Re: Determining circularity

[Craig Markwardt <craigmnet(at)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

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Craig B. Markwardt, Ph.D.         EMAIL:    craigmnet@cow.physics.wisc.edu
Astrophysics, IDL, Finance, Derivatives | Remove "net" for better response
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