Test images from "Structure-Aware Halftoning" by Pang et. al

Compared with those results in the paper, even there are not much percentage pixels used in our tree result, it looks not worse than their result. (After scaling it and looking at it again, I have to say it is worse than their result.) Our result for the cat example looks worse than their result. But the good thing is that at least our method did not destroy the structure for the cat a lot. Size(440 by 373)

Size(660 by 560)

59783(36.42%) pixels are used.

216678 (58.625% )pixels are used

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

Hatching styles for popuped models

Randomly directions

The hatching direction is based on the ETF and the density is based on the shaded image.

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.

NPR effects for popuped models

Heightening(line style)