MATLAB: Find ones blocks in upper triangular matrix

find ones blocks in upper triangular matrix

I have A

A=[0 0 0 0 0 0 0 0 0 0 0 0 0;
   0 0 0 0 1 0 1 0 0 0 0 0 0;
   0 0 0 0 0 1 0 0 0 0 0 0 0;
   0 0 0 0 1 0 1 0 0 0 0 0 0;
   0 0 0 0 0 0 0 0 0 0 0 0 0;
   0 0 0 0 0 0 0 1 1 1 0 0 0;
   0 0 0 0 0 0 0 0 1 1 0 0 0;
   0 0 0 0 0 0 0 0 0 0 0 0 0;
   0 0 0 0 0 0 0 0 0 0 0 1 0;
   0 0 0 0 0 0 0 0 0 0 1 1 0;
   0 0 0 0 0 0 0 0 0 0 0 1 0;
   0 0 0 0 0 0 0 0 0 0 0 0 0;
   0 0 0 0 0 0 0 0 0 0 0 0 0];

I want to find blocks of one in this matrix according to

blocks={[2,3,4,5,6,7],[6,7,8,9,10],[9,10,11,11,12]}

Best Answer

Let me plead for you to change how you are doing things. What you are asking to do is perhaps the most silly form of information storage I have seen in a while. To understand what I mean by that, what block is decribed by the set:

[7 8 9 10 11]

That is, does this describe a 1x4 rectangle, thus with 1 row (row 7) and 4 columns (8:11)? Or perhaps a 2x3 rectangle? Or perhaps a 3x2 rectangle? Or perhaps a 4x1 rectangle?

Do you recognize this is just an information storage idea that is just begging for a future head pounding bug, where you then need to disambiguate which of those many possible boxes was intended?

A far better solution is to just indicate the box by 4 numbers, ALWAYS, thus the first and last row and the first and last column in said box.

As far as how to find those bounding boxes, this should not be that difficult. For any 1 in the array, if another element is within 1 pixel, you would necessarily merge the two corresponding boxes, though I'm not sure what rules you may have for those mergers, so I must stop here for the moment. In fact, I am pretty confidant that if Image Analyst views this question, his response will be a simple, direct solution based on the IPT. If he does, then use it! :)

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MATLAB: Delete rows and columns with zeros in a multi level cell array matrix.

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MATLAB: Summation of image exceeds matrix dimention

You have two errors in your code. These errors are easy to make because, in my opinion, a) the documentation of regionprops does a poor job of explaining the coordinate system it uses and b) matlab coordinate system is not consistent.

Your first error is that you assume that regionprops return integer coordinates for the upper left point of the bounding box. It does not. It's all explained under <https://www.mathworks.com/help/images/image-coordinate-systems.html#brcu_cr Image Coordinates System - Spatial Coordinates). In short, the corder of pixel centered at (1,1) is (0.5,0.5). In my opinion, it's bonkers. I've complained to matlab about it. It's not going to change. So if you want to use the coordinates returned by regionprops as indices into your image you need to add 0.5 to them or round them up with ceil.

The second error you have made is that regionprops returns coordinates as (x, y) pairs but indexing in matlab uses (row, column) where row <==> y and column <==> x, so you need to swap the pair elements.

Also note, that your first g loop is not needed.

In short, to solve:

props = regionprops(image, 'BoundingBox');
boundingboxes = vertcat(props.BoundingBox);  %concatenate all the bounding boxes into Nx4 matrix
%1st column of boundingboxes is the x coordinate == columns, it is a fractional value
%2nd column of boundingboxes is the y coordinate == rows, it is a fractional value
%3rd column is the width 
%4th column is the height
%to change to 1st and 2nd to image indices and 3rd and 4th to index of bottom right corner:
boundingboxes(:, [1 2]) = ceil(boundingboxes(:, [1 2]);
boundingboxes(:, [3 4]) = boundingboxes(:, [3 4]) + boundingboxes(:, [1 2]);
%to calculate the sum:
sumnn = zeros(size(boundingbox, 1), 1);
for g = 1:size(boundingbox, 1)
  sumnn(g) = sum(sum(image(boundingboxes(g, 2):boundingboxes(g, 4), boundingboxes(g, 1):boundingboxes(g, 4))));
end

Or you can do it all in just two lines if you don't need all these intermediary variables:

props = regionprops(image, 'BoundingBox');
sumnn = arrayfun(@(p) sum(sum(image(floor(p.BoundingBox(2))+(1:p.BoundingBox(4)), floor(p.BoundingBox(1))+(1:p.BoundingBox(3))))), props);

Another option is to request SubarrayIdx rather than BoundingBox since SubarrayIdx is the list of all pixels in the bounding box. This leads to much simpler code:

 props = regionprops(image, 'SubarrayIdx');
 sumnn = arrayfun(@(p) sum(sum(image(p.SubarrayIdx{:}))), props);

Best Answer

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