Try this:
% Compute mean in 4-by-4 blocks
% kernel = ones(4);
meanImage = conv2(double(grayImage), kernel, 'same') / numel(kernel);
% Compare actual image to mean image.
binaryImage = grayImage >= meanImage;
There will be some errors at the edge of the image where the window does not fit onto the image, like it's only 4 by 3 or whatever. If this is important, then you can use conv2 twice, once to sum the image and once to count the pixels, then divide the gray level sum image from the pixel count image. But usually edge effects are not worth worrying about because they get removed later in the process naturally.
