云非均匀采样算法。首先,利用k-邻近点的Voronoi顶点计算出各点的负极点来逼近曲面中轴(MA);然后,根据近似中轴估计出曲面局部特征尺度(LFS);最后,结合Bound Cocone算法,删除多余的非边界点。实例表明,该算法可以准确、稳健地简化噪声点云,同时可以很好地保留曲面边界特征,经简化后的点云适用于基于Delaunay三角化的曲面重建方法。     

三维散乱点云模型的快速曲面重建算法

针对离散点云数据快速重构曲面的问题,提出一种基于紧支径向基函数(CSRBF)的2层隐式函数插值算法.首先在插值前设定一个中心减少阈值,以减少CSRBF的中心点,简化基于CSRBF的线性系统;然后在粗层上通过插值对点云模型进行逼近;再在细层上拟合曲面并对粗、细层曲面求和;最后引入一个正则化参数,将由CSRBF组成的矩阵正则化,处理携带噪声的三维点云模型.实验结果表明,该算法不仅能够简捷地处理含有噪声的三维点云数据,而且能够实现曲面快速重构,最终得到逼真、平滑的曲面模型.     

三维散乱点云快速曲面重建算法

提出了一种基于Delaunay三角剖分的三维散乱点云快速曲面重建算法。算法首先计算点云的Delaunay三角剖分, 从Delaunay四面体提取初始三角网格, 根据Voronoi体元的特征构造优先队列并生成种子三角网格, 然后通过区域生长的方式进行流形提取。实验结果表明, 该算法可以高效、稳定地重构具有复杂拓扑结构、非封闭曲面甚至是非均匀采样的点云数据。与传统的基于Delaunay的方法比较, 该算法仅需要进行一次Delaunay三角剖分, 无须极点的计算, 因此算法的重构速度快。     

一种保特征的隐式曲面算法

结合径向基函数和隐式曲面构造原理,提出了一种保特征的隐式曲面重建算法。应用紧支撑单元产生稀疏的矩阵,降低了计算复杂度,可重建大规模的点云数据。通过几次简单调整支撑域内点的个数,获得保持原特征的重建效果。实验结果证明,算法可以保持原模型的特征。     

规则特征曲面点云法向估计

目的 针对特征曲面点云法矢估计不准确,点云处理时容易丢失曲面的细节特征等问题,提出基于高斯映射的特征曲面散乱点云法向估计法。方法 首先,用主成分分析法粗略地估算点云法向和特征点;其次,将特征点的各向同性邻域映射到高斯球,用K均值聚类法对高斯球上的数据分割成多个子集,以最优子集对应的各向异性邻域拟合曲面来精确估算特征点的法向量;最后,通过测试估计法向与标准法向的误差来评价估计法矢的准确性,并且将估计的法向应用到点云曲面重建中来比较特征保留效果。结果 本文方法估计的法向最小误差接近0,对噪声有较好的鲁棒性,重建的曲面能保留曲面的尖锐特征,相比于其他法向估计法,所提出的方法估计的法向更准确。结论 本文方法能够比较准确的估算尖锐特征曲面法向量,对噪声鲁棒性强,具有较高的适用性。     

大规模孔洞点云的快速重建算法研究 *

针对实际中经常存在的含有孔洞的点云数据 ,在原多层重建算法的基础上提出了一种可以进行点云补洞的快速曲面重建算法。首先对散乱点云数据进行空间自适应八叉剖分 ,然后对点云数据进行由粗到精的多层插值 ,建立隐式曲面方程 ,最后提出了两种加快重建的方法。加速算法可以减少重建时间 ,非常有利于处理大规模点云。实验结果证明 ,本算法对点云孔洞修补效果良好 ,重建速度快 ,效率高。     

利用稳健非负矩阵分解实现无监督高光谱解混

目的 基于非负矩阵分解的高光谱图像无监督解混算法普遍存在着目标函数对噪声敏感、在低信噪比条件下端元提取和丰度估计性能不佳的缺点。因此,提出一种基于稳健非负矩阵分解的高光谱图像混合像元分解算法。方法 首先在传统基于非负矩阵分解的解混算法基础上,对目标函数加以改进,用更加稳健的L₁范数作为重建误差项,提高算法对噪声的适应能力,得到新的无监督解混目标函数。针对新目标函数的非凸特性,利用梯度下降法对端元矩阵和丰度矩阵交替迭代求解,进而完成优化求解,得到端元和丰度估计值。结果 分别利用模拟和真实高光谱数据,对算法性能进行定性和定量分析。在模拟数据集中,将本文算法与具有代表性的5种无监督解混算法进行比较,相比于对比算法中最优者,本文算法在典型信噪比20 dB下,光谱角距离（spectral angle distance,SAD）增大了10.5%,信号重构误差（signal to reconstruction error,SRE）减小了9.3%;在真实数据集中,利用光谱库中的地物光谱特征验证本文算法端元提取质量,并利用真实地物分布定性分析丰度估计结果。结论 提出的基于稳健非负矩阵分解的高光谱无监督解混算法,在低信噪比条件下,能够获得较好的端元提取和丰度估计精度,解混效果更好。     

Feature Preserving Mesh Generation from 3D Point Clouds

We address the problem of generating quality surface triangle meshes from 3D point clouds sampled on piecewise smooth surfaces. Using a feature detection process based on the covariance matrices of Voronoi cells, we first extract from the point cloud a set of sharp features. Our algorithm also runs on the input point cloud a reconstruction process, such as Poisson reconstruction, providing an implicit surface. A feature preserving variant of a Delaunay refinement process is then used to generate a mesh approximating the implicit surface and containing a faithful representation of the extracted sharp edges. Such a mesh provides an enhanced trade‐off between accuracy and mesh complexity. The whole process is robust to noise and made versatile through a small set of parameters which govern the mesh sizing, approximation error and shape of the elements. We demonstrate the effectiveness of our method on a variety of models including laser scanned datasets ranging from indoor to outdoor scenes.     

Robust and Efficient Surface Reconstruction From Range Data

We describe a robust but simple algorithm to reconstruct a surface from a set of merged range scans. Our key contribution is the formulation of the surface reconstruction problem as an energy minimisation problem that explicitly models the scanning process. The adaptivity of the Delaunay triangulation is exploited by restricting the energy to inside/outside labelings of Delaunay tetrahedra. Our energy measures both the output surface quality and how well the surface agrees with soft visibility constraints. Such energy is shown to perfectly fit into the minimum s ? t cuts optimisation framework, allowing fast computation of a globally optimal tetrahedra labeling, while avoiding the “shrinking bias” that usually plagues graph cuts methods. The behaviour of our method confronted to noise, undersampling and outliers is evaluated on several data sets and compared with other methods through different experiments: its strong robustness would make our method practical not only for reconstruction from range data but also from typically more difficult dense point clouds, resulting for instance from stereo image matching. Our effective modeling of the surface acquisition inverse problem, along with the unique combination of Delaunay triangulation and minimum s ? t cuts, makes the computational requirements of the algorithm scale well with respect to the size of the input point cloud.     

Robust dense reconstruction by range merging based on confidence estimation

Although the stereo matching problem has been extensively studied during the past decades, automatically computing a dense 3D reconstruction from several multiple views is still a difficult task owing to the problems of textureless regions, outliers, detail loss, and various other factors. In this paper, these difficult problems are handled effectively by a robust model that outputs an accurate and dense reconstruction as the final result from an input of multiple images captured by a normal camera. First, the positions of the camera and sparse 3D points are estimated by a structure-from-motion algorithm and we compute the range map with a confidence estimation for each image in our approach. Then all the range maps are integrated into a fine point cloud data set. In the final step we use a Poisson reconstruction algorithm to finish the reconstruction. The major contributions of the work lie in the following points: effective range-computation and confidence-estimation methods are proposed to handle the problems of textureless regions, outliers and detail loss. Then, the range maps are merged into the point cloud data in terms of a confidence-estimation. Finally, Poisson reconstruction algorithm completes the dense mesh. In addition, texture mapping is also implemented as a post-processing work for obtaining good visual effects. Experimental results are presented to demonstrate the effectiveness of the proposed approach.     

基于点云增强的网格化优化算法

针对三维点云在采用传统泊松算法进行网格化重建时,重建时间较长并且最终重建出的模型存在孔洞和局部细节缺失等问题,提出一种基于点云增强的网格化优化算法。该算法首先通过统计滤波对初始点云进行降噪处理,为了在保证细节特征的基础上提高重建效率,在通过体素滤波进行适当点云降采样的同时利用双三次样条插值进行点云孔洞修复,然后将移动最小二乘法误差函数引入到点云法向计算中以优化点云法向量的质量。实验结果表明,优化后的网格化算法较传统泊松重建算法耗时更短,并且在一定程度上提高了重建模型的准确度。     

Robust and Efficient Implicit Surface Reconstruction for Point Clouds Based on Convexified Image Segmentation

We present an implicit surface reconstruction algorithm for point clouds. We view the implicit surface reconstruction as a three dimensional binary image segmentation problem that segments the entire space $\mathbb R ^3$ or the computational domain into an interior region and an exterior region while the boundary between these two regions fits the data points properly. The key points with using an image segmentation formulation are: (1) an edge indicator function that gives a sharp indicator of the surface location, and (2) an initial image function that provides a good initial guess of the interior and exterior regions. In this work we propose novel ways to build both functions directly from the point cloud data. We then adopt recent convexified image segmentation models and fast computational algorithms to achieve efficient and robust implicit surface reconstruction for point clouds. We test our methods on various data sets that are noisy, non-uniform, and with holes or with open boundaries. Moreover, comparisons are also made to current state of the art point cloud surface reconstruction techniques.     

点云数据集的隐式曲面重构研究进展

点云数据的曲面重建就是对扫描设备获得的物体散乱数据点重建三维物体表面,它被广泛应用于计算机动画、目标识别、数据可视化以及地理信息系统。点云的隐式曲面重建由于能够去除点云噪声,修补孔洞和裂缝,不需要拼接和平滑等后续处理,成为点云数据集曲面重构的重要方法。文中综述了目前一些主要的隐式曲面重构方法,就隐式模型以及相应的曲面重构算法的优缺点进行了分析比较,并对隐式曲面重构存在的问题和未来发展方向作了相应的分析和讨论。     

考虑法向离群的自适应双边滤波点云平滑及IMLS评价方法

针对目前在点云双边滤波平滑算法中,人工输入不合理参数导致的点云平滑效果不佳,且易导致体积收缩及现有去噪后点云质量评价方法存在表达局限性等问题,提出一种自适应参数的点云双边滤波算法和基于隐性移动最小二乘(IMLS)的质量评价方法。首先构建KD-tree数据结构用于点云拓扑,之后搜索各点邻域,利用奇异值分解法计算法向量信息,并在双边滤波公式中引入法向离群因子以剔除邻域内离群点,然后通过扩展高斯核函数的权值计算式,在点云邻域内自适应获取空间与法向特征参数,最后应用改进模型进行点云平滑并引入IMLS方法评价点云质量。实验结果表明,考虑法向离群的自适应双边滤波点云平滑算法具有良好的去噪效果,相比其他算法体积收缩更小,且IMLS评价方法客观有效。     

Splat-based surface reconstruction from defect-laden point sets

We introduce a method for surface reconstruction from point sets that is able to cope with noise and outliers. First, a splat-based representation is computed from the point set. A robust local 3D RANSAC-based procedure is used to filter the point set for outliers, then a local jet surface – a low-degree surface approximation – is fitted to the inliers. Second, we extract the reconstructed surface in the form of a surface triangle mesh through Delaunay refinement. The Delaunay refinement meshing approach requires computing intersections between line segment queries and the surface to be meshed. In the present case, intersection queries are solved from the set of splats through a 1D RANSAC procedure.     

心内膜表面几何模型三维重建算法研究

心内膜三维表面重建是心内膜三维标测系统中的关键问题。为了满足实际应用需求, 根据采集到的散乱点云数据的特点, 提出了一种改进的泊松表面重建算法。在估计表面点云法向量的基础上, 对表面点云法向量进行法向量一致化处理, 有效地控制时间复杂度, 快速重建出平滑的心脏模型。针对泊松表面重建算法中构建MC曲面出现的二义性问题, 提出一种消除二义性的简化改进方法, 可以更加精确地获取模型逼真表面, 提高重建的速度和精度。同时, 可以根据医生的要求, 对重建出的模型实时修正, 满足临床应用。最后, 通过实验验证了算法的有效性和可行性。