The shapes and directionality of bathymetry at slow-spreading ridges are key to understanding the magmatic or tectonic emplacement of the crust. Magmatic terrain is marked by linearly fault-bounded abyssal hills, while tectonic terrain is marked by long-lived detachment faults, forming Oceanic Core Complexes (OCCs). However, the quantitative description of these crustal regimes is still limited. We develop a novel automated terrain classification technique and test it at the 13-15° N section of the Mid-Atlantic Ridge. The algorithm uses the Slope-Weighted Eccentricity (SWE) of the horizontal eigenvalues to represent surface directionality and reveal crustal tectonic fabric. The application of this new technique yields results consistent with qualitative interpretation. Thus, it provides both new insights into the mid-oceanic ridge spreading and the potential to automate such mapping with different sets of grids, such as gravity and magnetic data in regions further away from the ridge where sediments mask sea-bed features.