I gave this a shot. The article makes sense. However the implementation is pretty challenging.

Don't know how they manage to get such quasi-perfect outlines. My polygons only kinda adapt to the shape...

Nice!

And it's mainly about the quasi-perfect outlines but atleast it's a start :)

I hadn't the time to read the article yet, I was hoping they talked about this problem...
I suppose then we need to use an edge detection algorithm.

Some time ago i readed it and as mentioned i had problems understanding.
It can be done with edge detection i suppose, another way could be making changes to the dark line in position and see if that leads to be more/less the original image. If it's less reject the change, is it better keep it.

Well, they do describe their method. And after looking at the article again I noticed I only did the global features (section 4.2) but the second half of their method is the individual local adjustment (section 4.3). So I guess that also has some impact and I may try to include something like that as well. With just the global features using the error method based on site colors (as described in the article) I got the image posted earlier. When I use average colors per polygon and do about 40 runs, I get the image below. In both cases you could say pass for global features, but not yet for smoothness as in their image.



At second glance I did notice some other interesting remarks in the article.

In paragraph 4.1.

Moreover, the user can interactively specify regions and partially change the densities of the sites in those regions. As a result, the details of the reference image can be expressed easily.

In paragraph 4.4.

If the Voronoi sites are moved only through the automatic movement process described previously, it is sometimes difficult to express the features in the reference image where the Voronoi sites have not been located when initializing the Voronoi image (Section 4.1). Additionally, the user might want to edit the arrangement of the sites. Therefore the system enables the user to move, add or delete the Voronoi sites interactively. To be specific, the user can do the Voronoi site operations mentioned above through mouse operations, and then the system again optimizes the arrangement of the Voronoi sites automatically by the local adjustments explained in Section 4.3.

As stated in the other voronoi thread many programs leave all details to users or allow interactivity. Of course user interaction can hugely improve the quality of the image (which is not a bad thing at all, it's just not fully-automated then). From the description in the article it is not clear how much user interaction has been done to end up at their 'end result', but the description suggests there may have been at least some interaction to get such smooth results.

Some other thoughts:

• Indeed edge detection is something I thought about as well. Apart from user interaction, it seems a good way to find/trace important contours in the image.
• My mess of an unoptimized code has gotten so slow that I really wanted to find some relevant GLSL shaders to speed things up. Starting of course with a general Voronoi shader. But so far I did not find one that was compact and suitable as a starting point.
  

Hi, nice work.

  Sad it's to slow for processing, the shader thing didn't work out? 

1. It is considered an implementation detail may break other Processing code.
2. It completely throws out simplicity of Processing. More than that, with .NET and OpenTK we have at least some typing and can work with buffers as multidimensional arrays of structs (e.g. Color4[,]), while in Java you only have byte buffers.

how fast is it now? 

• for capturing global features (actually attributes most to the result): about 1 sec.
• for local adjustment (some final fine-tuning): about 10-40 sec. (depends on threshold value)

excuse me, i just saw you continued with it instead of amnon.owed.

Yup, put this one on hold while doing other things.

Good to see you got some good results webwarrior.ws.

Maybe I will investigate the GLSL route at some point, but don't know when...