Hyperspectral remote sensing plays an increasingly important role in many scientific domains and everyday life
problems. Indeed, this imaging concept ends up in applications as varied as catching tax-evaders red-handed by locating
new construction and building alterations, searching for aircraft and saving lives after fatal crashes, detecting oil spills for
marine life and environmental preservation, spying on enemies with reconnaissance satellites, watching algae grow as an
indicator of environmental health, forecasting weather to warn about natural disasters and much more. From an
instrumental point of view, we can say that the actual spectrometers have rather good characteristics, even if we can
always increase spatial resolution and spectral range. In order to extract ever more information from such experiments
and develop new applications, we must, therefore, propose multivariate data analysis tools able to capture the shape of
data sets and their specific features. Nevertheless, actual methods often impose a data model which implicitly defines the
geometry of the data set. The aim of the paper is thus to introduce the concept of topological data analysis in the
framework of remote sensing, making no assumptions about the global shape of the data set, but also allowing the capture
of its local features.