On the number of occurrences of all short factors in almost all words

We previously proved that almost all words of length n over a finite alphabet A with m letters contain as factors all words of length k(n) over A as n→∞, provided limsup_n→∞ k(n)/log n<1/log m.

In this note it is shown that if this condition holds, then the number of occurrences of any word of length k(n) as a factor into almost all words of length n is at least s(n), where lim_n→∞ log s(n)/log n=0. In particular, this number of occurrences is bounded below by C log n as n→∞, for any absolute constant C>0.     

Matching wire frame objects from their two dimensional perspective projections

A wire frame object consists of a set of three dimensional arcs, each arc being a sequence of conics and line segments lying in the same plane, with different arcs being allowed to lie on different planes. Given a picture taken by a camera focusing on one wire frame object, we show how to determine what the object is and where it is situated relative to the camera when the camera viewing parameters are unknown.

To accomplish the object identification, we begin with a segmented picture. Then we construct a ray from the lens to each point on the boundary of every region. For each region, the collection of its associated rays is a cone. We show that by constructing cones, the two-dimensional to three-dimensional matching problem is transformed into an equivalent three-dimensional to three-dimensional matching problem.

This matching problem is expressed as a nonlinear optimization search procedure on the 6 camera viewing parameters: the 3 translation parameters and the 3 rotation parameters. A solution is found when a viewing position and optical axis is determined which is consistent with the world knowledge we have of possible curves and the observed image data.     

BEM and estimate of actual error for exterior Dirichlet problem for two-dimensional Helmholtz equation

The actual error in the numerical solution of a boundary integral equation cannot be measured unless the true solution is known. Here it is shown that residual error in the H^1/2 norm measures the actual error. Since the solution of the integral equation from the exterior Dirichlet problem for the two-dimensional Helmholtz equation with an arc as its boundary is unbounded near the tips, singular elements are used. The numerical results show that the use of the singular elements significantly reduces the error.     

Skeleton computation of orthogonal polyhedra

Skeletons are powerful geometric abstractions that provide useful representations for a number of geometric operations. The straight skeleton has a lower combinatorial complexity compared with the medial axis. Moreover, while the medial axis of a polyhedron is composed of quadric surfaces the straight skeleton just consist of planar faces. Although there exist several methods to compute the straight skeleton of a polygon, the straight skeleton of polyhedra has been paid much less attention. We require to compute the skeleton of very large datasets storing orthogonal polyhedra. Furthermore, we need to treat geometric degeneracies that usually arise when dealing with orthogonal polyhedra. We present a new approach so as to robustly compute the straight skeleton of orthogonal polyhedra. We follow a geometric technique that works directly with the boundary of an orthogonal polyhedron. Our approach is output sensitive with respect to the number of vertices of the skeleton and solves geometric degeneracies. Unlike the existing straight skeleton algorithms that shrink the object boundary to obtain the skeleton, our algorithm relies on the plane sweep paradigm. The resulting skeleton is only composed of axis‐aligned and 45° rotated planar faces and edges.     

A quadtree normalization scheme based on cyclic translations

An image can be represented by a compact and hierarchical structure, i.e. a quadtree. The storage requirements of an image constructed by a quadtree is highly sensitive to its position. Ang and Samet [Pattern Recognition Lett. 15(1), 57–63 (1994)] proposed an algorithm capable of normalizing a quadtree in O(s²log₂s) time and O(s²) space, where s is the length of the image grid, such that the number of nodes of the quadtree after normalization can be minimal. However, s is twice as long as the length of one side of the image to be normalized. In this study, we propose a normalization scheme based on cyclic translations. The time complexity and the space requirements of this scheme have four times less than those in Ang and Samet's case. In addition, no translation is necessary to fit the image into the northwest quadrant of the grid before the process of normalization. Also, this scheme can normalize a quadtree to obtain less node numbers than that of Ang and Samet. Furthermore, if the image's four corners have the same color, the amount of reduction for node number becomes larger after cyclic translations; it can occasionally reach to 75%. The analytical and empirical results demonstrate the advantages of this scheme.     

基于UWB的自主跟随机器人系统设计

针对传统自主跟随机器人采用摄像头图像识别的方法存在跟随对象容易丢失的问题,该文研究并设计了一种基于UWB的自主跟随机器人系统。自主跟随机器人采用双边双向测距(SDS-TWR)的算法计算出标签到基站之间的距离,再通过反余弦定理求出标签和基站之间形成的角度,并将角度和距离信息形成的融合信息通过串口发送给主控制器,通过主控制器对获取的融合信息进行处理,完成跟随目标对象的任务。实践证明,在利用角度大小跟随中,通过减少跟随边长误差,进而减小跟随角度误差,以提高自主跟随机器人的跟随精度,实现自主跟随机器人系统在人员移动密集的环境下对目标对象实时地、准确地跟随。     

High-Precision Boundary Length Estimation by Utilizing Gray-Level Information

We present a novel method that provides an accurate and precise estimate of the length of the boundary (perimeter) of an object by taking into account gray levels on the boundary of the digitization of the same object. Assuming a model where pixel intensity is proportional to the coverage of a pixel, we show that the presented method provides error-free measurements of the length of straight boundary segments in the case of nonquantized pixel values. For a more realistic situation, where pixel values are quantized, we derive optimal estimates that minimize the maximal estimation error. We show that the estimate converges toward a correct value as the number of gray levels tends toward infinity. The method is easy to implement; we provide the complete pseudocode. Since the method utilizes only a small neighborhood, it is very easy to parallelize. We evaluate the estimator on a set of concave and convex shapes with known perimeters, digitized at increasing resolution. In addition, we provide an example of applicability of the method on real images, by suggesting appropriate preprocessing steps and presenting results of a comparison of the suggested method with other local approaches.     

A Recursive Subdivision Algorithm for Piecewise Circular Spline

We present an algorithm for generating a piecewise G ¹ circular spline curve from an arbitrary given control polygon. For every corner, a circular biarc is generated with each piece being parameterized by its arc length. This is the first subdivision scheme that produces a piecewise biarc curve that can interpolate an arbitrary set of points. It is easily adopted in a recursive subdivision surface scheme to generate surfaces with circular boundaries with pieces parameterized by arc length, a property not previously available. As an application, a modified version of Doo–Sabin subdivision algorithm is outlined making it possible to blend a subdivision surface with other surfaces having circular boundaries such as cylinders.     

On nonexistence of boundary arcs in control problems with bounded state variables

When solving optimal control problems with bounded state variables, one must determine whether the optimal trajectory intersects the boundary only at isolated points in time (boundary point) or remains on the boundary for a nonzero length of time (boundary arc). Previously, this determination has been made by trial and error. The task is complicated by the fact that the necessary conditions in common use for these problems assume that the solution has a boundary arc, and can thus yield a boundary arc when the solution has no boundary arc. In this paper the necessary conditions of [1] are used to derive conditions under which the optimal trajectory cannot have a boundary arc. These conditions include the condition for no boundary arcs developed in [1] as a special case. The application of these conditions is illustrated via several examples.     

Properties of the satisfiability threshold of the strictly d-regular random (3, 2s)-SAT problem

A k-CNF (conjunctive normal form) formula is a regular (k, s)-CNF one if every variable occurs s times in the formula, where k≥2 and s>0 are integers. Regular (3, s)- CNF formulas have some good structural properties, so carrying out a probability analysis of the structure for random formulas of this type is easier than conducting such an analysis for random 3-CNF formulas. Some subclasses of the regular (3, s)-CNF formula have also characteristics of intractability that differ from random 3-CNF formulas. For this purpose, we propose strictly d-regular (k, 2s)-CNF formula, which is a regular (k, 2s)-CNF formula for which d≥0 is an even number and each literal occurs s-\frac{d}{2} or s+\frac{d}{2} times (the literals from a variable x are x and \neg x, where x is positive and \neg x is negative). In this paper, we present a new model to generate strictly d-regular random (k, 2s)-CNF formulas, and focus on the strictly d-regular random (3, 2s)-CNF formulas. Let F be a strictly d-regular random (3, 2s)-CNF formula such that 2s>d. We show that there exists a real number s₀ such that the formula F is unsatisfiable with high probability when s>s₀, and present a numerical solution for the real number s₀. The result is supported by simulated experiments, and is consistent with the existing conclusion for the case of d= 0. Furthermore, we have a conjecture: for a given d, the strictly d-regular random (3, 2s)-SAT problem has an SAT-UNSAT (satisfiable-unsatisfiable) phase transition. Our experiments support this conjecture. Finally, our experiments also show that the parameter d is correlated with the intractability of the 3-SAT problem. Therefore, our research maybe helpful for generating random hard instances of the 3-CNF formula.     

凹角区域外问题基于椭圆弧人工边界的自然边界元与有限元耦合法

木文以具有凹角长条型内边界的调和方程外问题为例,研究一种以椭圆弧为人工边界的自然边界元与有限元耦合法,给出了耦合变分问题的适定性及近似解的误差估计．理论分析及数值结果表明,用该方法求解带凹角长条型内边界的外问题是十分有效的．     

渐缩管和直管流场中超声流量计的适应性研究

针对不具备直管段安装条件,如何选择前直管段长度,从数值仿真、流场分析、误差分析等方面,对DN100四声道超声流量计上游安装DN150变DN100渐缩管和安装直管的适应性进行了研究。数值仿真分析了不同安装条件下管道中流场分布特性,指出测量误差绝对值随前直管段长度的减小而增大。通过数值仿真,上游分别安装DN150变DN100渐缩管和直管时,为了保证测量误差±0.5%内,前直管段应大于4D和8D。     

交替测量式掘进机定位系统误差建模与分析

交替测量式掘进机定位技术在多次交替测量过程中会产生累计测量误差,从而影响掘进机定位精度。目前主要围绕单次测量误差产生原因、误差分布规律及误差减小方法展开研究,未有针对多次交替测量误差分布规律的研究成果。通过分析交替测量式掘进机定位系统工作原理及定位过程,构建了掘进机定位误差模型。采用作图法验证误差模型的正确性,结果表明作图法与误差模型得到的定位误差基本一致,二者仅存在10^-3数量级误差。通过误差模型研究了角度测量误差、测距误差、推移步长及掘进机与测量平台间距对掘进机定位误差的影响,结果表明:角度测量误差越大,定位误差曲线的曲率越大,即误差增大越快,且Y_T轴定位误差增大速度远大于X_T轴;测距误差对X_T轴定位误差影响较大,测距误差越小,初始X_T轴定位误差越小,但误差变化速度不受影响;随着推移步长增大,Y_T轴定位误差曲线曲率增大,即Y_T轴定位误差增大速度加快;掘进机与测量平台间距和推移步长对掘进机定位误差的影响基本是等效的。采用正交试验方法分析了各因素对掘进机定位误差的影响程度,结果表明:测距误差对X_T轴定位误差影响最大,其次为角度测量误差,推移步长和掘进机与测量平台间距影响最小且二者影响程度一致;角度测量误差对Y_T轴定位误差影响最大,其次为推移步长和掘进机与测量平台间距且二者影响程度一致,测距误差影响最小。通过极差分析方法得到了降低定位误差的最优参数组合。     

Nonexistence of finite-dimensional filters for conditional statistics of the cubic sensor problem

Consider the cubic sensor dx = dw, dy = x³dt + dv where w, v are two independent Brownian motions. Given a function φ(x) of the state x let φ_t(x) denote the conditional expectation given the observations y_s, 0 s t. This paper consists of a rather detailed discussion and outline of proof of the theorem that for nonconstant φ there cannot exist a recursive finite-dimensional filter for φ driven by the observations.     

On gray scale image measurements: I. Arc length and area

We investigate methods for approximating the arc length of a planar curve and the area of a region whose boundary is a closed curve where the data are taken from a rectangular lattice of gray scale values. The commonly used sample-count method is a simple idea. Arc length is estimated by counting pixels along the curve. Typically the relative error is larger than desired. Area is estimated by counting interior pixels. The relative error is usually smaller than that for arc length, but identifying interior pixels may be a difficult geometric problem and adds computational overhead. The sample-distance methods for measuring arc length is also standard. This method requires the curve pixels to be ordered geometrically. The distances between consecutive pixels are summed to give an estimate of arc length. Although the relative errors are small, the required geometric ordering adds complexity to the problem. We introduce the sample-normal method for estimating arc length and area from gray level data. This method requires construction of unit normal vectors for the sampled curve points. Local estimates of arc length at the pixels are made from the normal vectors. The area can be approximated by using the normal vectors in the divergence theorem from calculus. Two major advantages for this method are that no geometric ordering of data points is required and that the algorithms are easily implemented. We compare the sample-normal method to the sample-count and sample-distance methods using both artificially created data and actual 8-bit digital images.     

Step by step Tau method—Part I. Piecewise polynomial approximations

Lánczos remarked that approximations obtained with the Tau method using a Legendre polynomial perturbation term defined in a finite interval J, give accurate estimations at the end point of J. This fact, coupled with a recursive technique for the generation of Tau approximations described by the author elsewhere (Ortiz, 1969, 1974), is used to construct a step by step formulation of the Tau method in which the error is minimized at the matching point of successive steps. This formulation is applied to the construction of accurate piecewise polynomial approximations with an almost equioscillant error and various degrees of smoothness at the breaking points.

A technique based on the mapping of a master element Tau approximation defined over a finite interval of variable length is used in order to simplify the computational process.

Numerical examples and an estimation of the step size in relation to the size of the error in the equation are also discussed.     

基于视频图像的飞行姿态检测方法研究

利用流场实验平台对仿生实验的风洞环境进行模拟,以航模飞机为检测对象,给出了一种基于双摄像机的视频图像飞行姿态检测方法。利用颜色特征分别提取两路视频图像中的飞行航模目标,采用提取直线的方法获得航模目标中的直线参数,通过直线参数的变化分别解算飞行的横滚角和俯仰角姿态。与AHRS航姿参考系统MIN—IVA900的数据进行对比表明：该方法检测结果的最大偏差小于1°,取得了飞行姿态检测结果的一致性。     

基于梯度方向角量化的匹配新算法

提出了一种在复杂光照环境下具备旋转不变识别能力的匹配新算法。图像梯度方向角是一种在光照变化及目标发生旋转的情况下保持相对稳定的特征量。通过对该特征量的量化与统计分析,分2步实现在变化的光照条件下旋转目标的识别：(1)统计子图像块梯度方向角量化值的直方图,大概确定出目标旋转的角度;(2)利用确定的角度值对模板图像的梯度方向角量化值与子图像的量化值进行旋转匹配。实验证明该算法具有较强的鲁棒性。     

异构处理器间的一种图形并行生成方法

图形任务计算的复杂性及实时性要求高速计算。文中提出了一种异构处理器间的图形并行生成方法，在层次分割和多主体协作模式下，各处理器并行运作，一方面有效利用了环境中的计算资源，另一方面提高了各处理器的计算并行度。     

面向高速加工的微小线段平滑过渡算法研究

为满足微小线段高速加工的需求,在分析现有微小线段过渡算法不足的基础上,建立了圆弧过渡矢量夹角数学模型,并给出一种基于过渡圆弧的微小线段平滑过渡算法.该算法能够根据加工精度和微小线段长度确定出微小线段的转角点和过渡圆弧的大小,并可通过机床机械特性来限制过渡圆弧的最大进给速度,从而能够在保证加工精度和满足机床机械特性的条件下,最大限度的提高微小线段加工速度.最后对所提出的过渡算法进行了实际加工验证,验证结果表明该算法具有过渡平稳、误差易控、转角速度高的特点,可实现微小线段的高速和高精加工.