Robust principal axes determination for point-based shapes using least median of squares
Open accessAbstract
A robust technique for determining the principal axes of a 3D shape represented by a point set, possibly with noise, is presented. We use techniques from robust statistics to guide the classical principal component analysis (PCA) computation. Our algorithm is based on a robust statistics method: least median of squares (LMS), for outlier detection. Using this method, an outlier-free major region of the shape is extracted, which ignores the effect on other minor regions regarded as the outliers of the shape.In order to effectively approximate the LMS optimization, the forward search technique is utilized. We start from a small outlier-free subset robustly chosen as the major region, where an octree is used for accelerating computation. Then the region is iteratively increased by adding samples at a time. Finally, by treating the points on minor regions as outliers, we are able to define the principal axes of the shape as one of the major region. One of the advantages of our algorithm is that it automatically disregards outliers and distinguishes the shape as the major and minor regions during the principal axes determination without any extra segmentation procedure. The presented algorithm is simple and effective and gives good results for point-based shapes. The application on shape alignment is considered for demonstration purpose.
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A recent advance [49] combines PCA with the least median of squares, providing resistance to noise and outliers.
“A recent advance [49] combines PCA with the least median of squares, providing resistance to noise and outliers.”
From Registration of 3D Point Clouds and Meshes: A Survey from Rigid to Nonrigid (2013) · cites this paper as [49]
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Registration of 3D Point Clouds and Meshes: A Survey from Rigid to Nonrigid
Tam, G. K. L., Cheng, Z.-Q., Lai, Y.-K., Langbein, F. C., Liu, Y., Marshall, D., Martin, R. R., Sun, X.-F., & Rosin, P. L. (2013) · IEEE Transactions on Visualization and Computer Graphics · doi:10.1109/tvcg.2012.310 · Cited by 679 · see citing works
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- Authors
- Liu, Y.-S., & Ramani, K.
- Affiliations
- Purdue University West Lafayette (US)
- Corresponding author
- Liu, Yu-Shen
- ORCID
- Liu, Yu-Shen
- Venue
- Computer-Aided Design
- Publisher
- Elsevier BV
- Published
- 2009-04
- Volume
- 41
- Issue
- 4
- Pages
- 293-305
- ISSN
- 0010-4485 (ISSN-L)
- PMC
- PMC2710849
- OpenAlex
- W1964941300
- Cited by
- 46
- References
- 48
- Citations by year
- 2026: 1 · 2023: 6 · 2022: 5 · 2021: 2 · 2020: 5 · 2019: 2 · 2018: 6 · 2017: 3 · 2016: 2 · 2015: 4 · 2014: 2 · 2013: 3 · 2012: 2
- FWCI
- 1.05
- Type
- journal article
- Language
- en
- Open access
- green
- www.ncbi.nlm.nih.gov
- Licence
- Locations
- Computer-Aided Design (publishedVersion)
- PubMed (publishedVersion)
- PubMed Central (acceptedVersion)
- Funders
- National Institute of General Medical Sciences (R01GM075004)
- Topics
- Physical Sciences › Engineering › Computational Mechanics › 3D Shape Modeling and Analysis
- Physical Sciences › Mathematics › Statistics and Probability › Advanced Statistical Methods and Models
- Physical Sciences › Computer Science › Computer Graphics and Computer-Aided Design › Computer Graphics and Visualization Techniques
- Keywords
- least median of squares, robust statistics, outlier detection, forward search, 3D shape representation, octree, shape alignment, principal component analysis, noise robustness
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