Growing curves from a distribution

This should be very close to the example image after assigning region colors to the image. 

Left: stipples: The maximum cost is 2500 and the curve is created using random strategy.

Right: stipples: The maximum cost is 1000 and the curve is created using random strategy.

Next steps:

1. experiment different curves.

2. find a good color scheme.

3. wisely choose a better curve type for each stipple.

4. find a way to resolve the issue in weak magnitude of the vector field since those areas with weak direction could create annoying patterns.

5. increase the quality of a small number of curves.
6. assign stroke textures.
7. evaluate the quality in terms of structural preservation, tone matching, or aesthetic appearance.
8. avoid isolated curves.
9. add a variety of curve types.
10. different from the old AT paper, it seems that the similar curves should be avoided in this application.

Abstraction using curves

Ideas:
1. The old papers about image abstraction emphasizes edges and merges similar colors in order to represent tone and structure of the image content. Our idea is to placing interesting curves to abstract an image.  The novelty comes from the introduction of new primitive in image abstraction.
Some publications:
(1) Image and Video Abstraction using Cumulative Range Geodesic Filtering, David Mould, Comput. Graph., 2013
(2) Image Abstraction by Structure Adaptive Filtering, Jan Eric Kyprianidis and Jürgen Döllner, In: Proc. EG UK Theory and Practice of Computer Graphics, 2008
(3) Structure-preserving manipulation of photographs, Alexandrina Orzan, Adrien Bousseau, Pascal Barla, Joëlle Thollot, International Symposium on Non-Photorealistic Animation and Rendering (NPAR) - aug 2007

2. The proposed algorithms:
(1) draw curves along edge directions. Curves properties include length, the error to the directional filed, color, thickness, and the depth.
(2) determine the quality and the number of curves used
(3) Test different depth of each curve

Goal: The final placement should represent the image content in some way. Aesthetics may be more important than structural preservation.

Issues:
(1) curve generations: a curve could grow along a field.
a. the old particle system for the artistic tessellation paper; or b. the spiral curve
(2) the objective of the quality
This is hard. This matters when to stop the process.

Examples:
http://www.budanart.com/products