Parallel display of objects represented by linear octrees

The storage, display, and manipulation of three dimensional volumetric information requires large amounts of computing resources, both in terms of memory, and processing power. Most existing serial algorithms that display 3-D objects on a 2-D screen are found to be too slow to process the large amounts of volume data in a reasonable time. Hence, one way to increase the performance of the display algorithm is to process individual volume elements (voxels) in parallel. The first part of this paper presents a brief over view of the linear octree data structure which represents 3-D objects by an eight-way branching tree, while the second part focusses on the parallel display of such objects. We have shown that, for an object represented by a linear octree and enclosed in a 2ⁿ×2ⁿ×2ⁿ universe, the maximum number of voxels that can be processed in parallel is 3ⁿ, and the maximum number of time steps required to display such an object is 4ⁿ. This paper presents a set of formulae which identify the processing element (PE) as well as the time step in which a given linear octree node is processed. Similarly, a procedure which determines the locational code of a linear octree node which must be processed by a given PE, at some specific time step, is presented, along with a strategy for determining whether a PE is active or idle     

Linear octrees by volume intersection

The paper describes a new algorithm for constructing a 3D approximation of an object from three orthogonal 2D silhouettes. The 2D views are represented as binary arrays and 3D approximation is obtained as a linear octree. The algorithm makes use of volume intersection of three cylinders obtained by sweeping three views in respective directions. The algorithm takes less time than an existing algorithm which makes use of three quadtrees and an octree for 2D and 3D image representation, respectively. Unlike the previous algorithm, the present algorithm does not require any preprocessing stage or condensation. It is Shown that the proposed algorithm is of o(T), where T is the total number of nodes in the resulting octree.     

Octree Representation and Its Applications in CAD

In this paper,a survey of octree representation and its applications in CAD is presented.The octree representation may be categorized as pure octree representation and polytree(or extended octree),and the latter is actually a boundary representation decomposed by octree.Linear octree which is a variant of regular octree representation has the advantage of saving memory space.The mapping between Cartesian coordinates and node addresses in linear octree is discussed.Then,algorithms for converting a boundary representation of 3D object into an octree are investiged and major approaches for transforming an octree encoded object are presented.After that,some of the applications of octree representation in CAD are listed,in particular,the applications in solid modeling,in accelerating ray tracing and in generating meshes for FEM.     

Linear object classes and image synthesis from a single exampleimage

The need to generate new views of a 3D object from a single real image arises in several fields, including graphics and object recognition. While the traditional approach relies on the use of 3D models, simpler techniques are applicable under restricted conditions. The approach exploits image transformations that are specific to the relevant object class, and learnable from example views of other “prototypical” objects of the same class. In this paper, we introduce such a technique by extending the notion of linear class proposed by the authors (1992). For linear object classes, it is shown that linear transformations can be learned exactly from a basis set of 2D prototypical views. We demonstrate the approach on artificial objects and then show preliminary evidence that the technique can effectively “rotate” high-resolution face images from a single 2D view     

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.     

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。     

Recognition by linear combinations of models

An approach to visual object recognition in which a 3D object is represented by the linear combination of 2D images of the object is proposed. It is shown that for objects with sharp edges as well as with smooth bounding contours, the set of possible images of a given object is embedded in a linear space spanned by a small number of views. For objects with sharp edges, the linear combination representation is exact. For objects with smooth boundaries, it is an approximation that often holds over a wide range of viewing angles. Rigid transformations (with or without scaling) can be distinguished from more general linear transformations of the object by testing certain constraints placed on the coefficients of the linear combinations. Three alternative methods of determining the transformation that matches a model to a given image are proposed     

Fast Collision Detection Algorithms with Applications to Particle Flow

In this paper, we present efficient algorithms for collision detection of arbitrarily shaped rigid moving objects in a variety of interactive as well as non-interactive environments. The algorithms primarily consist of two stages. The first stage involves finding candidate objects for possible collisions. The second stage involves detecting exact (within a prespecified tolerance) collision between these candidates. The primary data structure used in the algorithms is an octree. In the first stage, we build an octree for the enclosure containing the objects, which is used to detect possible collisions. Assuming spatial/temporal coherence i.e., that the particles move slowly or that the time sampling is fast enough, the average time complexity of this stage can be shown to be O(n) (excluding the time complexity for a one time octree construction), where n is the number of particles. In the second stage, we build a surface-octree for each object. If the objects are convex and assuming coherence, the expected time complexity to detect precise (within a prespecified tolerance) collision for each pair is a constant (excluding the time complexity for a one time surface-octree construction). Therefore, the overall expected time complexity for convex object collision detection is linear with respect to n. For the concave objects, complexity analysis is nontrivial to perform and instead we provide a very practical (almost linear time) algorithm. We apply our algorithms to particle flow simulations by simulating flow density conditions often arising in granular flows.     

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     

基于三维点云数据的线性八叉树编码压缩算法

八叉树结构是三维数据建模中研究和应用最为广泛的栅格数据结构。由于三维扫描的点云数据是基于物体表面的，其空间离散程度远大于三维实体数据，一般的线性八叉树编码压缩方法都是基于实体数据的，不能直接应用于三维点云数据。提出的改进的线性八叉树地址码(Morton码)的方法可大大提高它的连续性，有效降低八叉树的深度，提高数据的压缩比，改进后的Morton码还可以应用多种编码压缩算法进一步压缩。     

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.     

基于八叉树空间分割的三维点云模型密写

针对三维点云模型的信息隐藏,提出一种基于八叉树空间分割的空域密写算法。对经过主成分分析后的三维点云模型建立包围盒,利用八叉树空间分割得到小体元并记录分割过程,通过顶点位移将信息嵌入到小体元内的不同空间位置。实验结果表明,该算法在提取信息时不需要原始模型数据,具有嵌入量高、失真度低的特点,能够抵抗旋转、平移、均匀缩放和顶点重排序攻击,适合于任意网格的三维模型信息隐藏。     

A generic scheme for progressive point cloud coding

In this paper, we propose a generic point cloud encoder that provides a unified framework for compressing different attributes of point samples corresponding to 3D objects with arbitrary topology. In the proposed scheme, the coding process is led by an iterative octree cell subdivision of the object space. At each level of subdivision, positions of point samples are approximated by the geometry centers of all tree-front cells while normals and colors are approximated by their statistical average within each of tree-front cells. With this framework, we employ attribute-dependent encoding techniques to exploit different characteristics of various attributes. All of these have led to significant improvement in the rate-distortion (R-D) performance and a computational advantage over the state of the art. Furthermore, given sufficient levels of octree expansion, normal space partitioning and resolution of color quantization, the proposed point cloud encoder can be potentially used for lossless coding of 3D point clouds.     

Multi-object reconstruction from dynamic scenes: An object-centered approach

In this paper, we present a new framework for three-dimensional (3D) reconstruction of multiple rigid objects from dynamic scenes. Conventional 3D reconstruction from multiple views is applicable to static scenes, in which the configuration of objects is fixed while the images are taken. In our framework, we aim to reconstruct the 3D models of multiple objects in a more general setting where the configuration of the objects varies among views. We solve this problem by object-centered decomposition of the dynamic scenes using unsupervised co-recognition approach. Unlike conventional motion segmentation algorithms that require small motion assumption between consecutive views, co-recognition method provides reliable accurate correspondences of a same object among unordered and wide-baseline views. In order to segment each object region, we benefit from the 3D sparse points obtained from the structure-from-motion. These points are reliable and serve as automatic seed points for a seeded-segmentation algorithm. Experiments on various real challenging image sequences demonstrate the effectiveness of our approach, especially in the presence of abrupt independent motions of objects.     

Genetic object recognition using combinations of views

Investigates the application of genetic algorithms (GAs) for recognizing real 2D or 3D objects from 2D intensity images, assuming that the viewpoint is arbitrary. Our approach is model-based (i.e. we assume a pre-defined set of models), while our recognition strategy relies on the theory of algebraic functions of views. According to this theory, the variety of 2D views depicting an object can be expressed as a combination of a small number of 2D views of the object. This implies a simple and powerful strategy for object recognition: novel 2D views of an object (2D or 3D) can be recognized by simply matching them to combinations of known 2D views of the object. In other words, objects in a scene are recognized by "predicting" their appearance through the combination of known views of the objects. This is an important idea, which is also supported by psychophysical findings indicating that the human visual system works in a similar way. The main difficulty in implementing this idea is determining the parameters of the combination of views. This problem can be solved either in the space of feature matches among the views ("image space") or the space of parameters ("transformation space"). In general, both of these spaces are very large, making the search very time-consuming. In this paper, we propose using GAs to search these spaces efficiently. To improve the efficiency of genetic searching in the transformation space, we use singular value decomposition and interval arithmetic to restrict the genetic search to the most feasible regions of the transformation space. The effectiveness of the GA approaches is shown on a set of increasingly complex real scenes where exact and near-exact matches are found reliably and quickly     

线性多视图重构的新算法

研究了由多幅图像恢复摄像机矩阵和空间物体三维几何形状这一多视图三维重构问题,改进了由Hartley和Rother等人分别给出的基于由无穷远平面诱导的单应进行射影重构的算法,提出了一种新的线性算法,它仅需要空间中3个点在每幅图像上均可见。因为空间中不在同一直线上的3个点恰好确定一个平面,所以它避免了Hartley和Rother等方法中需要确定空间4个点是否共面这一比较棘手的问题。大量实验结果表明,这种方法快速、准确且受噪声影响小。     

Embedding visual cognition in 3D reconstruction from multi-view engineering drawings

In this paper we discuss how to reconstruct 3D models from multi-view engineering draws by employing human engineers’ approaches. Human's ‘divide and conquer’ interpretation strategy in visual cognition is simulated, and successfully carried out on the basis of spatial division of 3D object space. At first, a volume-oriented method is utilized to decompose the 3D object space in a set of 3D ‘cell-boxes’ whose three-view bounding rectangles will isolate its related sub-projections from input projections views, and in every cell-box a cell primitive is implied. Then, a 3D model of each cell primitive is ‘locally’ generated from its ‘sub-projection’ views by wire-frame oriented algorithms. The final interpretation result of the overall projection-views is a ‘Union’ of these cell primitives. To deal with the ambiguity, a visual reasoning engine is implemented on the basis of principles from Gestalt psychology. It will be activated to pick out the most reasonable interpretation, when ambiguities are generated during the reconstruction process. The section views are also incorporated in getting rid of the ambiguity. Moreover, we design a natural and convenient interaction way to encourage the user to be involved in the process while interpreting complex projections. The key steps of this human-like reconstruction approach are presented in detail.     

On view likelihood and stability

We define two measures on views: view likelihood and view stability. View likelihood measures the probability that a certain view of a given 3D object is observed; it may be used to identify typical, or “characteristic” views. View stability measures how little the-image changes as the viewpoint is slightly perturbed; it may be used to identify “generic” views. Both definitions are shown to be identical up to the prior probability of camera orientations, and determined by the 2D metric used to compare images. We analytically derive the stability and likelihood measures for two feature-based 2D metrics, where the most stable and most likely view is shown to be the flattest view of the 3D shape. Incorporating view likelihood or stability in 3D object recognition and 3D reconstruction increases the chance of robust performance. In particular, we propose to use these measures to enhance 3D object recognition and 3D reconstruction algorithms, by adding a second step where the most likely solution is selected among all feasible solutions. These applications are demonstrated using simulated and real images     

基于多级线性结构和规则分块的虚拟八叉树

提出一种基于多级线性结构和规则分块、无指针/无位置码的虚拟八叉树模型,具有高效的结点访问效率和存储空间压缩效率,实现了指针八叉树在时间效率、线性八叉树在空间效率两方面优势的统一。新模型能够对三维实体及其内部的非均质属性进行建模,可以保证各种可视化与分析算法的处理效率,在空间信息系统和体图形学等实体建模相关的领域中具有重要的研究意义和应用价值。