含各向异性尺度形变数据集匹配问题的Lie群方法

Lie Group Method for Data Set Registration Problem with Anisotropic Scale Deformation

通过分析含各向异性尺度形变的数据集匹配问题,将尺度约束引入模型,再结合迭代最近点(Iterative closest point,ICP)方法的一般过程,将含各向异性尺度形变的数据集匹配问题描述为Lie群约束优化问题.通过Lie群的局部参数化和局部线性化方法,将带尺度上下界约束的Lie群约束优化问题转化为一系列的二次规划问题,最终形成了一个完整的匹配迭代算.该方法不仅具有传统ICP方法的快速准确的特点,而且还能够处理存在大尺度形变的数据集匹配问题.由于对尺度参数进行约束,因此比传统方法有更好的鲁棒性.最后,为确保匹配的全局性,给出了一套初始变换的选择方案.

By analyzing the data set registration problem with anisotropic scale deformation, we introduced the con- straints to the model. Combining with the procedure of traditional iterative closest point （ICP） method, the registration problem was described as a constrained optimization problem. Using parameterized method by Lie group and quadric approximation to the objective function, the registration problem was translated into a series of quadratic programming problems. Then, a novel scale-registration algorithm was proposed. The numerical simulations showed that such method not only was rapid and accurate as the traditional ICP method, but also could deal with the registration problem with large scale deformation. By introducing the constraints to the scale parameters, the algorithm was more robust. A way for choosing the initial transformations was proposed to assume the global registration.