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Context. Polarized dust emission can be used as a probe for magnetic fieldsat different scales. In particular, the analysis of the relative orientationbetween the density structures and the magnetic field projected on the plane ofthe sky can provide information on the role of magnetic fields in shaping thestructure of molecular clouds. Aims. The relative orientation has beeninvestigated using different methods. Our goal is to explicitly compare two ofthem: the Rolling Hough Transform (RHT) and the gradient technique. Methods. Wehave applied the RHT method and the gradient technique to two regions,identified in surface brightness maps at 353 GHz generated via MHD simulationspost-processed using radiative transfer modelling. For both methods we havederived the relative orientation between the magnetic field and the densitystructures, to which we have applied two different statistics, the histogram ofrelative orientation (HRO) statistic and the projected Rayleigh statistic(PRS). Results. The samples of pixels selected by each method are substantiallydifferent. When the methods are applied to the same pixel selection, theresults in terms of relative orientation as a function of column density areconsistent between each other. When each method is applied to its own pixelselection, the differences are apparent. In Region 1, the RHT method roughlyreproduces the observed trend of the relative orientation becoming moreperpendicular for increasing column density, while the gradient method, appliedat the same resolution as RHT, gives the opposite trend, with the relativeorientation moving towards a more parallel alignment. In Region 2, thesituation is reversed. The inconsistent results, which are due to the differentpixel selections operated by the methods and to the intrinsic differencesbetween them, provide complementary valuable information. Abridged.

Dust polarisation studies on MHD simulations of molecular clouds: methods comparison for the relative orientations analysis