Image processing and sub-array summation

I have a problem that seems fairly straight forward but I am having trouble pulling it off in an efficient (no for loops) manner. For a bit of background, I am processing an image of an array of similar objects and want to flag locations where an object is missing. I can assume that the pitch in x and y is the same and that each object (if present) generates roughly the same intensity in my image. The image will consist of around 10k objects and perhaps 100's of thousands of objects in the future, hence the need for efficiency.

The algorithm I had in mind would work something like this...

1) Partition image array into "sub-arrays" using the indicies of two vectors which are defined by the pitch of the object array on the image plane.

2) Compare "sub-array" sums to a given threshold

3) Generate array of 1's and 0's corresponding to precense or lack of object.

For example, assuming my pitch in x and y is 2,

Raw Data:

[ 1 1 2 1 1 1 2 2;

1 0 1 1 2 1 2 1;

0 0 1 2 2 1 0 0;

0 1 1 0 2 1 0 0;

2 1 2 2 2 1 1 1;

1 0 1 2 2 1 1 1]

Summation of Sub-arrays:

[ 3 5 5 7;

1 4 6 0;

4 7 6 4]

Threshold = 2

Output:

[1 1 1 1;

0 1 1 0;

1 1 1 1]

Anyway, I'm stuck at step one and was hoping someone might point me in the right direction.

Thanks in advance,

Julius

[KALYAN ACHARJYA]

Partition image array into "sub-arrays" using the indicies of two vectors

How, Can you show us one example?

Answer 1

[Image Analyst]

Try conv2():

bigMatrix = [ 1   1   2   1   1   1   2   2;
	1   0   1   1   2   1   2   1;
	0   0   1   2   2   1   0   0;
	0   1   1   0   2   1   0   0;
	2   1   2   2   2   1   1   1;
	1   0   1   2   2   1   1   1]
% Compute moving sums by using highly optimized conv2() function.
p = 2; % "Pitch"
kernel = ones(p);
out = conv2(bigMatrix, kernel, 'same')
% Sub sample to get just the elments we want.
out = out(1 : p : end, 1 : p : end)
% Now do the thresholding.
threshold = 2;
out = out > threshold

You'll see in the command window the different output from each step:

out =

3 4 5 5 5 6 7 3

1 2 5 7 6 4 3 1

1 3 4 6 6 2 0 0

4 5 5 6 6 3 2 1

4 4 7 8 6 4 4 2

1 1 3 4 3 2 2 1

out =

3 5 5 7

1 4 6 0

4 7 6 4

out =

3×4 logical array

1 1 1 1

0 1 1 0

1 1 1 1

Answer 2

[Matt J]

You can use sepblockfun from the File Exchange

https://www.mathworks.com/matlabcentral/fileexchange/48089-separable-block-wise-operations

Output = sepblockfun(RawData,[2,2],'sum')>threshold

Answer 3

[Julius]

Brilliant, this is exactly what I needed. Thank you Matt and "Image Analyst" for the suggestions!

Cheers,

Julius