What is differences between structured image and textured image
Imho there is no "mathematical" description of either terms. 

Both (texture and stucture) can be viewed as a repeating pattern. In the case of texture, the pattern might get a more random perturbation (think at an image of sand or grass).



In the case of a structured image you might get less random and more systematical perturbation (Think of a roof picture with tiles) Sometimes more info can be extracted from structured images. Imagine that you can actually get some 3D info by examining the way the pattern varies along one direction or another.



Of course I could be completely wrong and the "structure image" has a concrete definition for the author that you quote. 

Edit:

I found two examples where 3D info is extracted from textural information. Chapter 9.5 "Shape from Texture" from "Introductory Techniques for 3-D Computer Vision" by Emanuele Trucco, Alessandro Verri (1998 ed) and Chapter 12.4 3D Cues Available in 2D Images from "Computer Vision" by L. Shapiro and G. Stockman (2000 ed)

There, you have the idea of deterministic texture vs stochastic texture. Also read Jedi Commymullah answer for some other insights.

Images are free:

http://pixabay.com/en/roof-roofing-house-roof-186391/
http://pixabay.com/en/grass-grassy-stalks-green-275986/