Image stylization using anisotropic reaction diffusion

2015 ◽  
Vol 32 (12) ◽  
pp. 1549-1561 ◽  
Author(s):  
Ming-Te Chi ◽  
Wei-Ching Liu ◽  
Shu-Hsuan Hsu
Keyword(s):  
Reaction Diffusion ◽  
Image Stylization ◽  
Anisotropic Reaction Diffusion

scholarly journals Stereo Algorithm with Anisotropic Reaction-Diffusion Systems

10.5772/46025 ◽  
2012 ◽  
Author(s):  
Atsushi Nomura ◽  
Koichi Okada ◽  
Hidetoshi Miike ◽  
Yoshiki Mizukami ◽  
Makoto Ichikawa ◽  
...  
Keyword(s):  
Reaction Diffusion ◽  
Reaction Diffusion Systems ◽  
Diffusion Systems ◽  
Anisotropic Reaction Diffusion ◽  
Stereo Algorithm

scholarly journals Motion by anisotropic mean curvature as sharp interface limit of an inhomogeneous and anisotropic Allen–Cahn equation

2010 ◽  
Vol 140 (4) ◽  
pp. 673-706 ◽  
Author(s):  
Matthieu Alfaro ◽  
Harald Garcke ◽  
Danielle Hilhorst ◽  
Hiroshi Matano ◽  
Reiner Schätzle
Keyword(s):  
Transition Layer ◽  
Time Scale ◽  
Mean Curvature ◽  
Reaction Diffusion ◽  
Reaction Diffusion Equation ◽  
Finsler Metric ◽  
Diffusion Term ◽  
Almost Everywhere ◽  
Anisotropic Reaction Diffusion ◽  
Anisotropic Mean Curvature

We consider the spatially inhomogeneous and anisotropic reaction–diffusion equation ut = m(x)−1 div[m(x)ap(x,∇u)] + ε−2f(u), involving a small parameter ε > 0 and a bistable nonlinear term whose stable equilibria are 0 and 1. We use a Finsler metric related to the anisotropic diffusion term and work in relative geometry. We prove a weak comparison principle and perform an analysis of both the generation and the motion of interfaces. More precisely, we show that, within the time-scale of order ε2|ln ε|, the unique weak solution uε develops a steep transition layer that separates the regions {uε ≈ 0} and {uε | 1}. Then, on a much slower time-scale, the layer starts to propagate. Consequently, as ε → 0, the solution uε converges almost everywhere (a.e.) to 0 in Ω−t and 1 in Ω+t , where Ω−t and Ω+t are sub-domains of Ω separated by an interface Гt, whose motion is driven by its anisotropic mean curvature. We also prove that the thickness of the transition layer is of order ε.

Anisotropic reaction-diffusion stereo algorithm

2011 ◽  
Author(s):  
Atsushi Nomura ◽  
Makoto Ichikawa ◽  
Koichi Okada ◽  
Hidetoshi Miike ◽  
Tatsunari Sakurai ◽  
...  
Keyword(s):  
Reaction Diffusion ◽  
Anisotropic Reaction Diffusion ◽  
Stereo Algorithm

Directionality of Stripes Formed by Anisotropic Reaction–Diffusion Models

2002 ◽  
Vol 214 (4) ◽  
pp. 549-561 ◽  
Author(s):  
HIROTO SHOJI ◽  
YOH IWASA ◽  
ATUSHI MOCHIZUKI ◽  
SHIGERU KONDO
Keyword(s):  
Reaction Diffusion ◽  
Diffusion Models ◽  
Anisotropic Reaction Diffusion
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