A volumetric fusion technique for surface reconstruction from silhouettes and range data

Optical triangulation, an active reconstruction technique, is known to be an accurate method but has several shortcomings due to occlusion and laser reflectance properties of the object surface, that often lead to holes and inaccuracies on the recovered surface. Shape from silhouette, on the other hand, as a passive reconstruction technique, yields robust, hole-free reconstruction of the visual hull of the object. In this paper, a hybrid surface reconstruction method that fuses geometrical information acquired from silhouette images and optical triangulation is presented. Our motivation is to recover the geometry from silhouettes on those parts of the surface which the range data fail to capture. A volumetric octree representation is first obtained from the silhouette images and then carved by range points to amend the missing cavity information. An isolevel value on each surface cube of the carved octree structure is accumulated using local surface triangulations obtained separately from range data and silhouettes. The marching cubes algorithm is then applied for triangulation of the volumetric representation. The performance of the proposed technique is demonstrated on several real objects.     

带洞点云多层同步表面重建方法

针对法向信息缺失和采样点缺失的带有洞的散乱点云数据,提出了一种高效高质量的多层同步表面重建方法.首先利用动态等高线检测出含有洞的八叉树节点,并且基于HPR（hidden point removal）映射计算出八叉树顶点的内外状态,建立带有顶点内外标识的空间有向状态八叉树,然后基于八叉树节点内法向测试方法保证基于k近邻表面重建过程中采样点的法向的正确性,且该空间有向状态八叉树可以支持不同层次的点云同步重建,在保证重建结果正确性的前提下,提高重建效率.     

Reconstruction of 3D Object Meshes from Silhouette Images

In this work we propose a method for computing mesh representations of 3D objects reconstructed from a set of silhouette images. Our method is based on the polygonization of volumetric reconstructions by using a modified version of the dual contouring method. In order to apply dual contouring on volumetric reconstruction from silhouettes we devised a method that is able to determine the discrete topology of the surface in relation to the octree cells. We also developed a new scheme for computing hermitian data representing the intersections of conic volumes with the octree cells and their corresponding normals with subpixel accuracy. Due to the discrete and extremely noisy nature of the data used in the reconstruction we had to devise a different criterion for mesh simplification that applies topological consistency tests only when the geometric error measure is beyond a given tolerance. We present results of the application of the proposed method in the extraction of a mesh corresponding to the surface of objects of a real scene.     

Streaming Surface Reconstruction Using Wavelets

We present a streaming method for reconstructing surfaces from large data sets generated by a laser range scanner using wavelets. Wavelets provide a localized, multiresolution representation of functions and this makes them ideal candidates for streaming surface reconstruction algorithms. We show how wavelets can be used to reconstruct the indicator function of a shape from a cloud of points with associated normals. Our method proceeds in several steps. We first compute a low‐resolution approximation of the indicator function using an octree followed by a second pass that incrementally adds fine resolution details. The indicator function is then smoothed using a modified octree convolution step and contoured to produce the final surface. Due to the local, multiresolution nature of wavelets, our approach results in an algorithm over 10 times faster than previous methods and can process extremely large data sets in the order of several hundred million points in only an hour.     

Efficient surface reconstruction using generalized coulomb potentials

We propose a novel, geometrically adaptive method for surface reconstruction from noisy and sparse point clouds, without orientation information. The method employs a fast convection algorithm to attract the evolving surface towards the data points. The force field in which the surface is convected is based on generalized Coulomb potentials evaluated on an adaptive grid (i.e., an octree) using a fast, hierarchical algorithm. Formulating reconstruction as a convection problem in a velocity field generated by Coulomb potentials offers a number of advantages. Unlike methods which compute the distance from the data set to the implicit surface, which are sensitive to noise due to the very reliance on the distance transform, our method is highly resilient to shot noise since global, generalized Coulomb potentials can be used to disregard the presence of outliers due to noise. Coulomb potentials represent long-range interactions that consider all data points at once, and thus they convey global information which is crucial in the fitting process. Both the spatial and temporal complexities of our spatially-adaptive method are proportional to the size of the reconstructed object, which makes our method compare favorably with respect to previous approaches in terms of speed and flexibility. Experiments with sparse as well as noisy data sets show that the method is capable of delivering crisp and detailed yet smooth surfaces.     

Efficient implementation of point set reconstruction by multi-layer peeling algorithm

We present a memory and time efficient surface reconstruction algorithm for large sets of points, without normal information, that may not fit within the main memory. Our algorithm treats the input points as forming layers of surface patches, and then performs reconstruction by working on multiple layers of surface patches concurrently based on an out-of-core octree. Additionally, the memory usage of the algorithm can be pre-estimated through a few simple quantities in relation to the spatial coherence of the input points. Tests on the algorithm with large point sets verify that it produces good outputs too.     

基于图片序列的三维表面重建

根据非透明物体内部不可见的实际,提出了一种基于图片序列的三维表面重建算法.该算法首先利用传统的八叉树算法重建出物体的三维模型,然后利用一种新颖的表面点提取算法提取出物体表面点,最后利用这些表面点进行三角网格剖分,进而重建出光滑的三维物体表面.在表面点的提取过程中,算法对处于不同状态(处于立方体的顶点、棱、面)的点赋予不...     

一种拉格朗日粒子流体的高效表面重建方法

为了在几何表示层面捕获拉格朗日粒子流体的表面细节特征以进行真实感绘制,提 出一种高效的基于八叉树的自适应流体表面重建方法。首先进行流体表面粒子的精确检测;然后 根据结点中是否包含流体表面粒子,对流体粒子的包围盒进行基于八叉树的自适应剖分;最后只 在包含流体表面粒子的叶子结点里建立隐式距离场。该方法在流体表面重建过程中的内存消耗和 计算复杂度只取决于流体表面而不是流体体积,适合大规模粒子流体场景的表面提取和绘制。     

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。     

Octree-based fusion for realtime 3D reconstruction

This paper proposes an octree-based surface representation for KinectFusion, a realtime reconstruction technique of in-door scenes using a low-cost moving depth camera and a commodity graphics hardware. In KinectFusion, the scene is represented as a signed distance function (SDF) and stored as an uniform grid of voxels. Though the grid-based SDF is suitable for parallel computation in graphics hardware, most of the storage are wasted, because the geometry is very sparse in the scene volume. In order to reduce the memory cost and save the computation time, we represent the SDF in an octree, and developed several octree-based algorithms for reconstruction update and surface prediction that are suitable for parallel computation in graphics hardware. In the reconstruction update step, the octree nodes are adaptively split in breath-first order. To handle scenes with moving objects, the corresponding nodes are automatically detected and removed to avoid storage overflow. In the surface prediction step, an octree-based ray tracing method is adopted and parallelized for graphic hardware. To further reduce the computation time, the octree is organized into four layers, called top layer, branch layer, middle layer and data layer. The experiments showed that, the proposed method consumes only less than 10% memory of original KinectFusion method, and achieves faster performance. Consequently, it can reconstruct scenes with more than 10 times larger size than the original KinectFusion on the same hardware setup.     

Building binary orientation octree for an arbitrary scattered point set

The binary orientation tree (BOT), proposed in [Chen, Y.-L., Chen, B.-Y., Lai, S.-H., and Nishita, T. (2010). Binary orientation trees for volume and surface reconstruction from unoriented point clouds. Comput. Graph. Forum, 29(7), 2011–2019.], is a useful spatial hierarchical data structure for geometric processing such as 3D reconstruction and implicit surface approximation from an input point set. BOT is an octree in which all the vertices of the leaf nodes in the tree are tagged with an ‘in/out’ label based on their spatial relationship to the underlying surface enclosed by the octree. Unfortunately, such a data structure in [Chen, Y.-L., Chen, B.-Y., Lai, S.-H., and Nishita, T. (2010). Binary orientation trees for volume and surface reconstruction from unoriented point clouds. Comput. Graph. Forum, 29(7), 2011–2019.] is only valid for watertight surfaces, which restricts its application. In this paper, we extend the ‘in/out’ relationship to ‘front/back/NA’ relationship to either a closed or an open surface, and propose a new method to build such a spatial data structure from a given arbitrary point set. We first classify the edges of the leaf nodes into two different categories based on whether their two end points are in the same side of the surface or not, and attach respective labels to the edges accordingly. A global propagation process is then applied to get the consistent labels of those end points that are in the same side of the surface. Experiments show that our BOT building method is much more robust, efficient and applicable to various input compared to existing methods, and the applications of BOT when doing RBF reconstructions and envelope surface computations of given 3D objects are shown in the experimental part.     

The conformal alpha shape filtration

Conformal alpha shapes are a new filtration of the Delaunay triangulation of a finite set of points in ℝ^d. In contrast to (ordinary) alpha shapes the new filtration is parameterized by a local scale parameter instead of the global scale parameter in alpha shapes. The local scale parameter conforms to the local geometry and is motivated from applications and previous algorithms in surface reconstruction. We show how conformal alpha shapes can be used for surface reconstruction of non-uniformly sampled surfaces, which is not possible with alpha shapes.     

Volumetric stereo and silhouette fusion for image-based modeling

This paper presents a volumetric stereo and silhouette fusion algorithm for acquiring high quality models from multiple calibrated photographs. Our method is based on computing and merging depth maps. Different from previous methods of this category, the silhouette information is also applied in our algorithm to recover the shape information on the textureless and occluded areas. The proposed algorithm starts by computing visual hull using a volumetric method in which a novel projection test method is proposed for visual hull octree construction. Then, the depth map of each image is estimated by an expansion-based approach that returns a 3D point cloud with outliers and redundant information. After generating an oriented point cloud from stereo by rejecting outlier, reducing scale, and estimating surface normal for the depth maps, another oriented point cloud from silhouette is added by carving the visual hull octree structure using the point cloud from stereo to restore the textureless and occluded surfaces. Finally, Poisson Surface Reconstruction approach is applied to convert the oriented point cloud both from stereo and silhouette into a complete and accurate triangulated mesh model. The proposed approach has been implemented and the performance of the approach is demonstrated on several real data sets, along with qualitative comparisons with the state-of-the-art image-based modeling techniques according to the Middlebury benchmark.     

Surface reconstruction from scan paths

Given a finite set of points sampled from a surface, a particular important topic of surface reconstruction is to find a triangular mesh connecting the sampling points and approximating the surface. We introduce a new solution for this problem which takes into consideration hidden structural information in form of scan paths. The scan paths, which often are available in sampling data sets, allow us to cope with creases or ridges more reliably than algorithms assuming unstructured point clouds. Moreover, the consideration of scan paths leads to a better reconstruction of surface boundaries than other heuristics.     

Realistic surface geometry reconstruction using a hand-held RGB-D camera

In this paper, we have proposed a novel approach for the reconstruction of real object/scene with realistic surface geometry using a hand-held, low-cost, RGB-D camera. To achieve accurate reconstruction, the most important issues to consider are the quality of the geometry information provided and the global alignment method between frames. In our approach, new surface geometry refinement is used to recover finer scale surface geometry from depth data by utilizing high-quality RGB images. In addition, a weighted multi-scale iterative closest point method is exploited to align each scan to the global model accurately. We show the effectiveness of the proposed surface geometry refinement method by comparing it with other depth refinement methods. We also show both the qualitative and quantitative results of reconstructed models by comparing it with other reconstruction methods.     

Discrete shading of three-dimensional objects from medial axis transform

In this paper, we present a discrete shading technique using medial axis transform (MAT) of 3D binary image data based on digital generalized octagonal distances. Our method is computationally attractive as it does not require the explicit computation of surface normals. We have compared our results with images rendered from voxel and octree representations while using analytical surface rendered images as bench marks. The quality of rendering by our method is certainly superior to those obtained from voxel and octree representations.     

用于建立三维GIS的八叉树编码压缩算法

复杂的空间数据结构在三维GIS领域中占有突出的地位,它直接关系到GIS的功能和效率,为了有效地进行三维GIS大量数据的存储和管理,重点讨论了三维GIS栅格数据结构中的八叉树编码压缩技术,由于Morton码值的排序是实现八叉树编码压缩的基础,为此,根据Morton码排序的特殊性,提出了采用时间复杂度为O（n）的计数排序算法,使排序速度大为撇提高,在此基础上进行压缩处理,并对算法的时间及空间复杂度进行了分析,在PC机上进行的模拟实验结果表明,在目标复杂度一定的前提下,八叉树存储数据占用空间小（当分割阶次为9阶时,八叉树存储量只占栅格存储量的4.32%）,是一种较为理想的描述复杂海量地理空间数据的压缩结构。     

A TV Prior for High-Quality Scalable Multi-View Stereo Reconstruction

We present a scalable multi-view stereo method able to reconstruct accurate 3D models from hundreds of high-resolution input images. Local fusion of disparity maps obtained with semi-global matching enables the reconstruction of large scenes that do not fit into main memory. Since disparity maps may vary widely in quality and resolution, careful modeling of the 3D errors is crucial. We derive a sound stereo error model based on disparity uncertainty, which can vary spatially from tenths to several pixels. We introduce a feature based on total variation that allows pixel-wise classification of disparities into different error classes. For each class, we learn a disparity error distribution from ground-truth data using expectation maximization. We present a novel method for stochastic fusion of data with varying quality by adapting a multi-resolution volumetric fusion process that uses our error classes as a prior and models surface probabilities via an octree of voxels. Conflicts during surface extraction are resolved using visibility constraints and preference for voxels at higher resolutions. Experimental results on several challenging large-scale datasets demonstrate that our method yields improved performance both qualitatively and quantitatively.     

从表面重构的体数据实现三维网格剖分

针对有限元分析中网格最优化问题,本文提出一种改进的生成四面体网格的自组织算法。该算法首先应用几何方法将三角形表面模型重新构造成规定大小的分类体数据,同时由该表面模型建立平衡八叉树,计算用以控制网格尺寸的三维数组;然后将体数据转换成邻域内不同等值面的形态一致的边界指示数组;结合改进的自组织算法和相关三维数据的插值函数,达到生成四面体网格的目的。实验对比表明,该方法能够生成更高比例的优质四面体,同时很好地保证了边界的一致。在对封闭的三维表面网格进行有限元建模时,本文算法为其提供了一种有效、可靠的途径。     

A single-pass GPU ray casting framework for interactive out-of-core rendering of massive volumetric datasets

We present an adaptive out-of-core technique for rendering massive scalar volumes employing single-pass GPU ray casting. The method is based on the decomposition of a volumetric dataset into small cubical bricks, which are then organized into an octree structure maintained out-of-core. The octree contains the original data at the leaves, and a filtered representation of children at inner nodes. At runtime an adaptive loader, executing on the CPU, updates a view and transfer function-dependent working set of bricks maintained on GPU memory by asynchronously fetching data from the out-of-core octree representation. At each frame, a compact indexing structure, which spatially organizes the current working set into an octree hierarchy, is encoded in a small texture. This data structure is then exploited by an efficient stackless ray casting algorithm, which computes the volume rendering integral by visiting non-empty bricks in front-to-back order and adapting sampling density to brick resolution. Block visibility information is fed back to the loader to avoid refinement and data loading of occluded zones. The resulting method is able to interactively explore multi-gigavoxel datasets on a desktop PC.