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