creating a quad mesh for an image

Hello,

I am currently implementing this paper "Patch based image warping for content aware retargeting", and is attached along with this question. My basic question is, how to represent an image as a mesh? with vertices, edges and quad faces?

I am half way through the implementation, when I come across this, as mentioned in the paper

The referenced paper mentions the same. Basically, the question is how to represent an image as a mesh? with vertices, edges and quad faces in matlab?