# Anisotropic Diffusion Filter - Intuition Behind Parameters

I need to know what is iteration and divergence in anisotropic diffusion filter technique.

• Isotropic diffusion $$\frac{\partial I(x, y, z)}{\partial t}={\rm div}\left[c\cdot \nabla I\left(x, y, z\right)\right], \quad \text{where } c \text{ is the diffusion coefficient}$$

• Anisotropic diffusion $$\frac{\partial I(x, y, z)}{\partial t}={\rm div}\left[g\left(\left\| I\left(x, y, z\right)\right\|\right)\cdot \nabla I\left(x, y, z\right)\right], \quad \text{where } g \text{ is the anisotropic diffusion coefficient }\textbf{(Edge stopping function)}$$

• Here $t$ refers to iteration, what is this iteration ? How is it related to filtering ? I know that iteration refers to number of rounds but how it is related with filtering ?
• Also explain to me why we use divergence in these equation what is the purpose of divergence.
• You have to look for discretised versions of these equations. See the original paper of Perona and Malik on this. – Deniz Mar 27 '14 at 23:54
• One remark, though it is called "Anisotropic Diffusion", today this term is usually reserved to methods which changes the diffusion according to the Structure Tensor of the image. It is more appropriate to call this method Non Linear Diffusion. – Royi Oct 25 '14 at 17:44

The basic idea is to solve the heat equation where $$t$$ is the scale of the image, i.e. the amount of filtering to apply. For anisotropic diffusion the diffusion coefficient $$c$$ is replaced by $$g$$ which is dependent on the image gradient and therefore filters preferentially depending on the gradient.