  Hyperspectral image unmixing has proven to be a useful technique to interpret
hyperspectral data, and is a prolific research topic in the community. Most of
the approaches used to perform linear unmixing are based on convex geometry
concepts, because of the strong geometrical structure of the linear mixing
model. However, two main phenomena lead to question this model, namely
nonlinearities and the spectral variability of the materials. Many algorithms
based on convex geometry are still used when considering these two limitations
of the linear model. A natural question is to wonder to what extent these
concepts and tools (Intrinsic Dimensionality estimation, endmember extraction
algorithms, pixel purity) can be safely used in these different scenarios. In
this paper, we analyze them with a focus on endmember variability, assuming
that the linear model holds. In the light of this analysis, we propose an
integrated unmixing chain which tries to adress the shortcomings of the
classical tools used in the linear case, based on our previously proposed
extended linear mixing model. We show the interest of the proposed approach on
simulated and real datasets.
