How to find distance between two curves?

Hey guys, I have a set of binary images each consisting of two curves, one directly on top of the other. I want to find the normal distance between them. This is very similar to another question found here: https://www.mathworks.com/matlabcentral/answers/214151-how-to-find-the-distance-between-lines-in-a-image-in-matlab. I'm guessing I need to fit curves onto the image first. Any help would be much appreciated!

[Image Analyst]

OK, tell us how we can help.

[Image Analyst]

Do you want vertical distance or "radial"?

Have you seen the FAQ for fitting a circle: http://matlab.wikia.com/wiki/FAQ#How_can_I_fit_a_circle_to_a_set_of_XY_data.3F

[Jean Luo]

I'm thinking maybe finding the tangent lines to the highest points on the curves would be a good way to go, but do you have any ideas as to how I can find where the highest points are?

Answer 1

[Image Analyst]

I'd invert the image so that the curves are white (foreground). Then I'd make masks for each curve by dilating the image a bunch and using bwareafilt() to extract the 2 largest blobs. Then for each blob, mask the image of the original, undilated image so that you have only that blob. Then I'd use find() to get all the coordinates and then fit it to a circle to get an average radius. Then do the same for the other masked blob. Subtract the two radii to get the average, overall separation.

[Image Analyst]

Can you include your circfit() function, and I'll check back later today.

[Jean Luo]

I basically used the circle function you told me to look at earlier. I downloaded the file here: https://www.mathworks.com/matlabcentral/fileexchange/5557-circle-fit/content/circfit.m I think the problem is the fact that the centers of the two circles are not the same.

[Jean Luo]

The real question now is, is there a function I can use that fits a circle given the origin and some points on the curve?

[Image Analyst]

I don't think that's the real question, but anyway...... If you specify the origin, and by that I assume you mean the center of the circle, and assume all the points are out a radius away on the circumference/perimeter, then of course you can get the average radius by averaging the distance all the points are away from your center.

meanRadii = mean(sqrt((x - xCenter).^2 + (y - yCenter).^2));

Again, I don't think that will do you any good but I believe it answers the question you just asked.

[Jean Luo]

My question was, how do I fit a circle with a specific origin? All the functions I found didn't have the option of specifying a center. I think a simpler way to do this is to translate the circle, but I'm not sure how to do that either. Any ideas?

[Image Analyst]

Then the code in my last comment will work. You specify (xCenter,yCenter) and you'll get the radius. With those 3 things, the circle is specified. I don't know why you need any more "ideas" when that one works.

[Jean Luo]

I'm sorry, but I still don't completely understand what you mean. Do I need to use a circle-fitting function? How exactly do I get the radius?

[Image Analyst]

I gave you the formula for the radius. Here it is again:

meanRadii = mean(sqrt((x - xCenter).^2 + (y - yCenter).^2));

Recall that you said you have a known, specified center, so you know what xCenter and yCenter is. Don't you? I assume you did when you said "given the origin". Because if you just had the origin but not the center, then you'd just use the FAQ like I originally said.

No you don't need to use some circle fitting routine. The formula for radius I gave you is, in essence, the fitting code. It works because you have specified the center already so all we need to determine is the radius, which would just be the average of the distances of each point from your known center.

[Jean Luo]

Thank you so much for your help, I got it to work!