Re: Determining circularity

["Vince Hradil" <hradilv(at)yahoo.com>]

May be simpler to use this definition of circularity:  the variance of the
boundary pixels distance to the centroid.

1- compute centroid, (xc,yc): xc=sum(x)/area
2- find the boundary pixels
3- calcuate the mean distance from the centroid to the the boundary pixels
and the variance
4- circularity =variance/mean (circles are 0)

"Craig Markwardt" <craigmnet@cow.physics.wisc.edu> wrote in message
on8zjkeuhj.fsf@cow.physics.wisc.edu">news:on8zjkeuhj.fsf@cow.physics.wisc.edu...
>
> Todd Clements <mole6e23@hotmail.com> writes:
>
> > Hi all...
> >
> > I was wondering if anyone knew of routines to determine the circularity
> > of an image. We have images from our detector and for optimal
> > calibration, they need to be as circular as possible, and it's difficult
> > to tell by eye when it's close but not quite there.
> >
> > Generally these images have fairly well defined edges, although there is
> > definitely some gray area as to what consistutes the edge, which makes
> > it difficult to determine by eye sometimes.
> >
> > Basically, I guess it comes down to fitting the edge of the image to an
> > ellipse, but there has to be some determination of what the edge is as
> > well.
>
> Possible solution:
>
> 1. Edge filter with ROBERTSON (or perhaps SOBEL)
> 2. Extract X- and Y-position of edge points (use a threshold)
> 3. Fit to an ellipse using MPFITELLIPSE
>
> The last one is from my web page, and can be used for fitting an
> ellipse to a set of scattered points.  It's not theoretically perfect
> but is good for rough calcs.  Of course you need MPFIT as well.  Here
> is a sample go-round.  First I construct some fake data and then
> perform the steps above.
>
> ;; Construct a filled circle with a radius of 6
> x = findgen(101)*0.2 - 10. & y = x
> xx = x # (y *0 + 1)  ;; Construct X, Y, and R (radius) values
> yy = (x*0+1) # y
> rr = sqrt(xx^2 + yy^2)
> wh = where(rr LT 6.) ;; Fill the circle
> im = xx*0
> im(wh) = 1
>
> ;; Step 1. Extract edge-filtered image
> edge = roberts(im)
>
> ;; Step 2. Extract edge points using threshold value (value of 2 here)
> wh = where(edge EQ 2)
> xim = xx(wh) & yim = yy(wh)
>
> ;; Step 3. Fit the image
> print, mpfitellipse(xim, yim)
> ...  results are ...
>       5.96942      5.96942    -0.100046    -0.100019      0.00000
>       XSEMI        YSEMI      XCENTER      YCENTER        ROTATION = 0
>
> I make it look easy.  The real trick is to find the right threshold to
> select the points from the data, and filtering out any other noise
> which will surely screw up the edge enhancement.
>
> Craig
>
> --------------------------------------------------------------------------
> Craig B. Markwardt, Ph.D.         EMAIL:    craigmnet@cow.physics.wisc.edu
> Astrophysics, IDL, Finance, Derivatives | Remove "net" for better response
> --------------------------------------------------------------------------