Retrieving non-zero blocks from a matrix

Hi everyone,

I'd like to figure out a way to extract "blocks" of non-zero values from larger matrices. The following image shows an example of a matrix containing the "blocks" along the diagonal. I added the red brackets manually to better visualize the problem.

The problem I am having is that these "blocks " are not always as nice as the ones in the image above. Sometimes I get the following.

So the dimensionality of the blocks changes from matrix to matrix. Any help is greatly appreciated. Thank you

Answer 1

[Walter Roberson]

Data borrowed from @Oleg Iupikov

YourArray = [
    0.3899         0         0         0         0         0
         0    0.0492    0.3202    0.4881         0         0
         0    0.3074    0.4613    0.7067         0         0
         0         0         0         0    0.3673         0
         0         0         0         0    0.9414         0
         0         0         0         0         0    0.2682];

bw = logical(YourArray);
CC = bwconncomp(bw, 4);  %4 connectivity... no diagonals
S = regionprops(CC,'SubarrayIdx');

chunks = arrayfun(@(s)YourArray(s.SubarrayIdx{:}), S, 'uniform', 0)

chunks = 4×1 cell array
    {[  0.3899]}
    {2×3 double}
    {2×1 double}
    {[  0.2682]}

[NeGM]

Walter,

Imnot familiar with bwconncomp, what does the "4" do?

[Walter Roberson]

https://www.mathworks.com/help/images/ref/bwconncomp.html#bu2vpxm-1-conn

Answer 2

[Oleg Iupikov]

Here is one possible solution. Please see in-line comments for explanation.

% Generate some data matrix
Data = zeros(6,6);
Data(1,1) = rand;
Data(2:3,2:4) = rand(2,3);
Data(4:5,5) = rand(2,1);
Data(6,6) = rand;
Data

% This matrix will be used to determine if we have found all the blocks.
% 1 means that this element of the matrix has not been processed yet.
FlagMat = Data>0;

% Find all blocks
SubMatCnt = 0;
while true
    % Find 1st non-processed element of the matrix. It will correspond to the top-left corner of the sub-matrix.
    [irow,icol] = find(FlagMat,1); 
    
    % If all elements of FlagMat are 0, we have found everything, exit the loop
    if isempty(irow), break; end   

    % Find all neighboring non-zero elements along row
    icol2 = find(~FlagMat(irow,icol:end), 1) + icol - 2; % in fact, we are finding the 1st 0-element in the row irow starting from column icol
    if isempty(icol2), icol2 = size(FlagMat,2); end  % it is the case when icol pointing to the last column
    % Find all neighboring non-zero elements along column
    irow2 = find(~FlagMat(irow:end,icol), 1) + irow - 2;
    if isempty(irow2), irow2 = size(FlagMat,1); end  % it is the case when irow pointing to the last row
    
    % Form the submatrix indices
    irows = irow : irow2;
    icols = icol : icol2;
    
    % Mark elements of FlagMat correspontding to the submatrix as "processed"
    FlagMat(irows,icols) = false;
    
    % Print our submatrix
    SubMatCnt = SubMatCnt + 1;
    fprintf('Sub-matrix %i:\n',SubMatCnt);
    disp(Data(irows,icols));
end

And here is the output:

Data =
    0.3899         0         0         0         0         0
         0    0.0492    0.3202    0.4881         0         0
         0    0.3074    0.4613    0.7067         0         0
         0         0         0         0    0.3673         0
         0         0         0         0    0.9414         0
         0         0         0         0         0    0.2682

Sub-matrix 1:
    0.3899

Sub-matrix 2:
    0.0492    0.3202    0.4881
    0.3074    0.4613    0.7067

Sub-matrix 3:
    0.3673
    0.9414

Sub-matrix 4:
    0.2682

[NeGM]

Oleg,

Thank you so much this is great!