On the Motion of 3D Curves and Its Relationship to Optical Flow
Abstract
I establish fundamental equations that relate the three dimensional motion of a curve to its observed image motion. I introduce the notion of spatio-temporal surface and study its differential properties up to the second order. In order to do this, I only make the assumption that the 3D motion of the curve preserves arc-length, a more general assumption than that of rigid motion. I show that, contrarily to what is commonly believed, the full optical flow of the curve can never be recovered from this surface. I nonetheless then show that the hypothesis of a rigid 3D motion allows in general to recover the structure and the motion of the curve, in fact without explicitely computing the tangential optical flow.
Cite
Text
Faugeras. "On the Motion of 3D Curves and Its Relationship to Optical Flow." European Conference on Computer Vision, 1990. doi:10.1007/BFB0014856Markdown
[Faugeras. "On the Motion of 3D Curves and Its Relationship to Optical Flow." European Conference on Computer Vision, 1990.](https://mlanthology.org/eccv/1990/faugeras1990eccv-motion/) doi:10.1007/BFB0014856BibTeX
@inproceedings{faugeras1990eccv-motion,
title = {{On the Motion of 3D Curves and Its Relationship to Optical Flow}},
author = {Faugeras, Olivier D.},
booktitle = {European Conference on Computer Vision},
year = {1990},
pages = {107-117},
doi = {10.1007/BFB0014856},
url = {https://mlanthology.org/eccv/1990/faugeras1990eccv-motion/}
}