Shortest distance from a point to a fitted ellipse

The following code presents the implementation of the "Direct Least Square Fitting of Ellipses" (Fitzgibbon et al., 1999) manuscript and the calculation of the minimal distance from a set of arbitrary points to the fitted ellipse.

This implementation was done in the context of the manuscript "Semi-autonomous Prosthesis Control Using Minimal Depth Information and Vibrotactile Feedback" by Miguel Nobre Castro and Strahinja Dosen, which is available on arXiv:2210.00541.

Requirements

Eigen 3.0.0
PCL 1.11.1*

Steps

1. Generate a set of elliptically placed and noisy target points.
2. Perform ellipse fitting [1] to obtain the respective ellipse parametric equation values.
3. Given an arbitrary point P, which shortest distance is to be evaluated, infer the ellipse quadrant it belongs to.
4. From that quadrant range, use a golden section line search [2] to find the ellipse point at the minimum distance from P.

Results

Fig. 1: Shortest distances from arbitrary points (white) to an ellipse (yellow) fitted from 6 points (purple).

References

* Please see the following Point Cloud Library links for more details: PointCloudLibrary/pcl#5431 PointCloudLibrary/pcl#5430