Nonrigid Registration Using Gaussian Processes and Local Likelihood Estimation
Nonrigid Registration Using Gaussian Processes and Local Likelihood Estimation
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DOI：
10.1007/s11004-020-09917-7
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发表时间：
2020-06
影响因子：
2.6
通讯作者：
Ashton Wiens;W. Kleiber;D. Nychka;K. Barnhart
中科院分区：
文献类型：
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作者：
Ashton Wiens;W. Kleiber;D. Nychka;K. Barnhart
曲面配准是将多个多维点集对齐的任务，在许多科学领域中是一项必不可少的任务。在这项工作中，一种新的统计方法来解决非刚性配准的问题。虽然仿射变换的应用导致刚性配准，但当点集需要随空间变化的变形时，使用一般非线性函数来实现非刚性配准是必要的。使用局部似然为基础的方法，使用加窗高斯过程提供了一种灵活的方式来准确地估计非刚性变形。该策略还通过将数据划分为许多子集来实现海量数据集的注册。估计结果产生空间变化的局部刚性配准参数。然后，高斯过程表面模型拟合到参数字段，允许在未估计的位置处，特别是在未注册的数据集中的观察位置处预测变换参数。应用这些变换会导致全局非刚性配准。在似然目标函数中包括对变换参数的惩罚。结合平滑的局部估计的表面模型，非刚性配准模型可以防止过拟合的问题。非刚性配准方法的有效性进行了测试，在两个模拟研究中，不同的窗口数量和点的数量，以及变形的类型。非刚性的方法被施加到一对大规模的遥感高程数据集，表现出复杂的地质地形，提高精度和不确定性量化的交叉验证研究与两个刚性注册方法。
Surface registration, the task of aligning several multidimensional point sets, is a necessary task in many scientific fields. In this work, a novel statistical approach is developed to solve the problem of nonrigid registration. While the application of an affine transformation results in rigid registration, using a general nonlinear function to achieve nonrigid registration is necessary when the point sets require deformations that change over space. The use of a local likelihood-based approach using windowed Gaussian processes provides a flexible way to accurately estimate the nonrigid deformation. This strategy also makes registration of massive data sets feasible by splitting the data into many subsets. The estimation results yield spatially-varying local rigid registration parameters. Gaussian process surface models are then fit to the parameter fields, allowing prediction of the transformation parameters at unestimated locations, specifically at observation locations in the unregistered data set. Applying these transformations results in a global, nonrigid registration. A penalty on the transformation parameters is included in the likelihood objective function. Combined with smoothing of the local estimates from the surface models, the nonrigid registration model can prevent the problem of overfitting. The efficacy of the nonrigid registration method is tested in two simulation studies, varying the number of windows and number of points, as well as the type of deformation. The nonrigid method is applied to a pair of massive remote sensing elevation data sets exhibiting complex geological terrain, with improved accuracy and uncertainty quantification in a cross validation study versus two rigid registration methods.