ML Anthology

Modeling Generic Polyhedral Objects with Constraints

Van-Duc Nguyen, Joseph L. Mundy, Deepak Kapur
CVPR 1991 pp. 479-485
doi:10.1109/CVPR.1991.139739 /cvpr/1991/nguyen1991cvpr-modeling/

Abstract

A generic polyhedral model is represented as a network of nodes and constraints. Nodes are 3-D vectors representing the location and orientation of the geometric entities, or measure variables such as length or cosine. Constraints are polynomial equations in the node parameters. Modeling and recognition are viewed as solving for values of the node parameters such that all the constraint equations are satisfied and the mean square error between the model and the observed shape is minimized. Buchberger's Grobner basis algorithm and Ritt-Wu's triangulation algorithm can be used for eliminating dependent parameters as well as for detecting inconsistency among constraints. Numerical techniques are used to find the best-fit model subject to constraints.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

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Cite

Text

Nguyen et al. "Modeling Generic Polyhedral Objects with Constraints." IEEE/CVF Conference on Computer Vision and Pattern Recognition, 1991. doi:10.1109/CVPR.1991.139739

Markdown

[Nguyen et al. "Modeling Generic Polyhedral Objects with Constraints." IEEE/CVF Conference on Computer Vision and Pattern Recognition, 1991.](https://mlanthology.org/cvpr/1991/nguyen1991cvpr-modeling/) doi:10.1109/CVPR.1991.139739

BibTeX

@inproceedings{nguyen1991cvpr-modeling,
  title     = {{Modeling Generic Polyhedral Objects with Constraints}},
  author    = {Nguyen, Van-Duc and Mundy, Joseph L. and Kapur, Deepak},
  booktitle = {IEEE/CVF Conference on Computer Vision and Pattern Recognition},
  year      = {1991},
  pages     = {479-485},
  doi       = {10.1109/CVPR.1991.139739},
  url       = {https://mlanthology.org/cvpr/1991/nguyen1991cvpr-modeling/}
}