A Novel Contour Tracing Algorithm for Object Shape Reconstruction Using Parametric Curves

Parametric curves such as Bézier and B-splines, originally developedfor the design of automobile bodies, are now also used in image processing andcomputer vision. For example, reconstructing an object shape in an image,including different translations, scales, and orientations, can be performedusing these parametric curves. For this, Bézier and B-spline curves can be generatedusing a point set that belongs to the outer boundary of the object. Theresulting object shape can be used in computer vision fields, such as searchingand segmentation methods and training machine learning algorithms. Theprerequisite for reconstructing the shape with parametric curves is to obtainsequentially the points in the point set. In this study, a novel algorithm hasbeen developed that sequentially obtains the pixel locations constituting theouter boundary of the object. The proposed algorithm, unlike the methods inthe literature, is implemented using a filter containing weights and an outercircle surrounding the object. In a binary format image, the starting point ofthe tracing is determined using the outer circle, and the next tracing movementand the pixel to be labeled as the boundary point is found by the filter weights.Then, control points that define the curve shape are selected by reducing thenumber of sequential points. Thus, the Bézier and B-spline curve equationsdescribing the shape are obtained using these points. In addition, differenttranslations, scales, and rotations of the object shape are easily provided bychanging the positions of the control points. It has also been shown that themissing part of the object can be completed thanks to the parametric curves.

Efficient Construction of B-Spline Curves with Minimal Internal Energy

In this paper,we propose an efficient method to construct energy-minimizing B-spline curves by using discrete mask method.The linear relations between control points are firstly derived for different energy-minimization problems,then the construction of B-spline curve with minimal internal energy can be addressed by solving a sparse linear system.The existence and uniqueness of the solution for the linear system are also proved.Experimental results show the efficiency of the proposed approach,and its application in 1 G blending curve construction is also presented.

Approximate merging of B-spline curves and surfaces

Applying the distance function between two B-spline curves with respect to the L2 norm as the approximate error, we investigate the problem of approximate merging of two adjacent B-spline curves into one B-spline curve. Then this method can be easily extended to the approximate merging problem of multiple B-spline curves and of two adjacent surfaces. After minimizing the approximate error between curves or surfaces, the approximate merging problem can be transformed into equations solving. We express both the new control points and the precise error of approximation explicitly in matrix form. Based on homogeneous coordinates and quadratic programming, we also introduce a new framework for approximate merging of two adjacent NURBS curves. Finally, several numerical examples demonstrate the effectiveness and validity of the algorithm.

3D Target Localization Based on FrFT from Spaceborne Curve SAR

Synthetic aperture radar(SAR)three-dimensional(3D)imaging technology can reconstruct the complete structure of observed targets and has been a hot topic.Compared with tomographic SAR,array interferometric SAR,and circular SAR,curve SAR can use less data to achieve 3D positioning of targets.Most existing algorithms for estimating Doppler frequency modulation(FM)rate are based on sub aperture partitioning,resulting in low computational efficiency.To address this,this article establishes a target height estimation model,which reflects the relation-ship between the height and the residual Doppler FM rate for spaceborne curve SAR.Then,a fast SAR 3D localization processing flow based on fractional Fourier transform(FrFT)is proposed.Experimental verification demonstrates that this method can estimate the Doppler FM of the target column by column,and the 3D position error for non-overlapping targets is controlled within 1 m.For overlapping points with an intensity ratio greater than 1.5,the root mean square error(RMSE)of the estimation results is around 5 m.If the separation between overlapping points is greater than 35 m,the RMSE decreases to approximately 2 m.

Distribution of driving trajectory of passenger car in highway horizontal curves

In this paper the track behavior of passenger car was studied. The vehicle driving trajectory and driving direction were defined, and a classification of the type of vehicle trajectories along the curves was developed. The statistical parameters of vehicle trajectory samples in free flow and their frequency curves and cumulative frequency curves were achieved, K-S test and chi-square test were used to test normal distribution and gamma distribution for collected sample data, and the probabili- ty density functions were given. At last, dispersion degree between vehicle trajectory random varia- ble and the characteristic value of cumulative frequency curve in each key cross section in curves was analyzied. The proposed conclusion can provide theoretical support for the reasonable optimization of widen curve, design of alignment and the management of counter flow conflicts.

One Fairing Method of Cubic B-spline Curves Based on Weighted Progressive Iterative Approximation

A new method to the problem of fairing planar cubic B-spline curves is introduced in this paper. The method is based on weighted progressive iterative approximation （WPIA for short） and consists of following steps： finding the bad point which needs to fair, deleting the bad point, re-inserting a new data point to keep the structm-e of the curve and applying WPIA method with the new set of the data points to obtain the faired curve. The new set of the data points is formed by the rest of the original data points and the new inserted point. The method can be used for shape design and data processing. Numerical examples are provided to demonstrate the effectiveness of the method.

RECONSTRUCTION OF SYMMETRIC B-SPLINE CURVES AND SURFACES

A method to reconstruct symmetric B-spline curves and surfaces is presented. The symmetry property is realized by using symmetric knot vector and symmetric control points. Firstly, data points are divided into two parts based on the symmetry axis or symmetry plane extracted from data points. Then the divided data points are parameterized and a symmetric knot vector is selected in order to get symmetric B-spline basis functions. Constraint equations regarding the control points are deduced to keep the control points of the B-spline curve or surface to be symmetric with respect to the extracted symmetry axis or symmetry plane. Lastly, the constrained least squares fitting problem is solved with the Lagrange multiplier method. Two examples from industry are given to show that the proposed method is efficient, robust and able to meet the general engineering requirements.

THE RELATIONSHIP BETWEEN PROJECTIVE GEOMETRIC AND RATIONAL QUADRATIC B-SPLINE CURVES

Abstract For two rational quadratic B spline curves with same control vertexes, the cross ratio of four collinear points are represented: which are any one of the vertexes, and the two points that the ray initialing from the vertex intersects with the corresponding segments of the two curves, and the point the ray intersecting with the connecting line between the two neighboring vertexes. Different from rational quadratic Bézier curves, the value is generally related with the location of the ray, and the necessary and sufficient condition of the ratio being independent of the ray's location is showed. Also another cross ratio of the following four collinear points are suggested, i.e. one vertex, the points that the ray from the initial vertex intersects respectively with the curve segment, the line connecting the segments end points, and the line connecting the two neighboring vertexes. This cross ratio is concerned only with the ray's location, but not with the weights of the curve. Furthermore, the cross ratio is projective invariant under the projective transformation between the two segments.

Smooth Trajectory Planning for a Cable Driven Parallel Waist Rehabilitation Robot Based on Rehabilitation Evaluation Factors

Rehabilitation robots can help physiatrists to assist patients in improving their movement ability.Due to the interaction between rehabilitation robots and patients,the robots need to complete rehabilitation training on a safe basis.This paper presents an approach for smooth trajectory planning for a cable-driven parallel waist rehabilitation robot(CDPWRR)based on the rehabilitation evaluation factors.First,motion capture technology is used to collect the motion data of several volunteers in waist twisting.Considering the impact of motion variability,the feature points at the center of the human pelvis are obtained after eliminating unreasonable data through rationality judgments.Then,point-to-point waist training trajectory planning based on quintic polynomial and cycloid functions,and multipoint waist training trajectory planning based on quintic B-spline functions are carried out.The corresponding planned curves and kinematics characteristics using three methods are compared and analyzed.Subsequently,the rehabilitation evaluation factors are introduced to conduct smooth trajectory planning for waist training,and the waist trajectory with better compliance is obtained based on the safety and feasibility of waist motion.Finally,the physical prototype of the CDPWRR is built,and the feasibility and effectiveness of the proposed smooth trajectory planning method are proved by numerical analysis and experiments.

A promising resilience parameter for breeding:the use of weight and feed trajectories in growing pigs

Background Increasing resilience is a priority in modern pig breeding.Recent research shows that general resilience can be quantified via variability in longitudinal data.The collection of such longitudinal data on weight,feed intake and feeding behaviour in pigs has been facilitated by the development of technologies such as automated feeding stations.The goal of this study was to investigate resilience traits,which were estimated as deviations from longitudinal weight,feed intake and feeding behaviour data during the finishing phase.A dataset with 324,207 records between the age of 95 and 155 days on 5,939 Pietrain pigs with known pedigree and genomic information was used.We provided guidelines for a rigid quality control of longitudinal body weight data,as we found that outliers can significantly affect results.Gompertz growth curve analysis,linear modelling and trajectory analyses were used for quantifying resilience traits.Results To our knowledge,this is the first study comparing resilience traits from longitudinal body weight,feed intake and feeding behaviour data in pigs.We demonstrated that the resilience traits are lowly to moderately heritable for deviations in body weight(h2=2.9%–20.2%),in feed intake(9.4%–23.3%)and in feeding behaviour(16.2%–28.3%).Additionally,these traits have good predictive abilities in cross-validation analyses.Deviations in individual body weight and feed intake trajectories are highly correlated(rg=0.78)with low to moderate favourable genetic correlations with feed conversion ratio(rg=0.39–0.49).Lastly,we showed that some resilience traits,such as the natural logarithm of variances of observed versus predicted body weights(lnvarweight),are more robust to lower observation frequencies and are repeatable over three different time periods of the finishing phase.Conclusions Our results will help future studies investigating resilience traits and resilience-related traits.Moreover,our study provides first results on standardization of quality control and efficient data sampling from automated feeding station data.Our findings will be valuable for breeding organizations as they offer evidence that pigs’general resilience can be selected on with good accuracy.Moreover,this methodology might be extended to other species to quantify resilience based on longitudinal data.

挖掘机时间最优与脉动最优轨迹规划

为了在提高挖掘机工作效率的同时减小各个关节的振动,提出了一种使挖掘机关节运行时间和关节脉动达到某种综合最优的轨迹规划方法,在同时考虑挖掘机动臂、斗杆、铲斗的运动学约束以及动作时间约束条件的前提下,采用五次非均匀B样条曲线对离散序列点进行插值,然后运用自适应粒子群优化算法(ASPO)对目标函数进行优化求解得到一条动作时间较短且脉动连续关节轨迹,最后对优化后得到的关节轨迹进行仿真实验,结果表明,该方法最终可以得到比较理想的运动轨迹,从而验证了该方法的有效性。

基于改进NSGA-Ⅱ的纤维缠绕落纱点轨迹采样特征权重优化

针对基于空间特征曲线特征函数的纤维缠绕落纱点轨迹采样算法无法自动选择特征权重的问题,建立以特征权重为变量,以得到采样点线性插值生成曲线与原曲线的MAE,RMSE为目标函数的双目标优化模型。提出基于改进NSGA-Ⅱ算法的双目标优化求解方法以优化特征权重。实例验证表明,与传统NSGA-Ⅱ算法相比,改进NSGA-Ⅱ算法求得Pareto解集的MAE,RMSE平均下降了0.002和0.105,算法选取特征权重的MAE,RMSE比特征权重为(0.1,0.3)的MAE,RMSE分别降低了约12.9%和8.5%,比特征权重为(0.9,0.1)的MAE,RMSE分别降低了约20.6%和11.4%,有效地提高了落纱点轨迹采样的精度。

车辆轨迹数据驱动的急弯路段追尾冲突风险时空演化规律

为有效揭示急弯路段上车辆间追尾冲突风险的形成与变化态势,选取典型事故多发急弯路段使用无人机航拍等方式采集交通流数据,利用Tracker软件提取车辆轨迹信息,构建急弯路段追尾冲突后侵入时间PET判别指标,结合冲突先导车LV与跟随车FV的速度、加速度变化划分追尾冲突模式,进而界定临界冲突点、冲突风险范围及PET变化率指标DPET,运用回归分析量化LV与FV的速度、加速度、速度差及加速度差对DPET的影响,阐明临界冲突点及主要追尾冲突模式的微观变化特性及时空演化规律。结果表明:车辆追尾冲突存在空间集聚性,主要集中在入弯缓和曲线上游、曲中标志断面下游及出弯缓和曲线下游;在潜在追尾冲突的九大类别中发生频率最高的四大类冲突数量占比高达83.24%;PET在冲突临界点和冲突风险范围内均下降,导致DPET均为负值,在冲突临界点PET快速下降,其下降程度显著大于冲突风险范围;FV速度、加速度及LV、FV间速度差、加速度差四个指标显著影响追尾冲突临界点的DPET变化;T10模式(LV减速、FV加速)冲突过程中的DPET均值最小,PET序列下降最为剧烈,危险性显著高于其他冲突模式。

基于改进RRT-Connect算法的全局路径规划

针对RRT-Connect算法在复杂环境内的路径规划中存在探索性弱、收敛速度慢、冗余节点多、搜索路径较长等问题,提出一种改进的RRT-Connect算法。通过引入高质量随机点和动态步长的方法,提高了生成随机树的质量并减少了冗余节点数量;采用正向寻优和逆向贪婪的方式,改善了搜索路径较长的问题。实验结果表明,改进RRT-Connect算法平均路径规划时间缩短26.41%,平均路径规划长度缩短19.05%,平均路径规划节点个数减少41.91%,证明了改进RRT-Connect算法相比于原算法规划效率更高,规划时间更少,规划路径质量更优。

适应不同轨迹数据场景的道路线形组合优化提取方法

车辆轨迹数据是当前城市导航路网地图动态更新的一种重要数据源,从杂乱无序的轨迹点或轨迹线中提取并拟合道路几何形态,进而生成结构化的道路矢量地图是基于轨迹数据进行道路网地图构建与更新的关键步骤。现有的道路中心线提取方法主要采用单一的线形拟合算法进行轨迹数据拟合,然而真实道路的几何形态复杂多样和车辆轨迹数据质量参差不齐,导致单一的道路线形拟合算法只能在某些特定的数据场景下适用,无法针对不同的数据场景自适应的拟合出理想的道路中心线。此外,相比于专业测量方式采集的高频轨迹数据,出租车等采集的低频轨迹数据存在轨迹点稀疏、噪声多、定位误差大等问题,这使得从低频轨迹数据中提取理想的道路中心线仍具有挑战,尤其是针对复杂的交叉口区域。为此,本文基于分治策略的思想,提出了一种适应不同轨迹数据场景的道路线形组合优化提取方法。该方法在轨迹数据预处理的基础上,根据轨迹数据的分布特点对数据进行场景分类;进而,针对不同的数据场景匹配最优的线形拟合算法,通过组合优化策略生成理想的道路中心线。本文方法融合不同拟合算法的互补优势,可以有效解决数据分布稀疏、道路结构复杂(如自相交立交桥)等不同数据场景下的道路线形拟合问题。采用北京市出租车轨迹数据进行试验与对比分析,本文方法生成道路的平均位置精度为1.24 m,显著优于现有代表性方法。

改进的多项式曲线拟合轨迹预测算法

针对传统多项式曲线拟合轨迹预测算法对复杂多变的轨迹预测准确率不高问题,提出改进的多项式曲线拟合轨迹预测算法。首先,获得轨迹的曲率、挠率阈值;然后,通过该阈值识别预测误差可能较大的轨迹部位,并采用插值滚动预测算法进行预测;最后,采用双误差预测值更新算法,对预测值进行更新。仿真结果表明,相较于传统多项式曲线拟合轨迹预测算法,所提算法的平均位移误差(average displacement error,ADE)下降了42.77%,最终位移误差(final displacement error,FDE)下降了36.62%,从而验证了所提算法的可行性和有效性。

一种液压挖掘机最优能耗的轨迹规划方法

为了降低液压挖掘机的运动能量消耗,实现各关节的合理有效作业,提出了基于T型速度曲线的关节插值方法,以实现液压挖掘机最优能耗轨迹规划。该方法将各关节的速度设定为匀加速、匀速和匀减速的形式以保证液压挖掘机在作业过程中的平稳性,以关节角度、角速度和角加速度为约束条件,利用改进的自适应遗传算法优化求解各关节的匀加(减)速和匀速运动时间,获得了各关节最优运动曲线,实现了液压挖掘机最优能耗轨迹规划。对基于T型速度曲线的插值规划方法进行仿真实验,并在相同条件下与四次多项式插值结果进行了对比。结果表明,该方法规划的轨迹能耗低,避免了各关节产生不必要的运动,有效减少了摩擦损耗,使得挖掘机可平稳、低能耗地完成作业。

一种变速度条件下控制攻击角度和时间的制导律

对攻击角度和时间进行控制,可以使得多枚导弹按照特定的角度和时间对目标进行打击,在军事上有广泛的应用前景.目前已有控制攻击角度和时间的制导律极少考虑速度变化的情况,在实际运用中具有较大的局限性.本文基于贝塞尔曲线加直线的二段式轨迹,首先分析并证明了该轨迹长度和最大曲率的变化规律,在此基础上,通过二分法确定初始轨迹,针对飞行过程中的诱导阻力和其它扰动,设计了Bezier-PI控制算法,通过动态调整轨迹长度来实现攻击时间的高精度控制.该制导算法计算量小,鲁棒性强,适用于弹载计算机实时计算.通过仿真实验,验证了该算法可以高精度的控制攻击时间以及攻击角度.