Getting the values ​​of the pixels inside the sphere of radius (r1) and center (x1, y1, z1).

I want to get the values ​​of the pixels inside the sphere of radius (r1), center coordinates (x1, y1, z1) in the 3D image (xyz).

As a matter of fact, I'm not interested in the values ​​of individual pixels and want to get statistics such as mean and SD.

Since there is not one sphere, but hundreds or more, so I'm looking for an efficient way to quantify them.

I have the values ​​of radius (r1, r2, r3 ...) and center coordinates ((x1, y1, z1), (x2, y2, z2), (x3, y3, z3) ...) .

Please tell me how to do it easily.

If my explanation is inadequate, please ask and I'll get back to you soon.

Answer 1

[Walter Roberson]

Supposing you have a 3D grid Pixel_x, Pixel_y, Pixel_z, and you have Center_x, Center_y, Center_z, and Radii

Center_x_row = reshape(Center_x, 1, []);
Center_y_row = reshape(Center_y, 1, []);
Center_z_row = reshape(Center_z, 1, []);
Radiisq_row = reshape(Radii, 1, []).^2;

Pixel_x_col = reshape(Pixel_x, [], 1);
Pixel_y_col = reshape(Pixel_y, [], 1);
Pixel_z_col = reshape(Pixel_z, [], 1);

distssq = (Pixel_x_col - Center_x_row).^2 + (Pixel_y_col - Center_y_row).^2 + (Pixel_z_col - Center_z_row).^2;

%at this point, rows correspond to individual pixels, and columns correspond to sphere centers
%and distssq is distances squared

pixel_within_sphere = distssq <= Radiisq_row;
num_pixel_within_sphere = sum(pixel_within_sphere);   %single row, one column per sphere center

and now you can take mean(num_pixel_within_sphere) and so on.

[Yusaku Ohta]

Thank you for your prompt reply.

I'm sorry, my explanation was bad.

What I want to know is not the statistics of the coordinates within the sphere.

I want to know a statistic, for example, the average of the values of color intensity within a sphere in a grayscale image.

I think your method will only give us XYZ coordinate statistics.

Is it possible to get the color intensity statistic as well with the method you described?

If you don't mind me asking, how do you get a value for color intensity as well?

[Walter Roberson]

Average color intensity in a grayscale image does not appear to make sense, unless you are taking about brightness as color. If so then

grayscale_col = Grayscale_Intensities(:);
pixel_within_sphere = distssq <= Radiisq_row;
num_pixel_within_sphere = sum(pixel_within_sphere);   %single row, one column per sphere center
weighted_gray = pixel_with_sphere .* grayscale_col;
total_gray = sum(weighted_gray, 1);
mean_gray = total_gray ./ num_pixel_within_sphere;
std_gray = sqrt(sum((weighted_gray - mean_gray).^2 .* pixel_with_sphere,1) ./ (num_pixel_within_sphere - 1));

I used N-1 weighting instead of N weighting, as is appropriate for a finite population.

[Yusaku Ohta]

Sorry for the late reply.

Thank you for your very smart response.

It took me a while to figure it out because it was too smart!

It's amazing how easy it is to do.

I learned a lot, thank you.