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

Using the same order in the whole previous algorithm

Finally the tone is matched after dealing with the first pixel

The spiral masks are used.

Better for tone change but artefacts are too clear.

Algorithms:

1. Sort each pixels based on the brightness into a heap.

2. For each pixel grows the spiral

%% accum is the accumulation; target is the goal; counter is

%%for a long spiral over the limit

(1): initial states: accum = 0; target = 255; counter = 0;

(2): grow the spiral( for each step the real codes as follows)

%% full; stop

if(accum >= target) break;

Ii = ppTemp[v.y][v.x].GetGreyscaleValue ();

%% return the increase based on the accumulation function

out = accumulate(I0,Ii, m_ppDoneMap[v.y][v.x]);

accum = accum + out;%% accumulation

%% update the original image and the done map

in = min(255,Ii + out);

ppTemp[v.y][v.x] = COLOR(in, in, in);

m_ppDoneMap[v.y][v.x] =0;// flag for used pixels

%% the error at the last pixel

if (accum > target)

{

in = Ii-(accum-out-target);%% too much

ppTemp[v.y][v.x] = COLOR(in,in, in);

}

%% counter for the length of the spiral

counter++;

%% too long and cut it out; might have a problem

if(counter>spiralmask.size ()) break;

---------------------------------------------

%% the accumulation function

int accumulation(...)

{

Ti = 80;

if(255-Ii less than Ti)

in = 255 - Ii;

else

in = Ti;

return in;

}

---------------------------

Intensity response diagram based on the ramp image
Some results

Still no luck

intensity = 200intensity = 50

I guess this is the effect we want, but still has issues.

It seems the method catches the constrast or maybe we can say it obeys the edges. But it does not follow the tone correctly.

It seems the artefacts are from the function I chosen. But right now I do not know how to avoid them.

Strange effects

Effect 1

Effect 2

The threshold is based on the accumulation and the discontinuous increase for the chosen function.

Still not good

The traditional error diffusion algorithm

Much better than our results! More smoother!! Also smoother than the results from "structure-aware halftoning" paper. But the results from the paper is clearer to show the edges.

the Floyd-Steinberg algorithm

Several questions about halftoning

1. What kind of effects for haltoning is perfect(or for printing)?--blue-noise property? What's an interesting halftoning?

2. Density means? Density and harmonity?

3. The constrast for halftoning?

4. Maintain the original structure

5. The pattern creation(means new pattern): how to deal with the original structure or pattern?

6. What do you think about the above image?

Another more related paper: digital halftoning with space filling curves by Velho and Gomes; and some halftoning by fractal path