Direct Least Square Fitting of Ellipses
By Maurizio Pilu, Andrew Ftzgibbon, and Robert B. Fisher @
Machine Vision Unit
Department of Artificial Intellegence, University of Edinburgh
5 Forrest Hill, Edinburgh EH1 2QL
This page gives an interactive demo of the first ellipse-specific direct
fitting method presented in the papers:
- M. Pilu, A. Fitzgibbon, R.Fisher ``Ellipse-specific
Direct least-square Fitting '' ,
IEEE International Conference on Image Processing, Lausanne, September
- A. Fitzgibbon, M. Pilu , R.Fisher ``Direct least-square
fitting of Ellipses '' , International
Conference on Pattern Recognition, Vienna, August 1996.
The most stable and correct MATLAB code is here
and some MATLAB code for drawing ellipses is here
Note: Your Browser must be Java-enabled, such as Netscape 2,
in order for the demo to work.
This demo was compiled with the beta 1.0 release of Java, so will not be
viewable with HotJava. The Taubin's method will be incuded soon.
- Click in a cloud of 10-20 points and see the differences between the two
results. Often Bookstein method yields hyperbolae. Also try to drag one
point across and see how the ellispes-specific method retains ellipticity
and show more stability, whereas the others erraticaly flip from ellipses to hyperbolae.
- Click in a coarse 30-40% arc of ellipse or part of an hyperbola and see how
the ellipse-specific method always yield good ellipses. Also
note the low-eccentricity bias of the ellipse-specific method.
- Create any shape, and see how the ellipse-specific method bounds the
points whereas the other methods often give unpleasant results.
About The Source.....
This demo was written by
Maurizio Pilu , University of Edinburgh.
The scruffy java source code is available on line. Click here
to download it. Even if you don't know java, you will find amazingly easy to convert
it to C or C++.
The applet's graphic interface was much inspired by the
Curve Applet written by Michael Heinrichs at SFU, Vancouver.
Some math routines were adapted from the "Numerical Recipes in C" by
Press/Teukolsky/Vettering/Flannery, Cambridge Uiniversity Press, Second Edition (1988)
and therefore the code is subject to that copyright.
Mail the author firstname.lastname@example.org
if you want to know more about it.
Up to the
MVU home page
Maurizio Pilu, 19 Jul 1996.