基于全局关系探测的几何体一致拟合

人造物体往往包含平面、球、圆柱和圆锥等基本几何体,并且这些几何体之间通常都存在相互平行、垂直和对齐等全局关系.传统的RANSAC方法能够从点云中局部地拟合基本几何体,使拟合结果很好的忠实于采样数据,但是RANSAC并没有考虑基本几何体之间的全局关系,其拟合的基本几何体之间完全独立,因此噪声、稀疏性以及不完整性的往往极大影响RANSAC的结果.针对该问题,提出了一种新的从点云拟合基本几何体的方法:使拟合结果既忠实于采样数据也满足全局关系.该方法从RANSAC局部拟合的基本几何体出发,然后迭代地探测它们之间的全局关系和更新它们的拟合,使得拟合的基本几何体一致地满足探测出的全局关系的情况下最大程度地忠实于采样数据.通过大量的合成数据和真实数据实验表明,这种结合了全局关系的方法在存在大量噪声、异常点和非均匀采样的情况下都具有很好的鲁棒性.

GlobFit: Consistently Fitting Primitives by Discovering Global Relations

Given a noisy and incomplete point set,we introduce a method that simultaneously recovers a set of locally fitted primitives along with their global mutual relations.We operate under the assumption that the data corresponds to a man-made engineering object consisting of basic primitives,possibly repeated and globally aligned under common relations.We introduce an algorithm to directly couple the local and global aspects of the problem.The local fit of the model is determined by how well the inferred model agrees to the observed data,while the global relations are iteratively learned and enforced through a constrained optimization.Starting with a set of initial RANSAC based locally fitted primitives,relations across the primitives such as orientation,placement,and equality are progressively learned and conformed to.In each stage,a set of feasible relations are extracted among the candidate relations,and then aligned to,while best fitting to the input data.The global coupling corrects the primitives obtained in the local RANSAC stage,and brings them to precise global alignment.We test the robustness of our algorithm on a range of synthesized and scanned data,with varying amounts of noise,outliers,and non-uniform sampling,and validate the results against ground truth,where available.