  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. It has been shown that the removal of a diffuse background from SFR
tracers, such as H$\alpha$, 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.We used multiwavelength data obtained as part of the
surveys such as SINGS, KINGFISH, THINGS, and HERACLES. 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.
The fraction of diffuse background varies from galaxy to galaxy and accounts to
$\sim$34 % in H$\alpha$, $\sim$43 % in FUV, $\sim$37 % in 24 $\mu$m, and
$\sim$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 $\sim$1.4
$\pm$ 0.1, which agrees with dynamical models of star formation accounting for
flaring effects in the outer regions of galaxies.
