Computational complexity of spatial reasoning with directional relationship

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Computational complexity of spatial reasoning with directional relationship

The property of NP-completeness of topologic spatial reasoning problem has been proved. According to the similarity of uncertainty with topologic spatial reasoning, the problem of directional spatial reasoning should be also an NP-complete problem. The proof for the property of NP-completeness in directional spatial reasoning problem is based on two important transformations. After these transformations, a spatial configuration has been constructed based on directional constraints, and the property of NP-completeness in directional spatial reasoning has been proved with the help of the consistency of the constraints in the configuration.     

附加空间约束的径向点质量模型方法反演区域地表质量变化

径向点质量模型反演方法本质上是空间扰动重力的向下延拓,属于病态问题,通常采用正则化方法求解。针对该问题,对径向点质量模型方法进行改进,提出附加空间约束的径向点质量模型方法,引入符合实际的空间约束条件,建立空间约束条件的虚拟观测方程,并采用赫尔默特方差分量估计确定原始观测方程和虚拟观测方程的合理权比,使反演结果更加稳定。以南美大陆区域为研究区域进行陆地水储量变化反演,试验结果表明：增加空间约束后,法方程组条件数明显减小、病态程度降低,反演结果与球谐系数法反演结果、GLDAS模型结果整体相一致,验证了方法的正确性,说明该方法可有效应用于区域地表质量变化反演,为利用卫星重力监测地表质量变化提供了一种新途径。     

基于混合罚函数法的多尺度电离层层析确权方法

在利用GNSS进行像素基电离层层析时,多尺度层析方法利用权重因子将反演区域不同像素层析模型结合在一起,最终得到电离层电子密度反演结果,可以有效地解决电离层层析过程中不适应问题和最终的电离层电子密度失真现象。在多尺度电离层层析中,不同像素尺度层析模型之间权重是影响最终的电离层电子密度精度的重要因素。为了获得高精度电离层层析模型,考虑到权重因子存在着等式和不等式限制条件,采用解决最优化问题的罚函数法确定不同像素尺度电离层层析模型之间的权重。通过采用实测GNSS观测数据进行电离层多尺度电离层层析,对比了多尺度层析模型的各个子模型建模精度并进行分析,同时将罚函数法获得的模型精度与其他确权方法进行了对比,该方法可以有效地应用于多尺电离层度层析,且最终的层析模型精度优于其他确权方法,更优于单尺度电离层层析模型精度。     

道路与建筑物空间冲突的几何相似性移位算法

保持建筑物群的空间分布模式一致是道路与建筑物空间冲突处理问题的难点。按道路对建筑物的包围程度,将道路与建筑物之间的关系类型划分为开放型、半开放型和闭合型。本文提出了基于几何相似性的建筑物移位算法,并以距离、角度和面积作为满足几何相似性的约束条件。以道路网眼为单位,采用最小生成树的方法生成建筑物群的骨架,以骨架的长度和角度特征分别作为建筑物移位的距离和角度约束条件,以建筑物与网眼的面积比作为建筑物移位的面积约束条件。针对可能出现的次生冲突,探讨了次生冲突的处理方法。试验结果表明,本文方法能够消除因道路拓宽导致的道路与建筑物冲突,并能完备地保持建筑物群的空间分布模式。     

On weighted total least-squares with linear and quadratic constraints

A weighted total least-squares (WTLS) approach with linear and quadratic constraints is developed. This method is according to the traditional Lagrange approach to optimize the target function of this problem. The WTLS and constrained total least-squares (CTLS) approach had been distinctively investigated, however, these two problems have not been simultaneously considered yet; furthermore, among the contributions on the CTLS problem, only Schaffrin and Felus considered linear and quadratic constraints together; nevertheless, in many practical examples, some elements of the design/coefficient matrix are fixed and should not be modified and this approach cannot deal with these cases. The main necessity of this research appears after the desirable property of the WTLS approach in preserving the structure of the design matrix was proven by Mahboub. In other words, currently, the WTLS approach is one of the most efficient methods for solving the so-called errors-in-variables model and an attempt for equipping it with constraints seems necessary. Also it is demonstrated that the additional constraints have a ’regularization role’ for ill-conditioned problems and the unconstrained solution suffers from ill-conditioning effects which give it an added advantage over the unconstrained WTLS algorithm. Four geodetic applications indicate the significant of this problem in the presence of colored and white noise in the data.     

Spatial optimization for land acquisition problems: A review of models,solution methods,and GIS support

This article reviews the interdisciplinary research field of spatial optimization for land acquisition problems. We start with a theoretical framework to identify three categories of spatial optimization models: problems with aspatial constraints, location models, and problems with topological constraints. Exact, heuristic, and metaheuristic approaches to solving these problems are critically discussed. Tools that are available in commercial and open‐source GIS packages are reviewed from four aspects. We first survey the off‐the‐shelf support and then the development environments in these packages. A case study of the one‐center problem is used to illustrate the computational performance of different solution methods. Finally the advantages and disadvantages of current GIS data models are discussed. The article concludes with challenges and future directions for solving spatial optimization problems for land acquisition.     

高分辨率光学卫星影像线段融合方法

针对高分辨率光学卫星影像线段断裂问题,基于不同方法线段提取结果优势互补的思想,提出一种简单的线段融合方法。首先,从边缘提取、边缘跟踪入手,对不同方法试验结果进行对比分析,以此验证融合不同方法线段提取结果的必要性;其次,选取边缘提取、边缘跟踪差异性较大的两种线段提取方法作为融合基元,并对戴激光等提出的线段提取方法进行了改进;然后,通过相位分组、端点约束、拓扑约束,构建不同方法线段的匹配模型;最后,依据线段长度优先的原则,建立线段融合决策模型。通过多幅不同类型、不同大小、不同覆盖区域的高分辨率光学卫星影像试验结果对比分析,本文方法相对于其他方法,具有线段结果完整度高的优势。     

视觉驱动的变分配准方法

针对传统整体配准模型不能充分顾及局部变形的问题,提出了一种视觉驱动的变分配准方法。该方法在变分模型建立中综合考虑了局部变换、整体平滑和视觉约束,同时兼顾了亮度和对比度差异。首先,基于灰度均方根误差建立配准模型的数据项;其次,为了保证整体平滑,模型采用H¹半范数进行自适应约束;最后,为了保证影像中的空间属性满足视觉的要求,不能出现扭曲变形,采用直线特征进行先验约束。在变分模型求解过程中先利用整个影像估计影像之间的整体变换参数,然后采用小的邻域范围进行局部估计。整个过程在多水平差分框架下迭代求解变换参数,进而兼顾了整体平滑和局部变形。笔者利用ZY-3卫星数据进行了试验,采用目视和量化指标进行了评价,验证了本文方法的优越性。     

Convex optimization under inequality constraints in rank-deficient systems

Many geodetic applications require the minimization of a convex objective function subject to some linear equality and/or inequality constraints. If a system is singular (e.g., a geodetic network without a defined datum) this results in a manifold of solutions. Most state-of-the-art algorithms for inequality constrained optimization (e.g., the Active-Set-Method or primal-dual Interior-Point-Methods) are either not able to deal with a rank-deficient objective function or yield only one of an infinite number of particular solutions. In this contribution, we develop a framework for the rigorous computation of a general solution of a rank-deficient problem with inequality constraints. We aim for the computation of a unique particular solution which fulfills predefined optimality criteria as well as for an adequate representation of the homogeneous solution including the constraints. Our theoretical findings are applied in a case study to determine optimal repetition numbers for a geodetic network to demonstrate the potential of the proposed framework.     

附加约束条件对GNSS/INS组合导航结果的影响分析

针对车载全球导航卫星系统/惯性导航系统（global navigation satellite system/inertial navigation system,GNSS/INS）组合导航中卫星信号中断,惯性导航系统单独导航误差积累较大的问题,提出了附加载体运动条件约束的卡尔曼（Kalman）滤波解算方法。通过利用载体固有的运动约束,包括近似高程约束、近似速度约束和近似姿态约束,减少载体自由度和模型参数;通过引入新的观测类型,增加观测冗余,可以加强Kalman滤波解,提高在GNSS信号中断时组合导航系统的定位精度,实现无缝导航。     

A Bayesian method for linear, inequality-constrained adjustment and its application to GPS positioning

One of the typical approaches to linear, inequality-constrained adjustment (LICA) is to solve a least-squares (LS) problem subject to the linear inequality constraints. The main disadvantage of this approach is that the statistical properties of the estimate are not easily determined and thus no general conclusions about the superiority of the estimate can be made. A new approach to solving the LICA problem is proposed. The linear inequality constraints are converted into prior information on the parameters with a uniform distribution, and consequently the LICA problem is reformulated into a Bayesian estimation problem. It is shown that the LS estimate of the LICA problem is identical to the Bayesian estimate based on the mode of the posterior distribution. Finally, the Bayesian method is applied to GPS positioning. Results for four field tests show that, when height information is used, the GPS phase ambiguity resolution can be improved significantly and the new approach is feasible.     

An Aggregate Constraint Method for Inequality-constrained Least Squares Problems

The inequality-constrained least squares (ICLS) problem can be solved by the simplex algorithm of quadratic programming. The ICLS problem may also be reformulated as a Bayesian problem and solved by using the Bayesian principle. This paper proposes using the aggregate constraint method of non-linear programming to solve the ICLS problem by converting many inequality constraints into one equality constraint, which is a basic augmented Lagrangean algorithm for deriving the solution to equality-constrained non-linear programming problems. Since the new approach finds the active constraints, we can derive the approximate algorithm-dependent statistical properties of the solution. As a result, some conclusions about the superiority of the estimator can be approximately made. Two simulated examples are given to show how to compute the approximate statistical properties and to show that the reasonable inequality constraints can improve the results of geodetic network with an ill-conditioned normal matrix.     

遥感反演中约束最优化方法的拓展

遥感反演大多是典型的约束是最优化问题。本文对现有的约束最优化方法在遥感反演中的适用性进行了分析，从提高反演速度有降低优化方法病态特性两个方面考虑，提出了罚矩阵的概念，对约束优化方法中的乘子法进行了拓展，并进行了理论证明。经过大量的模拟反演实验表明，拓展后的乘子法的反演速度提高了大约30％，病态程度也得到了进一步的改善。     

跨媒介的地图色域映射方法研究

颜色设备相关性的特点导致地图在跨媒介再现时容易出现丢色、偏色等现象,影响地图视觉效果,甚至传输错误的属性、数量等信息。从地图色域特征出发,将地图色域映射问题转换为目标设备色域约束下的地图色域离散点云形变问题。进一步引入Delaunay剖分和几何矩,定义CIE1976LAB色空间下地图色域形变的目标函数,给出全局最优解的求解流程。将算法结果与ICC再现意图结果进行对比,结果表明该方法能够很好保持地图整体的色貌特征以及局部图斑之间的色彩对比、连续等色彩特征,能够显著提高地图跨媒介地图颜色复制精度。     

融合正交几何信息的非线性等式约束整体最小二乘平差及迭代算法

正交距离最小二乘和加权整体最小二乘是解自变量含误差拟合问题的两种独立准则。加权整体最小二乘与正交距离最小二乘不同,它不考虑测量点与拟合点之间的连线垂直于拟合对象的几何信息,不能确保测量点到拟合对象的距离的平方和为极小值。针对该问题,本文将正交几何信息作为约束条件融入加权整体最小二乘,提出一种约束方程带有误差改正数的非线性等式约束整体最小二乘平差法。首先,把加权整体最小二乘平差的函数式看作是非线性方程,连同正交几何约束方程一并线性化,得到线性的平差函数方程;然后,采用拉格朗日乘数法推导其参数估计及精度评定公式,并给出迭代计算算法;最后,以平面直线拟合为例,对本文方法和计算算法进行验证。试验结果表明:①本文方法和算法具有可行性;②与加权最小二乘和加权整体最小二乘相比,本文方法计算的测量点到拟合直线的垂直距离平方和最小;③本文方法计算的测量点到拟合直线的距离与测量点到拟合点的距离相等。     

基于有效约束的附不等式约束平差的一种新算法

不等式约束是客观实际中普遍存在的一种约束,但目前大地测量数据处理领域并没有成熟、完整并被普遍接受的处理理论和方法。首先简要总结附不等式约束平差的各种方法及其存在的问题。然后对现有测量平差中附有等式约束的平差模型进行扩展,提出一种新的处理附有线性约束(包括等式和不等式约束)的平差方法。该方法在有效约束概念下,通过库恩-塔克条件来寻找有效约束条件,把不等式约束平差问题转化为我们熟知的等式约束平差问题,因此实现解向量与观测向量之间的显式表达。最后,用一个数值算例验证新方法的可行性,同时算例分析表明:用等式约束代替有效约束或集成约束进行平差计算,能得到正确的平差结果,但得不到正确的精度评定结果。     

基于极线及共面约束条件的Kinect点云配准方法

Kinect作为轻量级手持传感器,在室内场景恢复与模型重建中具有灵活、高效的特点。不同于大多数只基于彩色影像或只基于深度影像的重建算法,提出一种将彩色影像与深度影像相结合的点云配准算法并用于室内模型重建恢复,其过程包括相邻帧数据的配准与整体优化。在Kinect已被精确标定的基础上,将彩色影像匹配得到的同名点构成极线约束与深度图像迭代最近点配准的点到面约束相结合,以提高相邻帧数据配准算法的精度与鲁棒性。利用相邻4帧数据连续点共面约束,对相邻帧数据配准结果进行全局优化,以提高模型重建的精度。在理论分析基础上,通过实验验证了该算法在Kinect Fusion无法实现追踪、建模的场景中鲁棒性依然较好,点云配准及建模精度符合Kinect观测精度。     

A robust linear least-squares estimation of camera exterior orientation using multiple geometric features

For photogrammetric applications, solutions to camera exterior orientation problem can be classified into linear (direct) and non-linear. Direct solutions are important because of their computational efficiency. Existing linear solutions suffer from lack of robustness and accuracy partially due to the fact that the majority of the methods utilize only one type of geometric entity and their frameworks do not allow simultaneous use of different types of features. Furthermore, the orthonormality constraints are weakly enforced or not enforced at all. We have developed a new analytic linear least-squares framework for determining camera exterior orientation from the simultaneous use of multiple types of geometric features. The technique utilizes 2D/3D correspondences between points, lines, and ellipse–circle pairs. The redundancy provided by different geometric features improves the robustness and accuracy of the least-squares solution. A novel way of approximately imposing orthonormality constraints on the sought rotation matrix within the linear framework is presented. Results from experimental evaluation of the new technique using both synthetic data and real images reveal its improved robustness and accuracy over existing direct methods.     

A solution to EIV model with inequality constraints and its geodetic applications

In the field of surveying, mapping and geodesy, there have been a number of works on the error-in-variable (EIV) model with constraints, where equality constraints are imposed on the parameter vector. However, in some cases, these constraints may be inequalities. The EIV model with inequality constraints has not been fully investigated. Therefore, this paper presents an inequality-constrained total least squares (ICTLS) solution for the EIV model with inequality constraints (denoted as ICEIV). Employing the proposed ICTLS method, the ICEIV problem is first converted into an equality-constrained problem by distinguishing the active constraints through exhaustive searching, and it is then resolved employing the method of equality-constrained total least squares (ECTLS). The applicability and feasibility of the proposed method is illustrated in two examples.