Matlab : 256 binary matrices to one 256 levels grayscale image - matlab

Question

a process of mine produces 256 binary (logical) matrices, one for each level of a grayscale source image.
Here is the code :
so = imread('bio_sd.bmp');
co = rgb2gray(so);
for l = 1:256
bw = (co == l); % Binary image from level l of original image
be = ordfilt2(bw, 1, ones(3, 3)); % Convolution filter
bl(int16(l)) = {bwlabel(be, 8)}; % Component labelling
end
I obtain a cell array of 256 binary images. Such a binary image contains 1s if the source-image pixel at that location has the same level as the index of the binary image.
ie. the binary image bl{12} contains 1s where the source image has pixels with the level 12.
I'd like to create new image by combining the 256 binary matrices back to a grayscale image.
But i'm very new to Matlab and i wonder if someone can help me to code it :)
ps : i'm using matlab R2010a student edition.

Answer 1

this whole answer only applies to the original form of the question.
Lets assume you can get all your binary matrices together into a big n-by-m-by-256 matrix binaryimage(x,y,greyvalue). Then you can calculate your final image as
newimage=sum(bsxfun(#times,binaryimage,reshape(0:255,1,1,[])),3)
The magic here is done by bsxfun, which multiplies the 3D (n x m x 256) binaryimage with the 1 x 1 x 256 vector containing the grey values 0...255. This produces a 3D image where for fixed x and y, the vector (y,x,:) contains many zeros and (for the one grey value G where the binary image contained a 1) it contains the value G. So now you only need to sum over this third dimension to get a n x m image.
Update
To test that this works correctly, lets go the other way first:
fullimage=floor(rand(100,200)*256);
figure;imshow(fullimage,[0 255]);
is a random greyscale image. You can calculate the 256 binary matrices like this:
binaryimage=false([size(fullimage) 256]);
for i=1:size(fullimage,1)
for j=1:size(fullimage,2)
binaryimage(i,j,fullimage(i,j)+1)=true;
end
end
We can now apply the solution I gave above
newimage=sum(bsxfun(#times,binaryimage,reshape(0:255,1,1,[])),3);
and verify that I returns the original image:
all(newimage(:)==fullimage(:))
which gives 1 (true) :-).
Update 2
You now mention that your binary images are in a cell array, I assume binimg{1:256}, with each cell containing an n x m binary array. If you can it probably makes sense to change the code that produces this data to create the 3D binary array I use above - cells are mostly usefull if different cells contain data of different types, shapes or sizes.
If there are good reasons to stick with a cell array, you can convert it to a 3D array using
binaryimage = reshape(cell2mat(reshape(binimg,1,256)),n,m,256);
with n and m as used above. The inner reshape is not necessary if you already have size(binimg)==[1 256]. So to sum it up, you need to use your cell array binimg to calculate the 3D matrix binaryimage, which you can then use to calculate the newimage that you are interested in using the code at the very beginning of my answer.
Hope this helps...

Answer 2

What your code does...
I thought it may be best to first go through what the code you posted is actually doing, since there are a couple of inconsistencies. I'll go through each line in your loop:
bw = (co == l);
This simply creates a binary matrix bw with ones where your grayscale image co has a pixel intensity equal to the loop value l. I notice that you loop from 1 to 256, and this strikes me as odd. Typically, images loaded into MATLAB will be an unsigned 8-bit integer type, meaning that the grayscale values will span the range 0 to 255. In such a case, the last binary matrix bw that you compute when l = 256 will always contain all zeroes. Also, you don't do any processing for pixels with a grayscale level of 0. From your subsequent processing, I'm guessing you purposefully want to ignore grayscale values of 0, in which case you probably only need to loop from 1 to 255.
be = ordfilt2(bw, 1, ones(3, 3));
What you are essentially doing here with ORDFILT2 is performing a binary erosion operation. Any values of 1 in bw that have a 0 as one of their 8 neighbors will be set to 0, causing islands of ones to erode (i.e. shrink in size). Small islands of ones will disappear, leaving only the larger clusters of contiguous pixels with the same grayscale level.
bl(int16(l)) = {bwlabel(be, 8)};
Here's where you may be having some misunderstandings. Firstly, the matrices in bl are not logical matrices. In your example, the function BWLABEL will find clusters of 8-connected ones. The first cluster found will have its elements labeled as 1 in the output image, the second cluster found will have its elements labeled as 2, etc. The matrices will therefore contain positive integer values, with 0 representing the background.
Secondly, are you going to use these labeled clusters for anything? There may be further processing you do for which you need to identify separate clusters at a given grayscale intensity level, but with regard to creating a grayscale image from the elements in bl, the specific label value is unnecessary. You only need to identify zero versus non-zero values, so if you aren't using bl for anything else I would suggest that you just save the individual values of be in a cell array and use them to recreate a grayscale image.
Now, onto the answer...
A very simple solution is to concatenate your cell array of images into a 3-D matrix using the function CAT, then use the function MAX to find the indices where the non-zero values occur along the third dimension (which corresponds to the grayscale value from the original image). For a given pixel, if there is no non-zero value found along the third dimension (i.e. it is all zeroes) then we can assume the pixel value should be 0. However, the index for that pixel returned by MAX will default to 1, so you have to use the maximum value as a logical index to set the pixel to 0:
[maxValue,grayImage] = max(cat(3,bl{:}),[],3);
grayImage(~maxValue) = 0;
Note that for the purposes of displaying or saving the image you may want to change the type of the resulting image grayImage to an unsigned 8-bit integer type, like so:
grayImage = uint8(grayImage);

Answer 3

The simplest solution would be to iterate through each of your logical matrices in turn, multiply it by its corresponding weight, and accumulate into an output matrix which will represent your final image.