Binning points in an image based on radius

Question

What I'm trying to do is take an image,

and then make a list of intensities as a function of distance from some point. So I've used a clever algorithm I found here to detect the centre of these circles, it's the point {317.974, -136.362} (notice this is outside of the image). What I then want is a list where each element of the list is a list of the intensities at a given euclidean distance from the point {317.974, -136.362}. I'd like the binning on the radii to be fairly small as well, maybe adjustable?

My goal with this is that I then want to take the mean of each of these lists so that I have a mean intensity at a given radius and a standard deviation for that given intensity. I think I could do this procedurally but I'm wanting to do it with a more functional Mathematica style. Could anyone help me figure out the fest way to do this?

Answer 1

You can basically use the same tools as in my answer you mentioned. Define:

img = Import["https://i.stack.imgur.com/dYnlY.png"];
center = {317.974, -136.362};
{w, h} = ImageDimensions[img];
xArr = Array[N[#2] &, {h, w}] - 1;
yArr = h - Array[N[#1] &, {h, w}];

Now xArr is an array with the same dimensions as img, containing the x-coordinate of each point, and yArr contains the y-coordinate of each point.

Using this we can easily calculate an array that contains the radius for each point:

radius = Sqrt[(xArr - center[[1]])^2 + (yArr - center[[2]])^2];

And then simply use Pick to get the pixel values for some radius value, so:

Flatten[Pick[ImageData[img], Round[radius], 200]]

returns the pixels with radius 199.5..200.5

Binning can also be included:

grayvaluesAtRadius[r_, bin_: 1] := 
 Flatten[Pick[ImageData[img], Round[radius/bin], Round[r/bin]]]