What does Smoothness Prior mean in the context of image processing? I can quote from an article:


  "The first category of methods, known as diffusion-based inpainting,
  introduces smoothness priors via parametric models or partial
  differential equations (PDE) to propagate or diffuse local structures
  from the exterior to the interior of the hole."


What is Smoothness Prior?

What does this definition mean?
A prior is something that you know a priori (beforehand) about how the system you're looking at works.

A smoothness prior means that you know that the image you're looking at will be smooth in a particular way.

That paper goes on to say:


  The term diffusion comes from the idea of propagating local information with smoothness constraints, by analogy with physical phenomena like heat propagation in physical structures. These phenomena can be formalized with PDEs, and diffusion is therefore performed using PDE-based regularization.


So in this case the smoothness that you know about beforehand is enforced using a partial differential equation.