How do I make 3D sphere for convolution?

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Lieke Pullen 2022-1-12

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评论： Lieke Pullen 2022-1-13

采纳的回答： Rik

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Hi all,

I want to make a 3D sphere where the x, y and z coordinates are being solved in a 3D array, so I can convolute this with a kernel I have. But, I don't seem to both save the coordinates and get the shape right at the same time. I have the following code:

figure; 
half=50;
for k=1:100
    for j=1:100
        for i=1:100
            mesh_sphere(i,j,k)=((i-half).^2)+((j-half).^2)+((k-half).^2);
        end
    end
    surf(mesh_sphere(:,:,k));
    hold on
end
hold off

After this, I also want to use other shapes that I can test my kernel on, such as a hollow sphere and an ellipsoid. How can I make those and also same them in a 3D array? Thank you in advance!

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Rik 2022-1-12

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If you want a sphere in a 3D array, you should probably do something like this:

array_width=21;%must be odd
radius=5;%must be smaller than half the array width for the sphere to fit
a=(array_width-1)/2;
a=linspace(-a,a,array_width);
[X,Y,Z]=meshgrid(a);
solid_sphere= sqrt(X.^2 + Y.^2 + Z.^2) <= radius;

For a shell you can repeat this with two radii and use the or operator |. For an elipsoid you need you can scale the coordinate values in each direction according to the partial radius you want.

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Image Analyst 2022-1-13

编辑：Image Analyst 2022-1-13

@Lieke Pullen like I showed in my answer below, the strel() function creates the sphere in one line of code. The convolution is also done in one line of code.

Lieke Pullen 2022-1-13

@Image Analyst I know, and I very much appreciate the effort. But I wanted to manually also change some of the proposed parameters, and this what this does to the shape. For me, Rik's option worked best.

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Image Analyst 2022-1-12

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编辑：Image Analyst 2022-1-13

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SE = strel('sphere',r) % creates a 3-D spherical structuring element whose radius is r pixels.
out = convn(inputImage, SE.Neighborhood);

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Rik 2022-1-12

I don't remember this object notation. Admittedly, I haven't used this function in years, but I will look up this function in the release notes to see whether I forgot, or if they changed it.