Abstract— We present a novel vision-based grasp point detection algorithm that can reliably detect the corners of a piece of cloth, using only geometric cues that are robust to variation in texture. Furthermore, we demonstrate the effectiveness of our algorithm in the context of folding a towel using a generalpurpose two-armed mobile robotic platform without the use of specialized end-effectors or tools. The robot begins by picking up a randomly dropped towel from a table, goes through a sequence of vision-based re-grasps and manipulations— partially in the air, partially on the table—and finally stacks the folded towel in a target location. The reliability and robustness of our algorithm enables for the first time a robot with general purpose manipulators to reliably and fully-autonomously fold previously unseen towels, demonstrating success on all 50 out of 50 single-towel trials as well as on a pile of 5 towels.