How can I speed up (or avoid) a comparison in for loop?

Hi Everyone,

I'm analysing porosity in volumetric image data from CT scans. The input data is logical. 0 indicates background or pores while 1 indicates material.

The code shows a simplified example with two pores. The smaller pore needs to be removed because it's smaller than the threshold. bwlabeln (from the Image Processing Toolbox) changes the zeros of the pores to an ID (look in L-array). After the labelling I can quickly identify the undersized pores (step #1 f-vector).

My problem is the performance of the for-loop (step #2). For large data sets as in my case (A is typically 1000x300x1000 with over 20,000 pores that need to be removed) this takes forever. How can I improve the performance of the for-loop? Or do you have another idea how to delete (change 0 to 1) the small pores from the data set?

Kind regards,

Max

%% create synthetic specimen
A=ones(10,10,10); % background = 0, material = 1
threshold = 10; % min. amount of elements for pore
A(3:5,3:5,3:5)=0; % pore elements = 27 > threshold -> must be kept
A(7:8,7:8,7:8)=0; % pore elements =  8 < threshold -> must be removed

%% preprocessing
r = 1;      % rim size
s = size(A); % size of A
a = zeros(s+(r*2));
a(r+1:r+s(1),r+1:r+s(2),r+1:r+s(3)) = A;

A = imbinarize(a);      % make logical
AA = imcomplement(A);   % inverse image
[L,n] = bwlabeln(AA,6); % label pores
N = histcounts(L); % number of elements with certain value

%% #1. vector with too small pores (Voxel < threshold)
f = find(N<threshold); % find pores with too little elements
f = f-1;

%% #2. set critical values = 1
for i = 1:length(f)
    A(L==f(i)) = 1; % A=0 background or pore, A=1 material
%     disp(i) % shows that the loop takes forever if length(f) is large 
end

Answer 1

[Jan]

What about omitting the loop:

A(ismember(L, f)) = true;

Or:

LUT           = [false, N < threshold];
A(LUT(L + 1)) = true;

[Max Mierzwa]

Thank you :-)

[Jan]

I cannot test it due to the missing input data and I do not have the image processing toolbox. The lookup table method should be even faster, but might need some debugging.

[Max Mierzwa]

Time for omiting loop on my test data set with about 25.000 pores (i'm not allowed to share this data):

Method #1: 0.13 sec

Method #2: 0.86 sec

old for-loop: 2600 sec

[Matt J]

In my tests, this method is even slower than the original for loop, and certainly much slower than bwlareaopenn.

A=true(1000,300,1000);
N=numel(A);
A( randperm(N,2e4) )=false;
threshold = 10; % min. amount of elements for pore

A0=A;

A=A0;
tic;

    AA = imcomplement(A);   % inverse image
    [L,n] = bwlabeln(AA,6); % label pores
    N = histcounts(L); % number of elements with certain value
    %% #1. vector with too small pores (Voxel < threshold)
    f = find( N<threshold); % find pores with too little elements
    f = f-1;
    %% #2. set critical values = 1
     A(ismember(L, f)) = true;

toc

Elapsed time is 8.438911 seconds.

res1=A;
Nf=numel(f)

Nf = 39993

A=A0;
tic
 A=~bwlareaopenn(~A,threshold-1);
toc

Elapsed time is 1.724570 seconds.

res2=A;

isequal(res1,res2)

ans = logical
   1

[Max Mierzwa]

I think my posted example was misleading.

The problem was that the loop took forever because of the large length(f). In the given example with length(f)=1 there were no performance issues. In my data from the CT-scans (lenght(f) > 10000) the other issues of the code had a negligible impact on processing time.

@Matt J Thanks for your help

[Matt J]

In my data from the CT-scans (lenght(f) > 10000) the other issues of the code had a negligible impact on processing time.

Maybe negligible compared to the original for-loop, but the use of bwlabeln and histcounts is unnecessary and quite inefficient. I've modified my example above with length(f)=40000 and you can still see that it is much slower than bwlareaopenn.

Answer 2

[Matt J]

You might try bwlareaopenn from this submission

https://www.mathworks.com/matlabcentral/fileexchange/90762-further-tools-for-analyzing-objects-in-n-dimensional-images

A=~bwlareaopenn(~A,threshold);