ML Anthology

Using Differential Geometry in R4 to Extract Typical Features in 3D Images

Olivier Monga, Serge Benayoun
CVPR 1993 pp. 684-685
doi:10.1109/CVPR.1993.341028 /cvpr/1993/monga1993cvpr-using/

Abstract

A new approach is presented to extract differential characteristics of surfaces in 3-D images from the second partial derivatives of the grey level function provided by separable recursive filters. The basic idea is to consider a 3-D image as a hypersurface in R/sup 4/ and to express the curvatures of the surface with the curvatures of the hypersurface. This yields a very compact and efficient approach where filtering is used for both edge detection and curvature extraction. Experimental results on real data can be compared with more classical approaches. It is noted that smoothing in the fourth-dimensional space could be more efficient than smoothing in the three-dimensional space.< <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

Monga and Benayoun. "Using Differential Geometry in R4 to Extract Typical Features in 3D Images." IEEE/CVF Conference on Computer Vision and Pattern Recognition, 1993. doi:10.1109/CVPR.1993.341028

Markdown

[Monga and Benayoun. "Using Differential Geometry in R4 to Extract Typical Features in 3D Images." IEEE/CVF Conference on Computer Vision and Pattern Recognition, 1993.](https://mlanthology.org/cvpr/1993/monga1993cvpr-using/) doi:10.1109/CVPR.1993.341028

BibTeX

@inproceedings{monga1993cvpr-using,
  title     = {{Using Differential Geometry in R4 to Extract Typical Features in 3D Images}},
  author    = {Monga, Olivier and Benayoun, Serge},
  booktitle = {IEEE/CVF Conference on Computer Vision and Pattern Recognition},
  year      = {1993},
  pages     = {684-685},
  doi       = {10.1109/CVPR.1993.341028},
  url       = {https://mlanthology.org/cvpr/1993/monga1993cvpr-using/}
}