Filter centroids to find only those of interest in binary image

I have defined the following centroids within a region of interest (blue rectangle) for my binary image. How can I remove or centroids within the red boxed region?

Answer 1

[Image Analyst]

If you know the rows and columns outlining your box you can erase the image inside that box before computing the centroids

mask(row1:row2, col1:col2) = false;
props = regionprops(mask, 'Centroid');

Or you can keep the mask as-is, and just remove the measurements from the output of regionprops():

xy = vertcat(props.Centroid);
xCentroids = xy(:, 1);
yCentroids = xy(:, 2);
badIndexes = xCentroids >= col1 & xCentroids <= col2 & yCentroids >= row1 & yCentroids <= row2;
% Delete the bad ones.
prop(badIndexes) = [];

[Lauren]

Thank you for the help! I was able to make a few changes to your code to fit my purposes. This is what I ended up using:

 xCentroids = CentroidsInsideROI(:, 1);
   yCentroids = CentroidsInsideROI(:, 2);
   badIndexes = yCentroids >= 300 & yCentroids <= 600 ;
   for c = 1:length(badIndexes)
       if badIndexes(c) == 0
           idx = c;
           Centroids = CentroidsInsideROI(idx,:);           
           plot(Centroids(:,1),Centroids(:,2),'m*')
       end
   end
   

and this was my final result!

[Image Analyst]

Instead of that for loop, you could have just inverted the badIndexes and used that as a logical index to the centroids to plot only those good locations:

xCentroids = CentroidsInsideROI(:, 1);
yCentroids = CentroidsInsideROI(:, 2);
badIndexes = yCentroids >= 300 & yCentroids <= 600 ;
plot(xCentroids(~badIndexes), yCentroids(~badIndexes), 'm*')

Answer 2

[Lauren]

I'm not sure the mask is working correctly. I used the following and it shows props as empty and mask as all zero values.

   mask(800:1145, 300:600) = false;
   props = regionprops(mask, 'Centroid');
   xy = vertcat(props.Centroid);
   xCentroids = xy(:, 1);
   yCentroids = xy(:, 2);
   badIndexes = xCentroids >= 300 & xCentroids <= 600 & yCentroids >= 800 & yCentroids <= 1145;
   % Delete the bad ones.
   prop(badIndexes) = [];    

I think overlaying the mask and deleting the bad indices is the way I would prefer to do it.