The morphology of galaxies can be quantified to some degree using a set of scale-invariant parameters. Concentration (C), Asymmetry (A), Smoothness (S), the Gini index (G), relative contribution of the brightest pixels to the second order moment of the flux (M20), ellipticity (E), and the Gini index of the second order moment (GM) have all been applied to morphologically classify galaxies at various wavelengths. Here we present a catalog of these parameters for the Spitzer Survey of Stellar Structure in Galaxies (S4G), a volume-limited near-infrared imaging survey of nearby galaxies using the 3.6 and 4.5 micron channels of the IRAC camera. Our goal is to provide a reference catalog of near-infrared quantified morphology for high-redshift studies and galaxy evolution models with enough detail to resolve stellar mass morphology. We explore where normal, non-interacting galaxies -those typically found on the Hubble tuning fork- lie in this parameter space and show that there is a tight relation between Concentration and M20 for normal galaxies. M20 can be used to classify galaxies into earlier and later types (e.g., to separate spirals from irregulars). Several criteria using these parameters exist to select systems with a disturbed morphology, i.e., those that appear to be undergoing a tidal interaction. We examine the applicability of these criteria to Spitzer near-infrared imaging. We find that four relations, based on the parameters A&S, G&M20, GM, and C&M20, respectively, select outliers in the morphological parameter space, but each selects different subsets of galaxies. Two criteria (GM > 0.6, G > -0.115 x M20 + 0.384) seem most appropriate to identify possible mergers and the merger fraction in near-infrared surveys. We find no strong relation between lopsidedness and most of these morphological parameters, except for a weak dependence of lopsidedness on Concentration and M20.
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