Octree generation from object silhouettes in perspective views

Octrees are useful for object representation when fast access to coarse spatial occupancy information is necessary. This paper presents an efficient algorithm for generating octrees from multiple perspective views of an object. The algorithm first obtains a polygonal approximation of the object silhouette. This polygon is then decomposed into convex components. For each convex component, a pyramid is formed treating the view point as its apex and the convex components as a cross section. The octree representation of each of these pyramids is obtained by performing intersection detection of the object with the cubes corresponding to octree nodes. The intersection detection step is made efficient by decomposing it into a coarse-to-fine sequence of intersection tests. The octree for one silhouette is obtained by taking the union of octrees obtained for each component. An intersection of octrees corresponding to different viewing directions gives the final octree of the object. An implementation of the algorithm is given. The accuracy of the octree representation of the objects is evaluated. The ratio of the actual volume of the object to the volume of the object reconstructed from the octree representation is used as a performance index of the algorithm.     

Generating octrees from object silhouettes in orthographic views

An algorithm to construct the octree representation of a three-dimensional object from silhouette images of the object is described. The images must be obtained from thirteen viewing directions corresponding to the three face views, six edge views, and four corner views of an upright cube. These views where chosen because they provide a simple relationship between pixels in the image and the octant labels in the octree, thus replacing the computation of detecting intersections between the octree space and the objects by a table lookup operation. The average ratio of the object volume to the octree volume is found to be greater than 90%. The sequential use made of the chosen viewing directions results in a coarse-to-fine acquisition of occupancy information. The number and order of the viewpoints used provides a mechanism for trading accuracy of the representation against the computational effort needed to obtain the representation     

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...     

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.     

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.     

System for reconstruction of three-dimensional micro objects from multiple photographic images

We introduce a system to reconstruct a three-dimensiojnal (3D) polygonal model of 3D micro objects with outer dimensions ranging from several hundred microns to several millimeters from multiple two-dimensional (2D) images of an object taken from different views. The data acquisition system consists of a digital microscope that captures still images at a resolution of 1600 × 1200 pixels and a computer-controlled turntable. We employ the shape-from-silhouette (SFS) method to construct a voxel-based 3D model from silhouette images. The concave shapes are further carved by using the space carving technique. In order to make the resulting model compatible with a commercial CAD/CAM system, the voxel model is converted into a triangular mesh using the marching cubes algorithm. Because the mesh generated from the voxel model by using the marching cubes algorithm inherits the staircase effect, the mesh is adjusted to recover the object precisely by using silhouette images. Finally, we evaluate the accuracy of the proposed method. The reconstructed models of complex micro objects indicate the effectiveness of the 3D shape reconstruction system for micro objects.     

GPU-based parallel construction of compact visual hull meshes

Building a visual hull model from multiple two-dimensional images provides an effective way of understanding the three-dimensional geometries inherent in the images. In this paper, we present a GPU accelerated algorithm for volumetric visual hull reconstruction that aims to harness the full compute power of the many-core processor. From a set of binary silhouette images with respective camera parameters, our parallel algorithm directly outputs the triangular mesh of the resulting visual hull in the indexed face set format for a compact mesh representation. Unlike previous approaches, the presented method extracts a smooth silhouette contour on the fly from each binary image, which markedly reduces the bumpy artifacts on the visual hull surface due to a simple binary in/out classification. In addition, it applies several optimization techniques that allow an efficient CUDA implementation. We also demonstrate that the compact mesh construction scheme can easily be modified for also producing a time- and space-efficient GPU implementation of the marching cubes algorithm.     

Multilevel representation and transmission of real objects with progressive octree particles

We present a multilevel representation scheme adapted to storage, progressive transmission, and rendering of dense data sampled on the surface of real objects. Geometry and object attributes, such as color and normal, are encoded in terms of surface particles associated to a hierarchical space partitioning based on an octree. Appropriate ordering of surface particles results in a compact multilevel representation without increasing the size of the uniresolution model corresponding to the highest level of detail. This compact representation can progressively be decoded by the viewer and transformed by a fast direct triangulation technique into a sequence of triangle meshes with increasing levels of detail. The representation requires approximately 5 bits per particle (2.5 bits per triangle) to encode the basic geometrical structure. The vertex positions can then be refined by means of additional precision bits, resulting in 5 to 9 bits per triangle for representing a 12-bit quantized geometry. The proposed representation scheme is demonstrated with the surface data of various real objects.     

Model construction and shape recognition from occluding contours

A technique is presented for recognizing a 3D object (a model in an image library) from a single 2D silhouette using information such as corners (points with high positive curvatures) and occluding contours, rather than straight line segments. The silhouette is assumed to be a parallel projection of the object. Each model is stored as a set of the principal quadtrees, from which the volume/surface octree of the model is generated. Feature points (i.e. corners) are extracted to guide the recognition process. Four-point correspondences between the 2D feature points of the observed object and 3D feature points of each model are hypothesized, and then verified by applying a variety of constraints to their associated viewing parameters. The result of the hypothesis and verification process is further validated by 2D contour matching. This approach allows for a method of handling both planar and curved objects in a uniform manner, and provides a solution to the recognition of multiple objects with occlusion as demonstrated by the experimental results     

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.     

Implicit Surface-Based Geometric Fusion

This paper introduces a general purpose algorithm for reliable integration of sets of surface measurements into a single 3D model. The new algorithm constructs a single continuous implicit surface representation which is the zero-set of a scalar field function. An explicit object model is obtained using any implicit surface polygonization algorithm. Object models are reconstructed from both multiple view conventional 2.5D range images and hand-held sensor range data. To our knowledge this is the first geometric fusion algorithm capable of reconstructing 3D object models from noisy hand-held sensor range data.This approach has several important advantages over existing techniques. The implicit surface representation allows reconstruction of unknown objects of arbitrary topology and geometry. A continuous implicit surface representation enables reliable reconstruction of complex geometry. Correct integration of overlapping surface measurements in the presence of noise is achieved using geometric constraints based on measurement uncertainty. The use of measurement uncertainty ensures that the algorithm is robust to significant levels of measurement noise. Previous implicit surface-based approaches use discrete representations resulting in unreliable reconstruction for regions of high curvature or thin surface sections. Direct representation of the implicit surface boundary ensures correct reconstruction of arbitrary topology object surfaces. Fusion of overlapping measurements is performed using operations in 3D space only. This avoids the local 2D projection required for many previous methods which results in limitations on the object surface geometry that is reliably reconstructed. All previous geometric fusion algorithms developed for conventional range sensor data are based on the 2.5D image structure preventing their use for hand-held sensor data. Performance evaluation of the new integration algorithm against existing techniques demonstrates improved reconstruction of complex geometry.     

一种改进的八元树三维目标表示方法

利用八元树表示三维物体是一种十分有效的方法。传统指针表示的八元树结构具有占据内存容量大、节点间关系少等缺点。在分析了物体的空间布局和八元树结构的基础上,文章提出了一种改进的八元树三维表示方法。从医学图像三维重建的实验结果看,提出的方法可行并且在内存存储结构和访问方式等方面优于传统的表示方法。     

广义线性八元树表示及物体的广义三维重建

提出物体的广义线性八元树表示法,推广线性八元树的构造方法完成物体的广义三 维重建--广义线性八元树表示,从而为物体三维重建降低约束、增加灵活性.     

一种基于激光散斑去相关技术的三维重建方法

为了解决测量范围有限和摄像机标定复杂的问题,本文在传统的数字散斑相关计量方法基础上,提出一种基于数字散斑去相关测量的三维重建方法。首先通过激光照射散射体的不同面元发生干涉,在物体表面叠加形成散斑图像;其次利用不同空间距离处参考散斑图像的去相关特性来估计物体的位置;最后通过三角测量原理求出物体散斑图像和参考图像局部偏移量来确定物体的三维图。仿真实验结果表明,该系统能够在误差允许范围内得到基本完整的物体深度图像,并且与物体自身特性无关,具有良好的鲁棒性。     

Alias-free voxelization of geometric objects

Introduces a new concept for alias-free voxelization of geometric objects based on a voxelization model (V-model). The V-model of an object is its representation in 3D continuous space by a trivariate density function. This function is sampled during the voxelization and the resulting values are stored in a volume buffer. This concept enables us to study general issues of sampling and rendering separately from object-specific design issues. It provides us with a possibility to design such V-models, which are correct from the point of view of both the sampling and rendering, thus leading to both alias-free volumetric representation and alias-free rendered images. We performed numerous experiments with different combinations of V-models and reconstruction techniques. We have shown that the V-model with a Gaussian surface density profile combined with tricubic interpolation and Gabor derivative reconstruction outperforms the previously published technique with a linear density profile. This enables higher fidelity of images rendered from volume data due to increased sharpness of edges and thinner surface patches     

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.     

Volumetric Reconstruction of Objects and Scenes Using Range Images

This paper reviews volumetric methods for fusing sets of range images to create 3D models of objects or scenes. It also presents a new reconstruction method, which is a hybrid that combines several desirable aspects of techniques discussed in the literature. The proposed reconstruction method projects each point, or voxel, within a volumetric grid back onto a collection of range images. Each voxel value represents the degree of certainty that the point is inside the sensed object. The certainty value is a function of the distance from the grid point to the range image, as well as the sensor's noise characteristics. The super-Bayesian combination formula is used to fuse the data created from the individual range images into an overall volumetric grid. We obtain the object model by extracting an isosurface from the volumetric data using a version of the marching cubes algorithm. Results are shown from simulations and real range finders.     

Non-rigid 3D shape tracking from multiview video

We present a fast and efficient non-rigid shape tracking method for modeling dynamic 3D objects from multiview video. Starting from an initial mesh representation, the shape of a dynamic object is tracked over time, both in geometry and topology, based on multiview silhouette and 3D scene flow information. The mesh representation of each frame is obtained by deforming the mesh representation of the previous frame towards the optimal surface defined by the time-varying multiview silhouette information with the aid of 3D scene flow vectors. The whole time-varying shape is then represented as a mesh sequence which can efficiently be encoded in terms of restructuring and topological operations, and small-scale vertex displacements along with the initial model. The proposed method has the ability to deal with dynamic objects that may undergo non-rigid transformations and topological changes. The time-varying mesh representations of such non-rigid shapes, which are not necessarily of fixed connectivity, can successfully be tracked thanks to restructuring and topological operations employed in our deformation scheme. We demonstrate the performance of the proposed method both on real and synthetic sequences.     

重建小凸多面物体面形的新方法

为实现小凸多面物体面形快速重建,提出了基于投影轮廓的新方法。首先处理被测小凸多面物体各平行旋转角度下纵投影轮廓图像,得到对应轮廓序列集及横截面切片投影长度曲线集,然后由该曲线集得到所有疑似被测物体表平面的索引,将该索引对照各轮廓序列进行筛选,最后经计算得到被测物体的各表平面参数,完成面形重建。实验表明,该方法能够精确恢复被测小凸多面物体面形,与现有方法相比具有设备精简、速度快等特点,适用于针对小凸多面体工件的工程应用。     

Global,Dense Multiscale Reconstruction for a Billion Points

We present a variational approach for surface reconstruction from a set of oriented points with scale information. We focus particularly on scenarios with nonuniform point densities due to images taken from different distances. In contrast to previous methods, we integrate the scale information in the objective and globally optimize the signed distance function of the surface on a balanced octree grid. We use a finite element discretization on the dual structure of the octree minimizing the number of variables. The tetrahedral mesh is generated efficiently with a lookup table which allows to map octree cells to the nodes of the finite elements. We optimize memory efficiency by data aggregation, such that robust data terms can be used even on very large scenes. The surface normals are explicitly optimized and used for surface extraction to improve the reconstruction at edges and corners.