How to get average values of specific regions in each slice in 3d matrix using MATLAB boolean indexing
In Matlab,
If I have a 3D matrix like below, I want to know the average of the areas with values greater than 5 in each slice. How can I use a boolean pointer to do this, without any loops?
I would like to get a 3-by-1 array, with each element indicating the mean of the regions in their respective slice.
m3d = randi(10,[3,3,3])
m3d (:,:, 1) =
7 7 8
1 9 8
9 7 6
m3d (:,:, 2) =
10 10 5
9 7 8
5 3 3
m3d (:,:, 3) =
9 7 5
4 1 9
5 9 1
Getting the index
3d_index = m3d > 5;
My last
result = mean(m3d(3d_index));
in which I do not want to have an average for all regions
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One approach -
%// 3d mask of elements greater than 5 mask = m3d>5 %// Sum of all elements greater than 5 in each slice sumvals = sum(reshape(m3d.*mask,[],size(m3d,3))) %// Count of elements great than 5 in each slice counts = sum(reshape(mask,[],size(m3d,3))) %// Final output of mean values for the regions with >5 only out = sumvals./counts
Benchmarking
Here are some runtime tests to see where all the posted approaches are. For tests, we took a random 3D array 1500 x 1500 x 100
with values in the range [1,255]
. Following is the comparative code -
m3d = randi(255,1500,1500,100); %// Input 3D array
%// Warm up tic/toc.
for k = 1:50000
tic(); elapsed = toc();
end
disp('------------------------ With SUMMING and COUNTING ')
tic
%// .... Proposed approach in this solution
toc, clear out counts sumvals mask
disp('------------------------ With FOR-LOOP ')
tic
N = size(m3d, 3);
out = zeros(N, 1);
for k = 1:size(m3d,3)
val = m3d(:,:,k);
lix = val>5;
out(k) = mean(val(lix));
end;
toc, clear out lix val k N
disp('----------------------- With ACCUMARRAY')
tic
ind = m3d>5;
result = accumarray(ceil(find(ind)/size(m3d,1)/size(m3d,2)), m3d(ind), [], @mean);
toc, clear ind result
disp('----------------------- With NANMEAN')
tic
m3d(m3d<5) = NaN; %// Please note: This is a bad practice to change input
out = nanmean(nanmean(m3d,1),2);
toc
Runtimes
------------------------ With SUMMING and COUNTING
Elapsed time is 0.904139 seconds.
------------------------ With FOR-LOOP
Elapsed time is 2.321151 seconds.
----------------------- With ACCUMARRAY
Elapsed time is 4.350005 seconds.
----------------------- With NANMEAN
Elapsed time is 1.827613 seconds.
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This can be done very easily with accumarray
:
ind = m3d>5;
result = accumarray(ceil(find(ind)/size(m3d,1)/size(m3d,2)), m3d(ind), [], @mean);
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