Manipulating textile objects with a robot is a challenging task, especially because the garment perception is difficult due to the endless configurations it can adopt, coupled with a large variety of colors and designs. Most current approaches follow a multiple re-grasp strategy, in which clothes are sequentially grasped from different points until one of them yields a recognizable configuration. In this work we propose a method that combines 3D and appearance information to directly select a suitable grasping point for the task at hand, which in our case consists of hanging a shirt or a polo shirt from a hook. Our method follows a coarse-to-fine approach in which, first, the collar of the garment is detected and, next, a grasping point on the lapel is chosen using a novel 3D descriptor. In contrast to current 3D descriptors, ours can run in real time, even when it needs to be densely computed over the input image. Our central idea is to take advantage of the structured nature of range images that most depth sensors provide and, by exploiting integral imaging, achieve speed-ups of two orders of magnitude with respect to competing approaches, while maintaining performance. This makes it especially adequate for robotic applications as we thoroughly demonstrate in the experimental section. This research is partially funded by the Spanish Ministry of Economy and Competitiveness under project TIN2014-58178-R, by the CSIC project MANIPlus (201350E102), and by the ERA-Net CHISTERA projects ViSen PCIN-2013-047 and I-DRESS PCIN-2015-147. A. Ramisa worked under the JAE-DOC grant from CSIC and FSE. The authors are grateful to the Nvidia donation program for its support with GPU cards. Peer Reviewed