Algorithm of ellipse fitting in OpenCV

Question

I read the code of ellipse fitting in OpenCV, the following link gives the source code of ellipse fitting in OpenCV: http://lpaste.net/161378.

I want to know some details about ellipse fitting in OpenCV, but I can not find any documents of the algorithm. In the comments, it said " New fitellipse algorithm, contributed by Dr. Daniel Weiss". But I can not find any paper about ellipse fitting of Dr. Daniel Weiss.

I have some questions of the algorithm:

1. Why does the algorithm need re-fit. It first fit for parameters A - E, and then re-fit for parameters A - C with those center coordinates.
2. Ellipse need the satisfy the constraint of 4*a*b - c^2 > 0, how does the algorithm satisfy it?

Answer 1

You might find this repo useful (with pip set-up):

https://github.com/bdhammel/least-squares-ellipse-fitting

which works from an upgrade to the Fitzgibbon algorithm (as a starting point), as authored by Halir here:

https://github.com/bdhammel/least-squares-ellipse-fitting/blob/master/media/WSCG98.pdf

I've since tested this a little and seems to be very effective. Note that the 'example' on the repo home page is out of date -- look to the example.py module in the code itself for usage that seems to work as to module imports, etc.

Answer 2

I'm wondering about this myself since I've discovered that the algorithm is bugged. See this bug-report: https://github.com/Itseez/opencv/issues/6544

I tried to find any relevant papers by Dr. Daniel Weiss and failed.

Answer 3

The documentation of the OpenCV function cv::fitEllipse mentions this paper:

Andrew W Fitzgibbon and Robert B Fisher. A buyer's guide to conic fitting. In Proceedings of the 6th British conference on Machine vision (Vol. 2), pages 513–522. BMVA Press, 1995.

Also related link: OpenCV Ellipse fitting: extract parameters.