Abstract:

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.

Results:

(Right) Starting from a noisy scan, our algorithm recovers the primitive faces along with their global mutual relations, when are then used to produce a final model (all lengths in mm).

(Bottom) Cylinder, plane, and sphere primitives are aligned using extracted coaxis, coplanar, parallel/orthogonal axes, equal angle as well as equal length constraints. They converge to the final model after two iterations of RANSAC fitting and constraint optimization. We overlap the final result on the initial RANSAC results for comparison; the histograms demonstrate the effect in the primitive pair angle space.

(Left) Starting from a noisy scan, our algorithm recovers the primitive faces along with their global mutual relations, when are then used to produce a final model (all lengths in mm).

(Right) Aligning to global relations corrects for significant misaligned RANSAC primitives obtained using local fits. However, when the data quality is sufficiently poor, our algorithm may fail to recover all global relations, and hence the reconstruction is only partially correct.

@article{li_globFit_sigg11,
AUTHOR = "Yangyan Li and Xiaokun Wu and Yiorgos Chrysanthou and Andrei Sharf and Daniel Cohen-Or and Niloy J. Mitra",
TITLE = "GlobFit: Consistently Fitting Primitives by Discovering Global Relations",
JOURNAL = "ACM Transactions on Graphics",
VOLUME = "30",
NUMBER = "4",
pages = {52:1--52:12},
articleno = {52},
numpages = {12},
YEAR = "2011",
}