How do I make 3D sphere for convolution?
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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!
采纳的回答
Rik
2022-1-12
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.
9 个评论
Lieke Pullen
2022-1-12
编辑：Lieke Pullen
2022-1-12
Since the sphere variable is logical: between the two generated spheres.
Note that the difference between the two radii should be large enough, otherwise your shell will disappear.
Also, it shouldn't actually be or, it should be xor.
array_width=21;%must be odd
small_solid_sphere=create_solid_sphere(4,array_width);
big_solid_sphere=create_solid_sphere(5,array_width);
hollow1= xor(small_solid_sphere,big_solid_sphere);
small_solid_sphere=create_solid_sphere(4.9,array_width);
big_solid_sphere=create_solid_sphere(5,array_width);
hollow2= xor(small_solid_sphere,big_solid_sphere);
subplot(1,2,1),imshow(hollow1(:,:,11))
subplot(1,2,2),imshow(hollow2(:,:,11))
function solid_sphere=create_solid_sphere(radius,array_width)
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;
end
Lieke Pullen
2022-1-13
Rik
2022-1-13
I don't really understand what you mean. Isn't this equivalent to having radii of 20 and 5 for the big and small spheres?
Lieke Pullen
2022-1-13
The shell is a kind of hack. It takes two spheres of different radii and looks where only one of them exists. That sounds exactly what you want. You don't want two shells and fill what is in between them, you want a single sphere with a thick shell. So just subtract the sphere with a small radius from the sphere with the large radius and you have the shape you describe.
array_width=101;%must be odd
small_solid_sphere=create_solid_sphere(25,array_width);
big_solid_sphere =create_solid_sphere(5 ,array_width);
hollow1= xor(small_solid_sphere,big_solid_sphere);
imshow(hollow1(:,:,(end-1)/2))
function solid_sphere=create_solid_sphere(radius,array_width)
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;
end
Lieke Pullen
2022-1-13
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
更多回答（1 个）
Image Analyst
2022-1-12
编辑：Image Analyst
2022-1-13
SE = strel('sphere',r) % creates a 3-D spherical structuring element whose radius is r pixels.
out = convn(inputImage, SE.Neighborhood);
3 个评论
Matt J
2022-1-12
Possibly you meant,
out = convn(inputImage, SE.Neighborhood);
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.
Image Analyst
2022-1-12
Thanks Matt for the correction.
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