Calculate radius from scatter plot

Hi,

I need to calculate the radius of a circle, ignoring all surrounding particles (image attached). The circle itself consists of many particles (over 100,000). Note that the center of the circle is not at the origin.

Thanks.

EDIT: here is how I solved it:

posn=normal(poscm); %poscm is the coordinates matrix
[k,edges]=histcounts(posn,1e5);
[~,imaxk]=max(k);
R=edges(imaxk+find(k(imaxk:end)==0,1)); %find the first zero value after the maximum

[Adam Danz]

I assume you're computing the radius based on a set of coordinates, or are you computing it based on the image?

[yonatan s]

based on a set of coordinates

[Adam Danz]

Some ideas off the top of my head.....

There are several things you could try to get rid of the outliers. For example, you could try matlab's isoutlier function.

Since the signal to noise ratio looks very high, you could try fitting the circle directly without removing any of the outliers. There may be a file on the file exchange that fits a circle to a cluster of dots but avoid using circle-fitting algorithms that use least squares or that fit a circle according to dots along a circumference.

It may be helpful to see a distribution of point distances which may give you an approximate diameter estimate. pdist() would give you the distance between all points but it also may reach memory capacity since you have very many points.

You could also try a clustering technique. I wonder if kmeans() would be sufficient to find the center of the circle. Again, your SNR is very high so the outliers may not matter.

You might be able to use an image processing approach such as regionprops, too.

[yonatan s]

It's not perfect, but it seems isoutlier is the right approach.

pdist consumes too much memory.

I tried using some image processing tools, the problem is that axes change when transforming the plot to an image.

Thanks.

[Adam Danz]

If you're still looking for a solution, attach the fig file containing the data, or attach a mat file containing the (x,y) coordinates.

Answer 1

[Matt J]

You could try using clusterdata to find the big concentration of points. Then minboundcircle from the File Exchange to get the radius,

https://www.mathworks.com/matlabcentral/fileexchange/34767-a-suite-of-minimal-bounding-objects

[yonatan s]

I have too many particles for that, it requires a lot of memory

Answer 2

[darova]

Try density function hist3

r = rand(500,1)/5;
t = rand(500,1)*2*pi;
x = [rand(50,1); r.*cos(t)+0.5]; 
y = [rand(50,1); r.*sin(t)+0.5];
n = 20;
k = hist3([x y],[n n]);

k(k<2) = nan;
pcolor((0:n-1)/n,(0:n-1)/n,k)
hold on
plot(x,y,'.r')
hold off

[darova]

You can convert you data into an image and try imfindcircles

[yonatan s]

hist3 sounds like a good approach, but how would I get the radius of the circle out of it?

[Matt J]

[centers,radii] = imfindcircles(A,radiusRange)

[yonatan s]

the axes change as I transform a plot to an image.

Answer 3

[darova]

Here is the idea

• scale your data
• create an image (fill pixels)
• dilate image to create solid round object (circle)
• use imfindcircles

[Matt J]

And maybe also use bwareafilt to remove all but the biggest cluster of points.

[darova]

No

[Matt J]

Why not?

[darova]

There is no need for it

[yonatan s]

Hi darova, went over it again. How do I scale the radius back? If I simply multiply it by the scaling factor it doesnt come out right.