摘要
近年来,受概率论与统计学竞相发展以及交叠应用的趋势促进,基于非参数密度估计点样本分析建模的应用研究受到越来越多研究者的关注。非参数密度估计方法不需要对点样本分布的参数形式做事先假设,仅从采样数据本身就可对概率密度函数做出较为精确鲁棒的估计,为未知分布点样本的分析和建模提供了一条新的解决思路。通过非参数密度估计技术对传感器获得的采样点样本进行分析或者建模,能够为特定的研究任务提供关于采样数据的可靠信息,从而为具体问题的解决奠定基础。非参数密度估计点样本分析建模虽然已经在运动目标跟踪等领域得到了应用,但在与其他算法进行结合以解决问题的过程中尚存在一定不完善的地方,其应用领域也相对比较局限,有必要做进一步的深入研究和开拓。
为进一步深入对非参数密度估计点样本分析建模的应用并拓宽其应用领域,本文以像素点样本和距离点样本为主要分析和建模对象,在结合其他相关算法的同时分别对运动目标跟踪、立体图像匹配以及基于激光扫描距离点样本配准的移动机器人自定位问题进行了研究。主要研究工作包括;
(1)在深入研究直方图、核密度估计等非参数密度估计技术的基础上,分析和讨论了影响密度估计结果的因素并给出了分析结果。
给出了密度估计量的基本性质以及密度估计通用表达式,在此基础上对常用的非参数直方图密度估计方法以及核密度估计方法进行研究,分析了影响估计结果的因素并给出了不同情况下的密度估计结果,最后对参数密度估计和非参数密度估计方法进行分析对比。
(2)在已有的基于直方图密度估计像素点样本建模的运动目标跟踪方法基础上,提出一种基于“卡尔曼滤波目标位置预测—核直方图建模二次定位—局部直方图匹配、全局融合校正”策略的精确跟踪实现机制。
分析了经典的基于核直方图建模、均值位移定位跟踪方法存在的问题,在此基础上提出了改进的先预测再定位后校正的三步精确跟踪策略。首先利用卡尔曼滤波技术对目标的运动位置进行合理预测,进而有效避免目标丢失,保证二次定位过程的有效性。为实现在预测位置基础上进行二次定位的目的,采用像素点样本颜色特征核直方图建模、Bhattacharyya距离相似性度量的经典方法构建二次定位目标函数,将二次定位问题转化为目标函数最小化问题。与经典方法思路不同,采用具有全局收敛特性和超线性收敛速率等优点的BFGS拟牛顿最优化方法进行定位目标函数的最小化,从而实现对跟踪目标的二次定位。
进一步针对运动目标在受到部分遮挡等情况下跟踪精度不高的问题,提出采用局部直方图匹配、全局融合的方法进行位置校正。在筛选候选匹配点以及区域划分基础上,将参考区域与目标区域中直方图模型相互匹配的有效子块间的位置差值进行融合并计算校正位移,以使校正后的目标区域与参考区域在空间上更加匹配。最后通过跟踪实验对所提方法进行验证,并与基于核直方图建模、均值定位的方法进行对比,实验结果表明本文的方法在鲁棒性上有所增强,跟踪精度得到了提高。
(3)进一步发展了非参数密度估计理论在立体匹配中的应用。定义了一种基于差值匹配点样本核密度估计的匹配基元相似性测度,在立体匹配应用中结合改进的置信度传播算法得到了理想的匹配结果。
首先以对应窗口匹配基元所产生的差值匹配点样本作为分析研究对象,根据立体匹配的相容性约束条件,定义了一种基于差值匹配点样本核密度估计的匹配基元相似性测度函数。核密度估计的应用保证了匹配基元之间相似性度量的有效性,有利于最佳匹配点的寻找;同时还便于实现匹配基元在高维空间中的相似性度量,进一步提高相似性度量的精度。
为利用核密度相似性测度进行视差求解,建立立体匹配的马尔科夫随机场模型。在此基础上将立体匹配问题转化为基于核密度相似性测度先验项的全局能量函数最小化问题,并最终采用改进的置信度传播算法对全局能量函数进行最小化,实现了视差的有效计算。最后对两组立体图像对进行匹配实验,将本文提出的基于核密度相似性测度的立体匹配方法与基于经典SAD、SSD相似性测度的方法进行对比。实验结果表明,所提相似性测度在立体匹配应用中能够达到比SAD以及SSD更高的匹配精度,同时改进置信度传播算法的应用保证了整个匹配算法的计算效率。
(4)拓展了非参数核密度估计点样本建模的应用领域,将其应用于移动机器人自定位问题的解决中,提出了一种精度较高的基于激光扫描距离点样本核密度估计建模的移动机器人自定位方法。
首先以180度激光扫描仪采集的距离点样本为研究对象,以核密度估计为建模手段进行激光数据对的配准。采用核密度估计技术在二维位置特征空间对激光扫描距离点样本集合进行建模,得到二维核密度模型。非参数核密度估计的应用使得点样本模型的建立具有不依赖于特征提取、不易受噪声干扰以及适于对任意环境中采集的距离点样本进行建模等优点。在核密度相关的前提下对相邻的点样本核密度模型进行关联,建立不依赖于点与点精确对应、完全连接网络意义下的配准代价函数,将配准问题转化为以旋转平移量为参数的代价函数最小化问题。针对建立的代价函数,采用BFGS拟牛顿最优化方法进行求解进而实现配准。最后通过空间变换实现机器人在全局坐标系中位姿的确定。
另外,为使基于核密度估计建模的移动机器人自定位方法适于实时应用,在配准代价函数最小化的过程中还结合了快速高斯变换理论。快速高斯变换的采用能够在一定程度上解决由于激光扫描距离点样本数量较多,造成直接计算代价较大的问题,加快配准代价函数最小化过程。
仿真实验结果表明,上述方法在实现180度以及不具备结构特征的激光扫描距离点样本配准方面是非常有效的,配准精度要远远优于经典的依赖点与点对应的ICP方法。同时还搭建了自定位仿真实验平台,对真实环境中采集的激光扫描点样本进行配准,进一步验证了该方法在解决移动机器人自定位问题方面的可行性。
最后总结全文,并对下一步的研究工作进行展望。
Accelerated by the development of Probability Theory and Statistics and the trend of their combined use, application researches based on point sample analysis and modeling using nonparametric density estimation attract more and more attentions of researchers. Nonparametric density estimation method can make accurate and robust estimation only based on sample data without the assumption that the forms of the underlying densities are known. It provides a novel approach to the analysis and modeling of point samples which is unknown. Analysis and modeling of point samples gathered by the sensors using nonparametric density estimation can provide dependable information about the sampling data to given research and lay foundation for problem solution. Although nonparametric density estimation-based point sample analysis and modeling has been applied in fields such as moving object tracking, there are some insufficiencies when applied with other methods during the problem solution process and meanwhile its application fields are relatively narrow. Further study on application of nonparametric density estimation-based point sample analysis and modeling and extending its application fields is significant.
In order to make the application of nonparametric density estimation-based point sample analysis and modeling more in-depth and extend its application fields, this paper takes the pixel point sample and range point sample as the analysis and modeling targets and studies the problems of moving object tracking, stereo image matching and mobile robot self-localization based on laser data registration combined with other algorithms. The main researches are as follows:
(1) Based on study of the histogram and kernel density estimation methods, factors influencing the density estimation results are analyzed and discussed. The analysis results are given.
The basic properties and common expression of nonparametric density estimation methods are given and the histogram and kernel density estimation methods are studied based on the normal expression. Factors influencing the results of density estimation are analyzed and some instances about the factors are given. Finally the parametric and nonparametric density estimation methods are analyzed and compared.
(2) A novel tracking method with "object position prediction using Kalman Filter -secondary localization using kernel histogram modeling-local histogram matching and global syncretion rectification" mechanism is proposed based on the moving object tracking method with the application of histogram density estimation point sample modeling.
Problems of the classical tracking method with the application of kernel histogram modeling and mean shift localization are analyzed. Therefore, a novel tracking method based on "prediction-secondary localization-rectification" mechanism is proposed. Firstly the kalman filter technology is used to predict the position of the moving object and this can avoid losing of the object and ensure the validity of the secondary localization process. In order to realize the secondary localization from the predictive position, the classical method based on kernel-histogram modeling and Bhattacharyya distance similarity measure are used to construct a object function for secondary localization. Then the secondary localization problem is transformed into function optimization problem. Different from the classical method, the BFGS Quasi-Newton optimization method which has super-linear convergence rate and global convergence is used to solve the object function and realize the secondary localization.
Aiming at the problem that the tracking accuracy under some circumstances such as with part occlusion is usually not high, a method using local histogram matching and global syncretion is proposed to rectify the object position. Basing on candidate matching point filtration and region dividing, position difference between effective subregions whose histogram models are matching in reference region and object region is syncretized to compute the rectification displacement. Object region after rectified and the reference region can be more matching in spatial characteristic. Finally the proposed method and the classical method are compared through tracking experiment. The experiment results show the improvements of the proposed method in robustness and accuracy.
(3) Application of nonparametric density estimation in stereo image matching is furtherly developed. A new similarity measure using kernel density estimation based on difference matching point samples is defined. The proposed similarity measure can be applied in stereo matching and reach satisfactory results combined with the improved belief propagation method.
Firstly the difference matching point samples derived from window matching elements are taken as the analysis and study target of matching, and the similarity measure function based on kernel density estimation of difference matching point samples is defined according to the consistent constraint of stereo matching. Application of kernel density estimation guarantees the validity of similarity measure and is propitious to the searching of optimal matching point. At the same time it is convenient for similarity measure in high-dimensional feature space to improve the accuracy of similarity measure.
In order to compute the disparities using the kernel density similarity measure, the Markov Random Field Model of stereo matching is established and the stereo matching problem is transformed into the problem of global energy function minimization based on prior term of kernel density similarity measure. An improved Belief Propagation method is used to minimize the global energy function and realize the efficient computaion of disparities. Finally two pairs of stereo image are tested using the proposed method and methods based on SAD and SSD similarity measure. Experiment results show the improvements of the proposed similarity measure in matching accuracy. The computation efficiency is guaranteed also due to the implementation of the improved Belief Propagation method.
(4) The application of point sample modeling using nonparametric kernel density estimation is extended to the field of mobile robot self-localization. A more accurate method for mobile robot self-localization based on laser scan range point sample modeling using kernel density estimation is proposed.
Firstly, the 180°laser scan range point sample is taken as the study object and the kernel density estimation is used as the modeling means to realize registration of laser data pairs. The kernel density estimation method is used to modeling the laser scan range point samples in 2D position feature space and the 2D kernel density model can be got. This modeling method of point samples has advantages that it does not depend on character extractions and is unliable to be influenced by noises, and range point samples gathered from any environments can be modeled by this method. A registration cost function in the meaning of fully connected network which is independent on point-to-point correspondence is constructed based on kernel density correlation. Then the registration problem is transformed into function minimization problem with the translation-rotation vector parameter. The BFGS quasi-Newton optimization method is used to solve the cost function and complete the registration. Lastly the robot's pose in global coordinate can be computed through coordinate transformation.
In addition, the Fast Gauss Transform method is used during the optimization process of the registration cost function for real time application. The Fast Gauss Transform can solve the problem that the computational cost is large due to large numbers of range point samples, and it can accelerate the process of cost function minimization to a certain extent.
The simulation experiment results demonstrate that the proposed method is very effective in realizing registration of laser range point samples which are 180°and not having characters. The accuracy of the proposed method is higher than the classical ICP method which is depends on point-to-point correspondence. A self-localization simulation platform is also built to test the proposed method when dealing with real laser range point samples gathered by the mobile robot. The simulation result furtherly shows the validity of the proposed method in solving the mobile robot self-localization problem.
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