The filamentary, non-Gaussian patterns observed in the ISM result from the non-linear interplay between turbulence, gravity, and magnetic fields. Our understanding of ISM physics relies on heavy numerical simulations and their comparison to ever-improving observational results. This requires a quantitative way to compare observations and numerical simulations of the ISM, and therefore warrants an adequate statistical description of non-Gaussian structures.
The WST, RWST, and WPH are such a consistent and general ensemble of statistical descriptors able to characterize non-linear phenomena by encoding the couplings between oriented scales. I will present these tools and their applications to various types of fields, in particular numerical simulations of interstellar turbulence and observations of thermal dust continuum in total intensity and polarization.