Nonlinear Coupled Diffusion

This package implements isotropic nonlinear scalar valued/ coupled vector/matrix valued diffusion.

The code supports homogeneous and linear and nonlinear (Total Variation and Edge Enhancing flow) isotropic diffusion of arbitrary dimensioned fields(scalar~grayscale image, vector ~ color image and matrix~structure tensor). Additive Operator Splitting(AOS) as well as Gaussian regularization are implemented to speedup the computations.
Two point 1 sided differences is implemented for spatial discretization which is more accurate than the central differences. A semi implicit time discretization as well as epsilon regularization is utilized to make the diffusion process stable for arbitrary time-step sizes. The code is commented, the definition and dimensions of the input/output variables can be found in the header of the nonlinear_diffusion.m. A sample script is provided to visualize the diffusion process of two sample images.
The AOS implementation uses the Thomas algorithm implemented in mex to achieve the fastest speed.