Influence of the simplified stochastic model of TLS measurements on geometry-based deformation analysis
Influence of the simplified stochastic model of TLS measurements on geometry-based deformation analysis
复制标题
TLS 测量的简化随机模型对基于几何的变形分析的影响
作者：
Xin Zhao;G. Kermarrec;B. Kargoll;H. Alkhatib;I. Neumann
摘要地面激光扫描仪（TLS）是一种功能强大的仪器，可用于变形监测，由于其在捕获三维点云的高精度和空间分辨率。从散乱点云数据中进行变形检测可以采用不同的比较方法，其中基于几何的方法是最常用的方法之一。与用预定的几何基元（如平面或球面）逼近曲面相比，B样条曲面逼近具有很大的灵活性，几乎可以拟合所有TLS扫描的物体。然而，方差-协方差矩阵（VCM）的观察参与近似的离散点B样条曲面的影响一致性检验的结果，这是一致的最强大的不变（UMPI）测试之间的零变形的零假设和它的备择假设进行区分。因此，简化的随机模型可能会削弱UMPI属性。基于Monte Carlo模拟，研究了B样条函数逼近中常被忽略的异方差性和数学相关性的影响。当原始测量值转换为笛卡尔坐标时，这些相关性在近似TLS测量值方面是特定的。一致性检验中的零假设被拒绝率被用来反映未指定的VCM对一致性检验功效的影响。在大变形区，点精度较高时，剔除率对随机模型的简化不敏感，而在小变形区，几何形状不理想时，剔除率明显受到影响。更大的不确定性。估计差异与相对标准差的阈值比突出，而一致性检验的结果是可靠的，当使用简化的VCM。结果表明，随机模型的简化对一致性检验的功效有显著影响，特别是在不确定性较大的小变形区域。
Abstract Terrestrial laser scanners (TLS) are powerful instruments that can be employed for deformation monitoring due to their high precision and spatial resolution in capturing 3D point clouds. Deformation detections from scatter point clouds can be based on different comparison methods, among which the geometry-based method is one of the most popular. Compared with approximating surfaces with predetermined geometric primitives, such as plane or sphere, the B-splines surface approximation offers a great flexibility and can be used to fit nearly every object scanned with TLS. However, a variance-covariance matrix (VCM) of the observations involved in approximating the scattered points to B-spline surfaces impact the results of a congruency test, which is the uniformly most powerful invariant (UMPI) test for discriminating between the null hypothesis of zero deformation and its alternative hypotheses. Consequently, simplified stochastic models may weaken the UMPI property. Based on Monte Carlo simulations, the impact of the heteroscedasticity and mathematical correlations often neglected in B-splines approximation are investigated. These correlations are specific in approximating TLS measurements when the raw measurements are transformed into Cartesian coordinates. The rates of rejecting the null hypothesis in a congruency test is employed to reflect the impact of unspecified VCMs on the power of the congruency test. The rejection rates are not sensitive to the simplification of the stochastic models, in the larger deformation area with higher point accuracy, while they are obviously influenced in the smaller deformation area with unfavourable geometries, i. e. larger uncertainties. A threshold ratio of estimated differences to the relative standard deviation highlights whereas the results of congruency test are reliable when using simplified VCMs. It is concluded that the simplification of the stochastic model has a significant impact on the power of the congruency test, especially in the smaller deformation area with larger uncertainties.
影响因子：
1.4
作者：
Kauker, Stephanie;Schwieger, Volker
通讯作者：
Schwieger, Volker