Upcoming large imaging surveys will allow detailed studies of the structure and morphology of galaxies aimed at addressing how galaxies form and evolve. Computational approaches are needed to characterize their morphologies over large samples. We introduce an automatic method to quantify the outer structure of galaxies. The key to our approach is the division of a galaxy image into two sections delineated by the isophote which encloses half the total brightness of the galaxy. We call the central section the inner half-flux region (IHR) and the outer section the outer half-flux region (OHR). From this division, we derive two parameters: $A_{rm o}$, which measures the asymmetry of the OHR, and $D_{rm o}$, which measures the deviation of the intensity weighted centroid of the OHR from that of the IHR relative to the effective radius. We derive the two parameters from $HST$/ACS $z_{850}$-band images for a sample of 764 galaxies with $z_{850}<22$ mag and $0.35<z<0.9$ selected from GEMS and GOODS-South surveys. We show that the sample galaxies having strong asymmetric structures, in particular tidal tails, are well-separated from those with regular morphologies in the $A_{rm o}$-$D_{rm o}$ space. Meanwhile, the widely used $CAS$ and Gini-$M_{20}$ methods turn out to be insensitive to such morphological features. We stress that the $A_{rm o}$-$D_{rm o}$ method is an efficient way to select galaxies with significant asymmetric features like tidal tails and study galaxy mergers in the dynamical phase traced by these delicate features.
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