Another comparison

Both images show non-thresholded pixels in white. The rest pixels are shown as the original image. 

(a) < T

(b) >T

Two images to separate the part above T and the part below T

It is using adaptive threshold and dilates the sign-flipped error. Error is - I_cur  when it is above T; otherwise, error is 255-I_cur. It did not use the CAH order and without ETF promotion. 

(1) It shows white when  I_cur  is above T and the rest shows as (255-I, 255-I,0).

(2) It shows black when I is below T and the rest shows as (255-I, 255-I,0).

Raster image for low black

black control

Low black with promoting ETF priorities

High black without promoting ETF priorities

Some small modifications

It is not using CAH order and the error is still using the older CAH values. The thing changed here is the weights. It is good for structure. Still I did not get the large black areas.

Results from adaptive threshold

BW using Adaptive threshold with the CAH order

Without error diffusion

Without error diffusion

If without error diffusion, it is a thresholding method. The new modification is very close to this quality, but clustering pixels better. It means the error diffusion works but it is not the major factor to the structure quality now.