GlobFit: consistently fitting primitives by discovering global relations

By Yangyan Li, Xiaokun Wu, Y. Chrysanthou, Andrei Sharf, Daniel Cohen-Or, Niloy J. Mitra. ACM Transactions on Graphics, 2011

350 citations recorded by the source corpus.

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.

Subfields: Aerospace Engineering, Computational Mechanics, Computer Vision and Pattern Recognition

View Paper: https://www.semanticscholar.org/paper/989182f25d30ddf0dd6ccb3e15b5d58fe2ccb162

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Citations in the corpus

PCN: Point Completion Network (2018, background): “There are also works [7, 25, 30, 41, 60] that use geometric primitives such as planes and quadrics in place of a shape database.”
High-Resolution Shape Completion Using Deep Neural Networks for Global Structure and Local Geometry Inference (2017, neutral): “Li et al. [15] further considered geometric relationships (eg. orientation, placement, equality, etc.) between primitives in the reconstruction procedure.”
FAST SEMANTIC SEGMENTATION OF 3D POINT CLOUDS WITH STRONGLY VARYING DENSITY (2016, background): “…buildings, another natural strategy is to model them with a limited number of geometric 2D (Schnabel et al., 2007, Pu and Vos-selman, 2009) or 3D (Li et al., 2011, Xiao and Furukawa, 2014) primitives, which are ﬁtted to the points – see also (Vosselman et al., 2004) for an overview of early work.”
Learning Shape Templates With Structured Implicit Functions (2019, background): “Primitive Fitting: Fitting of basic primitives is perhaps the oldest topic in 3D computer vision, beginning with Roberts [42] and continuing to today [2, 19, 29, 27].”
Multi-View Stereo: A Tutorial (2015, methodology): “Inverse CAD algorithms have been popular in the Computer Graphics community, where the input is a high quality 3D point cloud from laser range sensors [133].”
A Survey of Surface Reconstruction from Point Clouds (2017, background): “Under the prior of repetitive relationships between geometric primitives [LWC ∗ 11], a misaligned scan can be corrected if it fails to conform to the remaining discovered repetitions.”
ClipGen: A Deep Generative Model for Clipart Vectorization and Synthesis (2021, methodology): “tified group of a closed paths, our method progressively enforces the regularities in the following order (similar to [20], [65]): Axis-Aligned Lines.”