http://imagej.273.s1.nabble.com/FitCircle-circle-fitting-class-tp3691194p3691198.html
Aren't Hough Transforms the only practical way to multiple shape instances,
> Hi list,
>
> this all is most interesting! Is there also a robust "L0-norm" algorithm?
>
> To elaborate a bit: L2-norm would be the "usual" approach that minimizes
> thes sum of squared error. L1-norm would minimize the sum of absolute error
> (and so gives less weight to outliers)
> L0-norm would simply count the number of outliers (for real noisy data 0
> should not really be zero here, but a small number)
>
> (I know that distinction from a seemingly unrelated field, so-called phase
> unrwapping, where a L0-norm really makes sense and is preferred if
> possible)
>
> The idea of L->0-norm fit would be that it can fit robustly almost perfect
> circles with "breakouts", as what I exactly have. (I also would like to be
> able to fit ellipses instead of circles
> (due to aspect ratio not exactly one) or even with that main axes not in x
> and y)
>
> Any hint highly appreciated!
>
> BTW, I do not really like using any solution based on the Hough-transform,
> which I see as a brute-force approach with a shiny new name (My biased
> view). Yes, I know that there are now some
> "fast" versions, where I do not yet have any experience!
>
> Joachim Wesner
>
>
>
>
> Michael Doube
> <m.doube@IMPERIAL
> .AC.UK <
http://ac.uk/>>
> An
> Gesendet von:
[hidden email]
> ImageJ Interest Kopie
> Group
> <
[hidden email]. Thema
> GOV> Re: FitCircle circle-fitting class
>
>
> 11.09.2009 11:17
>
>
> Bitte antworten
> an
> ImageJ Interest
> Group
> <
[hidden email].
> GOV>
>
>
>
>
>
>
> Hi Johan
>
> From the practical standpoint rather than than the mathematical
> perspective:
>
> the Hough transform finds shapes within data; e.g. you supply an image
> and the Hough transform finds the shape (line, circle...) in it - there
> is an ImageJ plugin for this here:
>
http://rsbweb.nih.gov/ij/plugins/hough-circles.html>
> My FitCircle class finds the single best-fit circle for a set of (x, y)
> points. So if you have n coordinates in a 2D array (double[n][2]; I
> have displacement from a mean axis vs axis distance) you can call e.g.
> FitCircle.hyperStable(coordinates), which returns the centre and radius
> of the best fitting circle.
>
> Chernov has written a huge, detailed manual on the methods which you can
> read here:
http://www.math.uab.edu/~chernov/cl/book.pdf . I'm still
> suspicious that my Taubin fits are buggy as they break when supplied
> with samples from an arc of less than 2*PI radians. So far, the Hyper
> fits are doing well in terms of stability and speed.
>
> Mike
>
> Johan Henriksson wrote:
> > I see that you have one that searches all of (a,b,R). how do these
> > compare to the classic algorithms based on hough transform?
> >
> > /Johan
> >
> > Michael Doube wrote:
> >> Hi all
> >>
> >> I've been working on a Java port of some MATLAB scripts that fit
> >> circles to data. I originally started it to find a good method to
> >> work out radii of curvature, and it's grown (since Monday) to be
> >> something that might be useful to other people.
> >>
> >> The algorithms are described in detail by Nikolai Chernov on his page,
> >>
http://www.math.uab.edu/~chernov/cl/MATLABcircle.html> >>
> >> It includes Chernov's Hyper non-biased algebraic (non iterative, fast
> >> and accurate) circle fitting method and a couple of the geometric
> >> methods.
> >>
> >> The class is designed to be generic, and I've written an example
> >> testing plugin, here:
http://doube.org/files/Test_Circle.java> >>
> >> If you'd like to check it out, I've posted an initial, mostly-working
> >> version at
http://doube.org/files/FitCircle.java> >>
> >> It's also in my git repo,
http://github.com/mdoube/BoneJ/tree/master.
> >>
> >> Cheers,
> >>
> >> Mike
> >
> >
>
>
>
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