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     

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.     

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。     

多分辨率下资源感知的图像目标自适应缩放检测

边缘视频处理可以降低云平台视频处理系统的视频传输时延、视频处理开销和存储成本,但是视频参数(分辨率、帧率等)的多样性容易导致边缘视频处理的效果不尽人意。通常,在图像预处理阶段会先对图像进行缩放变换再进行后续处理,以保障图像处理的最佳效果,但是在视频监控等具有不确定性的场景中对所有分辨率的图像直接成倍缩小容易降低目标检测率。基于以上问题,把图像水平像素点和垂直像素点的缩放倍数记作图像缩放因子,对于不同分辨率的视频数据,分析了图像缩放因子对视频数据处理效果的影响,提出了图像缩放因子动态设置方案。该方案以系统性能指标(服务器端系统功耗和内存使用率)为视频处理性能指标(人脸检测率)的约束条件,获取该分辨率下人脸检测率最优时对应的图像缩放因子。实验结果表明,对于不同分辨率的视频数据,图像缩放因子动态设置方案可以在保证视频处理性能的基础上,减少系统功耗和内存使用率,提高视频处理效率。     

硬件加速的大数据量自适应体绘制

利用树形结构和纹理映射技术,在普通微机上实现对大数据量体数据的实时交互.依靠八叉树结构和显卡的硬件加速功能,将体数据划分为不同精度的数据块,打破了大数据显示时显存与内存间容量和带宽的限制,通过交互策略动态遍历该树,实现对大数据量体数据多精度的绘制.实验结果表明,文中方法在普通微机上可以大于10帧/s的速度交互操纵GB级以上的体数据.该方法可有效地降低体绘制对于硬件的需求,使得在较低配置下对其交互成为可能.     

稀疏轨道条件下SAR几何校正轨道拟合策略

针对SAR影像头文件中提供的轨道矢量分布较为稀疏时,使用低阶多项式拟合轨道参数会存在较大误差,从而导致基于距离-多普勒模型的星载SAR影像几何校正精度较差的问题,提出了一种稀疏轨道条件下实用的轨道拟合策略。通过对轨道拟合误差进行分析,综合考虑距离-多普勒模型的解算与现有几何校正资源,选择使用高阶插值方法生成卫星成像时刻处足够的加密点轨道状态矢量,再对局部的轨道进行二阶多项式拟合,利用拟合的轨道模型系数进行几何校正。利用实测GPS点数据进行了SAR几何校正精度验证,结果表明该策略能够明显改善ALOS2 PALSAR影像几何校正精度,证明了该方法的有效性和良好的适用性。     

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.     

Coloring octrees

An octree is a recursive partition of the unit cube, such that in each step a cube is subdivided into eight smaller cubes. Those cubes that are not further subdivided are the leaves of the octree. We consider the problem of coloring the leaves of an octree using as few colors as possible such that no two of them get the same color if they share a facet. It turns out that the number of colors needed depends on a parameter that we call unbalancedness. Roughly speaking, this parameter measures how much adjacent cubes differ in size. For most values of this parameter we give tight bounds on the minimum number of colors, and extend the results to higher dimensions.     

Efficient optimal design of uncertain discrete time dynamical systems

In this paper we consider the problem of optimal design of an uncertain discrete time nonlinear dynamical system. The problem is formulated using an a-posterori design criterion, which can account for uncertainties generated by the dynamics of the system itself as well as parametric uncertainties. In general, for most uncertain complex dynamical systems, this type of method is difficult to solve analytically. A numerical scheme is developed for the optimal design that involves two steps. First, in order to obtain a numerical algorithm for the optimal solution, we apply randomized algorithms for average performance synthesis to approximate the optimal solution. Second, using the properties of the Perron–Frobenius operator we develop an efficient computation approach to calculate the stationary distribution for the uncertain dynamical systems and the average performance criteria.     

Interprocessor communication with limited memory

Many parallel applications require periodic redistribution of workloads and associated data. In a distributed memory computer, this redistribution can be difficult if limited memory is available for receiving messages. We propose a model for optimizing the exchange of messages under such circumstances which we call the minimum phase remapping problem. We first show that the problem is NP-complete, and then analyze several methodologies for addressing it. First, we show how the problem can be phrased as an instance of multicommodity flow. Next, we study a continuous approximation to the problem. We show that this continuous approximation has a solution which requires at most two more phases than the optimal discrete solution, but the question of how to consistently obtain a good discrete solution from the continuous problem remains open. We also devise a simple and practical approximation algorithm for the problem with a bound of 1.5 times the optimal number of phases. We also present an empirical study of variations of our algorithms which indicate that our approaches are quite practical.     

Scalable Feature‐Preserving Irregular Mesh Coding

This paper presents a novel wavelet‐based transform and coding scheme for irregular meshes. The transform preserves geometric features at lower resolutions by adaptive vertex sampling and retriangulation, resulting in more accurate subsampling and better avoidance of smoothing and aliasing artefacts. By employing octree‐based coding techniques, the encoding of both connectivity and geometry information is decoupled from any mesh traversal order, and allows for exploiting the intra‐band statistical dependencies between wavelet coefficients. Improvements over the state of the art obtained by our approach are three‐fold: (1) improved rate–distortion performance over Wavemesh and IPR for both the Hausdorff and root mean square distances at low‐to‐mid‐range bitrates, most obvious when clear geometric features are present while remaining competitive for smooth, feature‐poor models; (2) improved rendering performance at any triangle budget, translating to a better quality for the same runtime memory footprint; (3) improved visual quality when applying similar limits to the bitrate or triangle budget, showing more pronounced improvements than rate–distortion curves.     

三维激光点云数据的可视化研究

大量的点云数据是通过三维激光扫描得到的,而点云数据的显示快慢受到了数据索引的直接影响,这是一个基础性问题。经过研究,八叉树与叶节点KD树相结合的混合空间索引结构以及LOD构建的层次细节模型是用来解决点云数据管理与可视化效率不高的问题的有效方法。在局部,通过在叶子节点中构建的KD树实现高效的查询和显示;在全局,为了实现快速检索与调度使用了八叉树模型。采用这种混合数据模型进行点云组织,建立空间索引,并对点云数据进行LOD构建,实现了点云数据的高效检索以及可视化。     

Integrated optimization of the material and structure of composites based on the Heaviside penalization of discrete material model

Based on discrete material optimization and topology optimization technologies, this paper discusses the problem of integrated optimization design of the material and structure of fiber-reinforced composites by considering the characteristics of the discrete variable of fiber ply angle because of the manufacture requirements. An optimization model based on the minimum structural compliance with a specified composite volume constraint is established. The ply angle and the distribution of the composite material are introduced as independent variables in two geometric scales (material and structural scales). The void material is added into the optional discrete material set to realize the topology change of the structure. This paper proposes an improved HPDMO (Heaviside Penalization of Discrete Material Optimization) model to obtain a better convergent result, and an explicit sensitivity analysis is performed. The effects of the HPDMO model on the convergence rate of the optimization results, the objective function value and the iteration history are studied and compared with those from the classical Discrete Material Optimization model and the Continuous Discrete Material Optimization model in this paper. Numerical examples in this paper show that the HPDMO model can effectively achieve the integrated optimization of the fiber ply angle and its distribution in the structural domain, and can also considerably improve the convergence rate of the optimal results compared with other DMO models. This model will help to reduce the manufacture cost of the optimal design.     

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。     

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.     

Multiresolution Analysis for Optimal Binary Filters

The performance of a designed digital filter is measured by the sum of the errors of the optimal filter and the estimation error. Viewing an image at a high resolution results in optimal filters having smaller errors than at lower resolutions; however, higher resolutions bring increased estimation error. Hence, choosing an appropriate resolution for filter design is important. The present paper provides expressions for both the error of the optimal filter and the design error for estimating optimal filters in a pyramidal multiresolution framework. The analysis is facilitated by a general characterization of suitable sequences of resolution-constraint mappings. The error expressions are generated from resolution to resolution in a telescoping manner. To take advantage of data at all resolutions, one can use a hybrid multiresolution design to arrive at a multiresolution filter. A sequence of filters is designed using data at increasing resolutions, each filter serves as a prior filter for the next, and the last filter is taken as the designed filter. The value of the multiresolution filter at a given observation is based on the highest resolution at which conditioning by the observation is considered significant.     

Descent algorithms for optimal periodic output feedback control

Periodic output feedback is investigated in the context of linear-quadratic regulation for finite-dimensional time-invariant linear systems. Discrete output samples are multiplied by a periodic gain function to generate a continuous feedback control. The optimal solution is obtained in two steps by separating the continuous-time from the discrete-time structure. First, the optimal pole placement problem under periodic output feedback is solved explicitly under the assumption that the behavior at the sample times has been specified in terms of a gain matrix G. Then the minimum value, which depends on G, is substituted into the overall objective. This results in a finite-dimensional nonlinear programming problem over all admissible gain matrices G. The solution defines the optimal periodic output feedback control via the formulas of the optimal pole placement problem. A steepest descent and a direct iterative method for solving this problem are formulated and compared. Numerical examples show that the performance using periodic output feedback is almost equivalent to that using optimal continuous-state feedback     

A Sparse Multiscale Algorithm for Dense Optimal Transport

Discrete optimal transport solvers do not scale well on dense large problems since they do not explicitly exploit the geometric structure of the cost function. In analogy to continuous optimal transport, we provide a framework to verify global optimality of a discrete transport plan locally. This allows the construction of an algorithm to solve large dense problems by considering a sequence of sparse problems instead. The algorithm lends itself to being combined with a hierarchical multiscale scheme. Any existing discrete solver can be used as internal black-box. We explicitly describe how to select the sparse sub-problems for several cost functions, including the noisy squared Euclidean distance. Significant reductions in run-time and memory requirements have been observed.     

基于关系数据库的海量地学真三维体数据组织

在地学领域,体数据的海量性已经成为制约真三维GIS发展的瓶颈之一。由于受到目前数据库访问技术的限制,传统海量体数据的组织还主要依靠文件系统,从而导致安全性和共享性差、并发访问异常、数据冗余以及无法统一管理等诸多问题。针对以上缺陷,提出一种类八叉树空间划分思想,在此基础之上,给出了基于关系数据库的海量地学真三维体数据组织方法,并实现了相关的空间查找、多分辨率和海量数据内外存交换策略。实践证明,该方法在性能上可以满足海量数据的组织及三维可视化等实际应用的需要。鉴于关系数据库是目前实用性、普及性最高的数据库,因此该方法具有较高的推广性和实用价值。     

Continuous Global Optimization in Multiview 3D Reconstruction

In this article, we introduce a new global optimization method to the field of multiview 3D reconstruction. While global minimization has been proposed in a discrete formulation in form of the maxflow-mincut framework, we suggest the use of a continuous convex relaxation scheme. Specifically, we propose to cast the problem of 3D shape reconstruction as one of minimizing a spatially continuous convex functional. In qualitative and quantitative evaluation we demonstrate several advantages of the proposed continuous formulation over the discrete graph cut solution. Firstly, geometric properties such as weighted boundary length and surface area are represented in a numerically consistent manner: The continuous convex relaxation assures that the algorithm does not suffer from metrication errors in the sense that the reconstruction converges to the continuous solution as the spatial resolution is increased. Moreover, memory requirements are reduced, allowing for globally optimal reconstructions at higher resolutions. We study three different energy models for multiview reconstruction, which are based on a common variational template unifying regional volumetric terms and on-surface photoconsistency. The three models use data measurements at increasing levels of sophistication. While the first two approaches are based on a classical silhouette-based volume subdivision, the third one relies on stereo information to define regional costs. Furthermore, this scheme is exploited to compute a precise photoconsistency measure as opposed to the classical estimation. All three models are compared on standard data sets demonstrating their advantages and shortcomings. For the third one, which gives the most accurate results, a more exhaustive qualitative and quantitative evaluation is presented.