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

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.

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

A related paper about halftoning

I am not sure if you have read this paper "POLYOMINO BASED DIGITAL HALFTONING" by VANDERHAEGHE and OSTROMOUKHOV. Similar to our term the structure of masks, they use the term the threshold structure, but based on so-called polyomino. The reason for mentioning this is that we might want to give a theory-tied scheme like this paper.

For comparison, here is the Lena's halftoning effect from current results as follows.

The placement order based on gradients

The burrness is because the edges are not a single line. They have some thickness based on gradients.

Test the Lena, ramp and checkboard images for stippling

Another thought: The method I am using can be treated as a kind of randomized method without relaxation. But the use of the spiral mask may be treated as a new thing.

It seems the current process cannot do better work than Secord's work. Your paper" stipple placement using distances in a weighted graph" shows a stippling effect for the ramp. But I guess the ramp image is not from black to white, right? Both masks has some artefacts when the area has dense stipples.

eight directions for random choices

two directions for random choices

Based on the spiral mask

Based on regular mask

Stippling styles for popuped models

Experiences: It seems the spiral mask can do more precise control over the density in the space, but slower. The direction of the spiral mask has not much influence on the effects.
Randomly control the direction of the spiral mask.

Clockwise direction

Anti-clockwise direction

The rendered popuped model is merged from the original image and the lighted model by multiplication.

The popuped model after smoothing and doing process to the hair

(a)

(b)
The order of placement is based on the intensity of the rendered popuped model. The space of each stipple is based on the intensity.(a) and (b) have different lighting conditions.

Some intermediate results

Original

Lighted results(2000 iterations)

Connected skeletons