We present an extended morphometric system to automatically classify galaxies from astronomical images. The new system includes the original and modified versions of the CASGM coefficients (Concentration $C_1$, Asymmetry $A_3$, and Smoothness $S_3$), and the new parameters entropy, $H$, and spirality $\sigma_\psi$. The new parameters $A_3$, $S_3$ and $H$ are better to discriminate galaxy classes than $A_1$, $S_1$ and $G$, respectively. The new parameter $\sigma_\psi$ captures the amount of non-radial pattern on the image and is almost linearly dependent on T-type. Using a sample of spiral and elliptical galaxies from the Galaxy Zoo project as a training set, we employed the Linear Discriminant Analysis (LDA) technique to classify Baillard et al.(2011, 4478 galaxies), Nair \& Abraham (2010, 14123 galaxies) and SDSS Legacy (779,235 galaxies) samples. The cross-validation test shows that we can achieve an accuracy of more than 90\% with our classification scheme. Therefore, we are able to define a plane in the morphometric parameter space that separates the elliptical and spiral classes with a mismatch between classes smaller than 10\%. We use the distance to this plane as a morphometric index (M$_{\rm i}$) and we show that it follows the human based T-type index very closely. We calculate morphometric index M$_{\rm i}$ for $\sim$780k galaxies from SDSS Legacy Survey - DR7. We discuss how M$_{\rm i}$ correlates with stellar population parameters obtained using the spectra available from SDSS-DR7.
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