Finding the "center" of an extended ring

I have been experimenting with the image processing toolbox's function "imfindcircles", and it works well. However, there is one issue: I have an extended big ring in the image where I want to recognise its "center" instead of the outer end of the ring (see attached figure, where the outer end is plotted with viscircles and the center and radius found by imfindcircles).

This is also mirrored in the data itself: both the inner and outer end of the big ring have a lower intensity than its center. Is there a way to force "imfindcircles" to use the ring of maximum intensity? (Note that I have applied a thresholding to my image, otherwise the gradient at the ring ends would not be as harsh, and imfindcircles would struggle to differentiate between the ring and artifacts neighbouring the ring.)

Or is there maybe an alternative that includes a second step? After all, the circle center is properly recognised, so I can maybe vary the radius slightly? Maybe I could add up all the values of pixels that would lie on the circle, and see where that reaches its maximum. Is there an easy way to do something like that?

openfig findcircle-test.fig  

ans = 
  Figure (1) with properties:

      Number: 1
        Name: ''
       Color: [1 1 1]
    Position: [3.2978e+03 523.4000 468 411.2000]
       Units: 'pixels'

  Use GET to show all properties

[Garmit Pant]

Can you share additional images of the data that you are working with? The figure that you have shared still does not make it evident which "extended big ring" is the intended target of finding the radius.

[Matt J]

both the inner and outer end of the big ring...

Perhaps you mean the inner and outer "edge" of the annulus?

...have a lower intensity than its center.

Perhaps you mean the midline of the annulus, rather than the center?

[Dominik Rhiem]

@Matt J yes, sorry about the confusing terminology, you are absolutely right. I was unsure whether or not to call it an "edge" and unaware of the term "midline", but those are what I meant.

Answer 1

[Matt J]

load Image

BW0=BW;
A=bwareafilt( imfill(BW,'holes'),1);
BW=imclose(A.*BW, strel('disk',3));

B=bwconvhull(~(~A|BW));

midline=bwskel(BW&~B);  %midline of annulus

imshow(BW0+midline,[])

[Dominik Rhiem]

This looks really good and is pretty much what I meant, thank you. Do you have any suggestions to get the (average) radius of the "midline ring"?

[Matt J]

Yes, you can use circularFit() from this FEX download,

https://www.mathworks.com/matlabcentral/fileexchange/87584-object-oriented-tools-to-fit-plot-conics-and-quadrics

[y,x]=find(midline);

cfit=circularFit([x,y]')