Reconstructing Spheres by Fitting Planes


Erol Ozgur (Institut Pascal Clermont-Ferrand), Mohammad Alkhatib (Institut Pascal Clermont-Ferrand), Youcef Mezouar (Institut Pascal Clermont-Ferrand), Adrien Bartoli (Institut Pascal Clermont-Ferrand)
The 35th British Machine Vision Conference

Abstract

We address the problem of reconstructing a sphere of a prescribed radius from a single calibrated view of its occluding contour. A sphere's occluding contour generally appears as an ellipse and existing methods use ellipse fitting. Most methods thus require $\geq 5$ contour points though a few can also deal with the minimal case of $3$ points. However they all share two shortcomings: $(i)$ they fail for non-elliptic occluding contours, including parabola and hyperbola, and $(ii)$ they use the point-to-ellipse distance, whose computation is not closed-form. We make the observation that the spherically-normalised contour points form a circle in space, which we reconstruct by plane fitting. This handles minimal $3$-point and redundant $>3$ point fitting, copes with elliptic and non-elliptic contours, and benefits from the simple point-to-plane distance. The reconstructed circle then leads to a one-parameter sphere family from which the actual sphere of prescribed radius is uniquely retrieved. We robustify the method using random sampling at the plane fitting stage. We name our method $\texttt{SpherO}$, where letter `O' depicts a circle. Experimental comparisons show that $\texttt{SpherO}$ outperforms the current-best 3-point method.

Citation

@inproceedings{Ozgur_2024_BMVC,
author    = {Erol Ozgur and Mohammad Alkhatib and Youcef Mezouar and Adrien Bartoli},
title     = {Reconstructing Spheres by Fitting Planes},
booktitle = {35th British Machine Vision Conference 2024, {BMVC} 2024, Glasgow, UK, November 25-28, 2024},
publisher = {BMVA},
year      = {2024},
url       = {https://papers.bmvc2024.org/0729.pdf}
}


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