Context. The global Schmidt law of star formation provides a power-law relation between the surface densities of star-formation rate (SFR) and gas, and successfully explains plausible scenarios of galaxy formation and evolution. However, star formation being a multi-scale process, requires spatially-resolved analysis for a better understanding of the physics of star formation. Aims. It has been shown that the removal of a diffuse background from SFR tracers, such as Hα, far-ultraviolet (FUV), infrared, leads to an increase in the slope of the sub-galactic Schmidt relation. We reinvestigate the local Schmidt relations in nine nearby spiral galaxies taking into account the effect of inclusion and removal of diffuse background in SFR tracers as well as in the atomic gas. Methods. We used multiwavelength data obtained as part of the Spitzer Infrared Nearby Galaxies Survey, Key Insights on Nearby Galaxies: a Far-Infrared Survey with Herschel, The H I Nearby Galaxy Survey, and HERA CO-Line Extragalactic Survey. Making use of a novel split of the overall light distribution as a function of spatial scale, we subtracted the diffuse background in the SFR tracers as well as the atomic gas. Using aperture photometry, we study the Schmidt relations on background subtracted and unsubtracted data at physical scales varying between 0.5–2 kpc. Results. The fraction of diffuse background varies from galaxy to galaxy and accounts to ∼34% in Hα, ∼43% in FUV, ∼37% in 24 μm, and ∼75% in H I on average. We find that the inclusion of diffuse background in SFR tracers leads to a linear molecular gas Schmidt relation and a bimodal total gas Schmidt relation. However, the removal of diffuse background in SFR tracers leads to a super-linear molecular gas Schmidt relation. A further removal of the diffuse background from atomic gas results in a slope ∼1.4 ± 0.1, which agrees with dynamical models of star formation accounting for flaring effects in the outer regions of galaxies.