Application Study Based On Point Sample Analysis And Modeling Using Nonparametric Density Estimation

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.