Rings are distinctive features of many disc galaxies and their location and properties are closely related to the disc dynamics . In particular , rings are often associated to stellar bars , but the details of this connection are far from clear . We have studied the frequency and dimensions of inner and outer rings in the local Universe as a function of disc parameters and the amplitude of non-axisymmetries . We used the 1320 not highly inclined disc galaxies ( i < 65 ^ { \circ } ) from the S ^ { 4 } G survey . The ring fraction increases with bar Fourier density amplitude : this can be interpreted as evidence for the role of bars in ring formation . The sizes of inner rings are positively correlated with bar strength : this can be linked to the radial displacement of the 1/4 ultraharmonic resonance while the bar grows and the pattern speed decreases . The ring ’ s intrinsic ellipticity is weakly controlled by the non-axisymmetric perturbation strength : this relation is not as strong as expected from simulations , especially when we include the dark matter halo in the force calculation . The ratio of outer-to-inner ring semi-major axes is uncorrelated with bar strength : this questions the manifold origin of rings . In addition , we confirm that i ) \sim 1 / 3 ( \sim 1 / 4 ) of the galaxies hosting inner ( outer ) rings are not barred ; ii ) on average , the sizes and shapes of rings are roughly the same for barred and non-barred galaxies ; and iii ) the fraction of inner ( outer ) rings is a factor of 1.2 - 1.4 ( 1.65 - 1.9 ) larger in barred galaxies than in their non-barred counterparts . Finally , we apply unsupervised machine learning ( self-organising maps , SOMs ) to show that , among early-type galaxies , ringed or barred galaxies can not be univocally distinguished based on 20 internal and external fundamental parameters . We confirm , with the aid of SOMs , that rings are mainly hosted by red , massive , gas-deficient , dark-matter poor , and centrally concentrated galaxies . We conclude that the present-day coupling between rings and bars is not as robust as predicted by numerical models , and diverse physical mechanisms and timescales determine ring formation and evolution .