Localized Cocone surface reconstruction

We introduce a surface reconstruction algorithm suitable for large point sets. The algorithm is an octree-based version of the Cocone reconstruction algorithm [4], allowing independent processing of small subsets of the total input point set. When the points are sufficiently sampled from a smooth surface, the global guarantee of topological correctness of the original algorithm is preserved, together with the geometric accuracy guarantees.     

A Delaunay-based region-growing approach to surface reconstruction from unorganized points

This paper presents a Delaunay-based region-growing (DBRG) surface reconstruction algorithm that holds the advantages of both Delaunay-based and region-growing approaches. The proposed DBRG algorithm takes a set of unorganized sample points from the boundary surface of a three-dimensional object and produces an orientable manifold triangulated model with a correct geometry and topology that is faithful to the original object. Compared with the traditional Delaunay-based approach, the DBRG algorithm requires only one-pass Delaunay computation and needs no Voronoi information because it improves the non-trivial triangle extraction by using a region-growing technique. Compared with the traditional region-growing methods, the proposed DBRG algorithm makes the surface reconstruction more systematic and robust because it inherits the structural characteristics of the Delaunay triangulation, which nicely complements the absence of geometric information in a set of unorganized points. The proposed DBRG algorithm is capable of handling surfaces with complex topology, boundaries, and even non-uniform sample points. Experimental results show that it is highly efficient compared with other existing algorithms.     

Optimization-based approach for curve and surface reconstruction

This paper introduces an optimization-based approach for the curve reconstruction problem, where piecewise linear approximations are computed from sets of points sampled from target curves. In this approach, the problem is formulated as an optimization problem. To be more concrete, at first the Delaunay triangulation for the sample points is computed, and a weight is assigned with each Delaunay edge. Then the problem becomes minimization or maximization of the total weights of the edges that constitute the reconstruction. This paper proposes one exact method and two approximate methods, and shows that the obtained results are improved both theoretically and empirically. In addition, the optimization-based approach is further extended to three dimensions, where surfaces are to be reconstructed, and the quality of the reconstructions is examined.     

A greedy Delaunay-based surface reconstruction algorithm

In this paper, we present a new greedy algorithm for surface reconstruction from unorganized point sets. Starting from a seed facet, a piecewise linear surface is grown by adding Delaunay triangles one by one. The most plausible triangles are added first and in such a way as to prevent the appearance of topological singularities. The output is thus guaranteed to be a piecewise linear orientable manifold, possibly with boundary. Experiments show that this method is very fast and achieves topologically correct reconstruction in most cases. Moreover, it can handle surfaces with complex topology, boundaries, and nonuniform sampling.     

Continuous global optimization in surface reconstruction from an oriented point cloud

We introduce a continuous global optimization method to the field of surface reconstruction from discrete noisy cloud of points with weak information on orientation. The proposed method uses an energy functional combining flux-based data-fit measures and a regularization term. A continuous convex relaxation scheme assures the global minima of the geometric surface functional. The reconstructed surface is implicitly represented by the binary segmentation of vertices of a 3D uniform grid and a triangulated surface can be obtained by extracting an appropriate isosurface. Unlike the discrete graph-cut solution, the continuous global optimization entails advantages like memory requirements, reduction of metrication errors for geometric quantities, and allowing globally optimal surface reconstruction at higher grid resolutions. We demonstrate the performance of the proposed method on several oriented point clouds captured by laser scanners. Experimental results confirm that our approach is robust to noise, large holes and non-uniform sampling density under the condition of very coarse orientation information.     

Provably correct reconstruction of surfaces from sparse noisy samples

Automated three-dimensional surface reconstruction is a very large and still fast growing area of applied computer vision and there exists a huge number of heuristic algorithms. Nevertheless, the number of algorithms which give formal guarantees about the correctness of the reconstructed surface is quite limited. Moreover such theoretical approaches are proven to be correct only for objects with smooth surfaces and extremely dense samplings with no or very few noise. We define an alternative surface reconstruction method and prove that it preserves the topological structure of multi-region objects under much weaker constraints and thus under much more realistic conditions. We derive the necessary error bounds for some digitization methods often used in discrete geometry, i.e. supercover and m-cell intersection sampling. We also give a detailed analysis of the behavior of our algorithm and compare it with other approaches.     

Implicit surface reconstruction from contours

This paper presents a fast and efficient surface reconstruction method from contour data sets. The reconstructed surface is defined as an implicit surface. We need not create any geometric skeleton and the blending of the three dimensional contour functions enables us to avoid the correspondence and the branching problems that occur in geometrical methods. Tests carried out with medical scanner data-sets show that the reconstruction may be performed at interactive rates.     

Compact implicit surface reconstruction via low-rank tensor approximation

Implicit representations have gained an increasing popularity in geometric modeling and computer graphics due to their ability to represent shapes with complicated geometry and topology. However, the storage requirement, e.g. memory or disk usage, for implicit representations of complex models is relatively large. In this paper, we propose a compact representation for multilevel rational algebraic spline (MRAS) surfaces using low-rank tensor approximation technique, and exploit its applications in surface reconstruction. Given a set of 3D points equipped with oriented normals, we first fit them with an algebraic spline surface defined on a box that bounds the point cloud. We split the bounding box into eight sub-cells if the fitting error is greater than a given threshold. Then for each sub-cell over which the fitting error is greater than the threshold, an offset function represented by an algebraic spline function of low rank is computed by locally solving a convex optimization problem. An algorithm is presented to solve the optimization problem based on the alternating direction method of multipliers (ADMM) and the CANDECOMP/PARAFAC (CP) decomposition of tensors. The procedure is recursively performed until a certain accuracy is achieved. To ensure the global continuity of the MRAS surface, quadratic B-spline weight functions are used to blend the offset functions. Numerous experiments show that our approach can greatly reduce the storage of the reconstructed implicit surface while preserve the fitting accuracy compared with the state-of-the-art methods. Furthermore, our method has good adaptability and is able to produce reconstruction results with high quality.     

Dynamic Delaunay tetrahedralisation of a deforming surface

Reconstruction algorithms make it possible to retrieve a surface from the Delaunay tetrahedralisation (DT) of a point sampling, whose density reflects the surface local geometry and thickness. Most of these algorithms are static and some work remains to be done to handle deforming surfaces. In such case, we defend the idea that each point of the sampling should move with the surface using the information given by the motion to allow fast reconstruction. In this article, we tackle the problem of producing a good evolving sampling of a deforming surface S, and maintaining its DT along the motion. The surface is known only through a projection operator (O ₁):ℝ³→S, and a normal operator (O ₂) that returns the oriented normal at a point on the surface. On that basis, we offer some perspectives on how reconstruction algorithms can be extended to the tracking of deforming surfaces.     

基于Delaunay剖分的心内膜表面动态三维重建算法

心内膜表面三维重建技术在三维标测系统起着手术导航和靶点定位的作用。针对心内科手术中实时采集的散乱心内膜点云,提出了一种基于Delaunay剖分的表面动态三维重建算法。以CGAL非递归方式实现的逐点插入计算Delaunay剖分算法为基础,在剖分过程中,用关联采样点的伞局部替换原来表面中不满足Gabriel准则表面面片的集合,心内膜表面结构随着点云Delaunay剖分的变化而进行动态地更新。同时为了有效地表达心内膜表面及其点云的Delaunay剖分,并能够快速地索引四面体网格和表面三角面片,提出了一种以vtkDataArray为基础的几何数据结构。最后,实验表明该方法在重建结果和重建时间上可以满足心内科手术中的临床应用。     

基于鲁棒估计灭点分层重建的研究

灭点是分层重建过程的重要信息,其求解的准确程度直接关系到最后三维重建的效果。提出了一种基于Hough算法的直线聚类检测方法求取图像中的直线信息以及基于RANSAC的由直线信息估计灭点信息的改进算法,以提高估计灭点的鲁棒性。经试验证明,将所提出的算法应用到分层重建的系统中,在仅有两幅图像的情况下能准确地对目标模型进行重建。     

Efficient reconstruction from non-uniform point sets

We propose a method for non-uniform reconstruction of 3D scalar data. Typically, radial basis functions, trigonometric polynomials or shift-invariant functions are used in the functional approximation of 3D data. We adopt a variational approach for the reconstruction and rendering of 3D data. The principle idea is based on data fitting via thin-plate splines. An approximation by B-splines offers more compact support for fast reconstruction. We adopt this method for large datasets by introducing a block-based reconstruction approach. This makes the method practical for large datasets. Our reconstruction will be smooth across blocks. We give reconstruction measurements as error estimations based on different parameter settings and also an insight on the computational effort. We show that the block size used in reconstruction has a negligible effect on the reconstruction error. Finally we show rendering results to emphasize the quality of this 3D reconstruction technique.     

三维物体表面重建的分支处理算法研究

根据平面点集Delaunay三角剖分的特性,将Delaunay三角剖分应用到分支问题上,改进和实现了一种分支问题处理算法。将相邻层轮廓线投影到同一个剖面上形成一个带约束边的平面点集,并将它们Delaunay三角化,根据这些三角形组来生成新的轮廓线,使轮廓线一一对应。实验结果表明该算法实现的效果较符合实际情况,能有效地处理各种不同情况。     

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。     

Manifold surface reconstruction of an environment from sparse Structure-from-Motion data

The majority of methods for the automatic surface reconstruction of an environment from an image sequence have two steps: Structure-from-Motion and dense stereo. From the computational standpoint, it would be interesting to avoid dense stereo and to generate a surface directly from the sparse cloud of 3D points and their visibility information provided by Structure-from-Motion. The previous attempts to solve this problem are currently very limited: the surface is non-manifold or has zero genus, the experiments are done on small scenes or objects using a few dozens of images. Our solution does not have these limitations. Furthermore, we experiment with hand-held or helmet-held catadioptric cameras moving in a city and generate 3D models such that the camera trajectory can be longer than one kilometer.     

Orienting raw point sets by global contraction and visibility voting

We present a global method for consistently orienting a defective raw point set with noise, non-uniformities and thin sharp features. Our method seamlessly combines two simple but effective techniques—constrained Laplacian smoothing and visibility voting—to tackle this challenge. First, we apply a Laplacian contraction to the given point cloud, which shrinks the shape a little bit. Each shrunk point corresponds to an input point and shares a visibility confidence assigned by voting from multiple viewpoints. The confidence is increased (resp. decreased) if the input point (resp. its corresponding shrunk point) is visible. Then, the initial normals estimated by principal component analysis are flipped according to the contraction vectors from shrunk points to the corresponding input points and the visibility confidence. Finally, we apply a Laplacian smoothing twice to correct the orientation of points with zero or low confidence. Our method is conceptually simple and easy to implement, without resorting to any complicated data structures and advanced solvers. Numerous experiments demonstrate that our method can orient the defective raw point clouds in a consistent manner. By taking advantage of our orientation information, the classical implicit surface reconstruction algorithms can faithfully generate the surface.     

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。     

3D reconstruction using silhouettes from unordered viewpoints

In this paper, we present a novel approach for reconstructing an object surface from its silhouettes. The proposed approach directly estimates the differential structure of the surface, and results in a higher accuracy than existing volumetric approaches for object reconstruction. Compared with other existing differential approaches, our approach produces relatively complete 3D models similar to volumetric approaches, with the topology conforming to what is observed from the silhouettes. In addition, the method neither assumes nor depends on the spatial order of viewpoints. Experimental results on both synthetic and real world data are presented, and comparison is made with other existing approaches to demonstrate the superiority of the proposed approach.     

Nonuniform bilateral filtering for point sets and surface attributes

With the proliferation of three-dimensional (3D) scanning tools and the popularity of point sets in geometry processing and rendering, there is a need for developing smoothing techniques for the point sets and surface attributes defined at these points. In this paper, we present a nonuniform bilateral filtering (NBF) method for point sets and surface attributes based on local geometry feature. In order to adapt the algorithm to irregular sampling, local sampling density is introduced to traditional bilateral filtering, and a global approach for volume preservation is proposed. Experiments show that our approach is stable, effective and easy to use.