Scattered light images of transition discs in the near-infrared often show non-axisymmetric structures in the form of wide-open spiral arms in addition to their characteristic low-opacity inner gap region. We study self-gravitating discs and investigate the influence of gravitational instability on the shape and contrast of spiral arms induced by planet-disc interactions. Two-dimensional non-isothermal hydrodynamical simulations including viscous heating and a cooling prescription are combined with three-dimensional dust continuum radiative transfer models for direct comparison to observations. We find that the resulting contrast between the spirals and the surrounding disc in scattered light is by far higher for pressure scale height variations, i.e. thermal perturbations, than for pure surface density variations. Self-gravity effects suppress any vortex modes and tend to reduce the opening angle of planet-induced spirals, making them more tightly wound. If the disc is only marginally gravitationally stable with a Toomre parameter around unity, an embedded massive planet (planet-to-star mass ratio of $10^{-2}$) can trigger gravitational instability in the outer disc. The spirals created by this instability and the density waves launched by the planet can overlap resulting in large-scale, more open spiral arms in the outer disc. The contrast of these spirals is well above the detection limit of current telescopes.
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