Error diffusion with orders based on intensities

From the traditional methodFrom the modified method

It is almost the same method as the error diffusion method but based on the orders to do the error diffusion.

Larger radius

More clumping

Here are results based on the fixed circle mask and normalization

Problems:

1. Still clear patterns

2. The dark areas are too light and the white areas have too many pixels chosen.

3. Clumping

The radius of the mask is 3.

Ci is the contrast.

The chosen function is as follows.

maxin = max(0.5,((1-Ci)*I0 * (pow(Ii,0.4f)/(pow(255,0.4f))))/(3*r));

detI = min(maxin, 255-Ii);

MSSIM testing

MSSIM(A,OUR) = 0.1700

PSNR(A,OUR) = 13.2743
MSSIM(A,C)=0.3243

PSNR(A,C)=10.4887
MSSIM(A,255-A) = -0.1978

PSNR(A,255-A) = 6.8434
MSSIM(A,A) = 1

Error diffusion

Some patterns can be created.

These patterns are created by partially choosing some pixels around the center not to be updated by the function. But the tone matching is still not good.

Kind of smudging effects

I am not sure if this is what are called smearing effects. But for me, it smudges the images. It did not do a good job for images with textures.

About clumping

When two spirals are mixed together, this situation will raise the inbetween pixel vlaues. When we allow the spirals to have large size, actually the inbetween areas will be hit a lot of times, not few times as I guessed. In my testing, the hitting usually reaches around 20 times. The highest hitting times once was 37 times in my testing. Thus, to make sure the inbetween pixels will be our next choice. The accumulation function has to be tricky. It has to drop very quickly from the center to the boundary to make sure the inbetween pixels are only raised a little values. It kind of avoids some clumpings. It turns out our guess is correct. The clumping ruins the tone matching. Right now I got very good tone matching based on PSNR measurement, better than the error diffusion method. But the structure similarity is not matched well and the visual effects are not very good either. Now I am adjustting the settings to want to get higher vlaues in both PSNR and MSSIM measurements. But right now I did not get that yet.

Another thing about clumping, after checking the results from the error diffusion, they have clumping too. But their clumping happens in vertical or diagonal direction. It seems in visualization the eyes can identify more quickly when two pixels are sticked together in a horizonal direction than the vertical ways. But right now I cannot avoid the horizonal situations.

the ramp image

MSSIMPSNR

Some experiences

I tried the regular mask by using the same process. It turns out the regular mask will bring more artefacts than the spiral mask. In visualization, the same function will have similar effects. The differences are in different patterns introduced by different masks.

I also tried the floating points to store the values. Right now it gives more control for each step, but I cannot say what the other advantages are.

Right now it seems the limit of the size of the mask has a great effect on ruining tone.

The size of the mask has some influence in visual effects.

Performance: 512 by 512 takes 113 seconds.

I am going to put the tone down and try to find some interesting patterns from our method. Right now how to control patterns seems a mystry.

A few steps for running

The left side has 100 value in intensity and the right side has 200 value.

2000 stipples
3000 stipples
5000 stipples10000stipples
final

Strange effects

using the regular mask

using the spiral mask