Properties of $BV-G$ Structures $+$ Textures Decomposition Models. Application to Road Detection in Satellite Images

In this paper we present some theoretical results about a structures-textures image decomposition model which was proposed by the second author. We prove a theorem which gives the behavior of this model in different cases. Finally, as a consequence of the theorem we derive an algorithm for the detection of long and thin objects applied to a road networks detection application in aerial or satellite images.