Use the fixed length(20) to test all of images

It did a very good job for textures.

Set up a maximum cutout for each pixel based on the minimum length of the spiral

The minimum length is changable based on the center intensity.

The fixed length(10) is used always.
The fixed length(20) is used always.
The fixed length(25) is used always.
The fixed length(60) is used always.

Artefacts from the uniform region

the intensity value is 250.

Another thought

Arbitrarily to reduce the influence around the chosen spiral based on the distance and reordering is based on the distance and the intensity.

(5) Similar to (4) but with partial reordering

Do reordering when the intensity greater than 200; otherwise, no reordering.

All of four modifications have some change for the visual effect.

But the change is not very clear.

(1)Non-linearly reduce the influence based on the length of the sprial

Always reordering

length is the length of the spiral.

if(Ii>Tii)

in = 255-Ii;

else

{

in = 255 - Ii;

in = in * pow((double)(length+1),-0.2);// influence slow down based on the length

}

(2)Non-linearly reduce the influence based on the radius

Always reordering

r is the distance between the pixel and the center of the mask

if(Ii>Tii)

in = 255-Ii;

else

{

in = 255 - Ii;

in = in * pow((double)(r+1),-0.2);// (-0.5,-0.2,-0.01)non-linear;//influence slow down }

(3)Linearly reduce the influence based on the radius

Alway reordering

r is the distance between the pixel and the center of the spiral mask.

if(Ii>Tii)

in = 255-Ii;

else

{

in = 255 - Ii;

in = in * (1 - 0.03 * r);// linear

}

(4)LAHE always with reordering

http://en.wikipedia.org/wiki/Histogram_equalization

Their results(strucutre-aware halftoning) for comparison

Better results by compromise

By compromise, we can choose some pixels to do the reordering when the intensity reduced and others will not change the order during the whole process. It means we try to avoid the clumping where there is a brighter area since we think the clumping at the edges (assumed there are darkness) won't have much artefacts.

reordering when the original intensity greater than 150reordering when the original intensity greater than 100
reordering when the reduced intensity greater than 150
reordering when the reduced intensity greater than 200