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Non-Parametric Cell-Based Photometric Proxies for Galaxy Morphology: Methodology and Application to the Morphologically-Defined Star Formation -- Stellar Mass Relation of Spiral Galaxies in the Local Universe

(Abridged) We present a non-parametric cell-based method of selecting highly pure and largely complete samples of spiral galaxies using photometric and structural parameters as provided by standard photometric pipelines and simple shape fitting algorithms, demonstrably superior to commonly used proxies. Furthermore, we find structural parameters derived using passbands longwards of the $g$ band and linked to older stellar populations, especially the stellar mass surface density $μ_*$ and the $r$ band effective radius $r_e$, to perform at least equally well as parameters more traditionally linked to the identification of spirals by means of their young stellar populations. In particular the distinct bimodality in the parameter $μ_*$, consistent with expectations of different evolutionary paths for spirals and ellipticals, represents an often overlooked yet powerful parameter in differentiating between spiral and non-spiral/elliptical galaxies. We investigate the intrinsic specific star-formation rate - stellar mass relation ($ψ_* - M_*$) for a morphologically defined volume limited sample of local universe spiral galaxies, defined using the cell-based method with an appropriate parameter combination. The relation is found to be well described by $ψ_* \propto M_*^{-0.5}$ over the range of $10^{9.5} M_{\odot} \le M_* \le 10^{11} M_{\odot}$ with a mean interquartile range of $0.4\,$dex. This is somewhat steeper than previous determinations based on colour-selected samples of star-forming galaxies, primarily due to the inclusion in the sample of red quiescent disks.