4-points congruent sets for robust pairwise surface registration
Abstract
We introduce 4PCS, a fast and robust alignment scheme for 3D point sets that uses wide bases, which are known to be resilient to noise and outliers. The algorithm allows registering raw noisy data, possibly contaminated with outliers, without pre-filtering or denoising the data. Further, the method significantly reduces the number of trials required to establish a reliable registration between the underlying surfaces in the presence of noise, without any assumptions about starting alignment. Our method is based on a novel technique to extract all coplanar 4-points sets from a 3D point set that are approximately congruent, under rigid transformation, to a given set of coplanar 4-points. This extraction procedure runs in roughly O(n 2 + k) time, where n is the number of candidate points and k is the number of reported 4-points sets. In practice, when noise level is low and there is sufficient overlap, using local descriptors the time complexity reduces to O(n + k) . We also propose an extension to handle similarity and affine transforms. Our technique achieves an order of magnitude asymptotic acceleration compared to common randomized alignment techniques. We demonstrate the robustness of our algorithm on several sets of multiple range scans with varying degree of noise, outliers, and extent of overlap.
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[4] can handle up to 40% outliers and down to 40% overlap as demonstrated in their experiments.
“[4] which can handle up to 40% outliers, and down to 40% overlap as demonstrated in their experiments.”
From Registration of 3D Point Clouds and Meshes: A Survey from Rigid to Nonrigid (2013) · cites this paper as [4]
Given two surfaces P and Q in arbitrary initial poses, [4] randomly selects a 4-point tuple from P and another 4-point tuple from Q, and compares the affine ratios. If they form a correspondence, their affine ratio will match.
“Given two surfaces P and Q in arbitrary initial poses, [4] randomly selects a 4-point tuple from P and another 4-point tuple from Q, and compares the affine ratios.If they form a correspondence, their affine ratio will match.”
From Registration of 3D Point Clouds and Meshes: A Survey from Rigid to Nonrigid (2013) · cites this paper as [4]
These transformations are similar to the domain theory in analytical learning-a global rule, one reason why these techniques can be cast as optimization problems and solved using the Hough transform [17], [39] or RANSAC technique [4], [71] efficiently.
“These transformations are similar to the domain theory in analytical learning-a global rule, one reason why these techniques can be cast as optimization problems and solved using the Hough transform [17], [39] or RANSAC technique [4], [71] efficiently.”
From Registration of 3D Point Clouds and Meshes: A Survey from Rigid to Nonrigid (2013) · cites this paper as [4]
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- Authors
- Aiger, D., Mitra, N. J., & Cohen-Or, D.
- Affiliations
- Ben-Gurion University of the Negev (IL)
- TU Wien (AT)
- Tel Aviv University
- ORCID
- Mitra, Niloy J.
- Venue
- ACM Transactions on Graphics
- Published
- 2008-08
- Volume
- 27
- Issue
- 3
- Pages
- 1-10
- ISSN
- 0730-0301 (ISSN-L)
- 1557-7368
- OpenAlex
- W2064499898
- Cited by
- 677
- References
- 30
- Citations by year
- 2026: 27 · 2025: 36 · 2024: 51 · 2023: 50 · 2022: 47 · 2021: 53 · 2020: 64 · 2019: 65 · 2018: 46 · 2017: 53 · 2016: 30 · 2015: 38 · 2014: 26 · 2013: 21 · 2012: 23
- FWCI
- 16.03
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- ACM Transactions on Graphics (publishedVersion)
- HAL (submittedVersion)
- UCL Discovery (University College London) (submittedVersion)
- Topics
- Physical Sciences › Engineering › Computational Mechanics › 3D Shape Modeling and Analysis
- Physical Sciences › Computer Science › Computer Graphics and Computer-Aided Design › Computer Graphics and Visualization Techniques
- Physical Sciences › Computer Science › Computer Vision and Pattern Recognition › Advanced Image and Video Retrieval Techniques
- Keywords
- rigid transformation, outlier robustness, noise robustness, similarity transformation, affine transformation, range scans, local descriptors
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
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