基于广义叉积鲁棒性的识别式数据拟合  

Recognizing Data Fitting Based on the Robustness of Generalized Cross Product

作　　者：韦进文[1,2] 陈燕玲[3] 覃禾群[1] 郭俊杰[2] 

机构地区：[1]广西大学机械工程学院,南宁530004 [2]西安交通大学机械制造系统工程国家重点实验室,西安710049 [3]广西大学电气工程学院,南宁530004

出　　处：《机械工程学报》2011年第14期7-12,共6页Journal of Mechanical Engineering

基　　金：广西大学科研基金(XBZ100770);国家自然科学基金(50375119)资助项目

摘　　要：传统的数据拟合不能对数据进行合理分块,还会选用错误的几何元素。因此提出基于广义叉积鲁棒性原理的识别式数据拟合方法。该原理说明,叉矩阵正交时积矢量鲁棒性强。考察一个数据序列是否包含某几何元素,先用其局部数据点顺次提取该元素的特征参数,再构造正交的叉矩阵并将特征矢量序列映射到积矢量空间。该映射既能克服噪声对恒定特征参数的干扰,又能放大错误几何元素的特征参数的变化。若积矢量在一定范围内是恒定的,则可确认相应数据段中的几何元素并对其边界进行精确定位。试验证明了该方法的有效性。该方法可用于逆向工程的曲面重建,或用作模式分类的一般方法。Data can＇t be rationally segmented and even wrong geometric elements are used in traditional data fitting.Therefore recognizing data fitting is proposed,based on the robustness theorem of generalized cross product,which states that an orthogonal matrix brings a robust product vector.To identify the geometric element of a fitted data point cloud,firstly feature parameters are extracted with its local data points,then an orthogonal matrix is constructed and the extracted feature vectors are mapped to product vectors.The mappings of feature vectors can overcome the measurement noises and magnify the variation of the feature parameters of wrong geometric elements in fitted data.Right geometric element is easily identified if the product vectors are constant in a certain data segment and the corresponding boundaries are accurately positioned.This method is feasible and efficient in experiments,and it can be widely used in the surface reconstruction of reverse engineering or used as a universal method in pattern classification.

关 键 词：广义叉积 模式识别 点云 数据拟合 鲁棒性 

分 类 号：G241[文化科学] O235[理学—运筹学与控制论]