# What velue to use for "smooth3(A, 'gaussian', v)?

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John el 11 de Oct. de 2022
When using "smooth3(A, 'gaussian', v), unlike the 'box' method, the value v doesn't seem to take affect. Without v, or 5, or 99 it has the same effect. The 'doc smooth3' doesn't provide real information.
Thanks.
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Adam Danz el 11 de Oct. de 2022
Good question @John.
The syntax smooth3(A,'gaussian',V) passes the data A through a gaussian lowpass filter with a default standard deviation of 0.65 (you could specify that in an optional 4th argument). V defines the 3D window size for the filter.
Without seeing your data or the results, I can't explain why various V values produce the same results. If you attach a mat file that contains A and V I could dig deeper.
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John D'Errico el 12 de Oct. de 2022
Anyway, consider that a Gaussian smoothing kernel of size 15 is HUGE, in comparison to a an array of size only 20x20x20. Do you see that I did get differences in my example, for SMALL gaussian kernels?
Anyway, the size of the tiny difference in Frobenious norm you indicate is also not relevant. That is again no surprise. Taking the frobenenius norm just averages out any remnants of noise.
A = randn(100,100,100);
B1 = smooth3(A,'gaussian',3);
B2 = smooth3(A,'gaussian',9);
B3 = smooth3(A,'gaussian',15);
format long g
norm(B1 - B2,'fro')
ans =
11.5343687718617
norm(B1 - B3,'fro')
ans =
11.5343687719941
Again, there ARE Differences to be seen, but the law of large numbers averages those differences out.
LOOK AT THE ARRAYS THEMSELVES TO SEE THAT!
B1(1:3,1:3,1:3)
ans =
ans(:,:,1) = -0.234102312749705 0.382072219543637 0.339308902178634 0.287843370691201 -0.111414000006913 -0.0625339480640082 0.129363424476748 -0.390423770739839 0.00426595845787685 ans(:,:,2) = 0.094990454554044 0.44155534092969 0.575420147677844 -0.266089109123344 -0.0330899672385768 0.000463778487347755 -0.632685810434764 -0.612382934354194 -0.312260654482024 ans(:,:,3) = -0.435468586043421 -0.211167306940052 -0.064833858178933 -0.185984173044869 0.345543259401304 0.168109924813588 0.256538827469533 0.295591962534587 0.0558459484555244
B2(1:3,1:3,1:3)
ans =
ans(:,:,1) = -0.24001109353323 0.373849267934935 0.322000538123073 0.281420048281016 -0.0982743532723887 -0.0524519085140193 0.129767507354035 -0.37558919785582 0.00684001729650901 ans(:,:,2) = 0.0901436665433138 0.428674231870868 0.562958332174248 -0.259188944716559 -0.0291847019562449 0.011934896561421 -0.614651337056743 -0.594305007405726 -0.300844876871851 ans(:,:,3) = -0.430076302309084 -0.208657293818347 -0.0675240672893176 -0.182313648494426 0.330234304800294 0.163644475651634 0.238106150134462 0.278741479390564 0.0512551907513211
Different numbers.
Adam Danz el 17 de Oct. de 2022
Thanks for that detailed explanation and demo @John D'Errico!

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