In this paper, we investigate the contribution that visual perception affords to a robotic manipulation task in which a crumpled garment is flattened by eliminating visually detected wrinkles. In order to explore and validate visually guided clothing manipulation in a repeatable and controlled environment, we have developed a hand-eye interactive virtual robot manipulation system that incorporates a clothing simulator to close the effector-garment-visual sensing interaction loop. We present the technical details and compare the performance of two different methods for detecting, representing and interpreting wrinkles within clothing surfaces captured in high-resolution depth maps. The first method we present relies upon a clustering-based method for localizing and parametrizing wrinkles, while the second method adopts a more advanced geometrybased approach in which shape-topology analysis underpins the identification of the cloth configuration (i.e., maps wrinkles). Having interpreted the state of the cloth configuration by means of either of these methods, a heuristicbased flattening strategy is then executed to infer the appropriate forces, their directions and gripper contact locations that must be applied to the cloth in order to flatten the perceived wrinkles. A greedy approach, which attempts to flatten the largest detected wrinkle for each perception-iteration cycle, has been successfully adopted in this work. We present the results of our heuristic-based flattening methodology which relies upon clustering-based and geometry-based features respectively. Our experiments indicate that geometry-based features have the potential to provide a greater degree of clothing configuration understanding and, as a consequence, improve flattening performance. The results of experiments using a real robot (as opposed to simulated robot) also confirm our proposition that a more effective visual perception system can advance the performance of cloth manipulation.