Safety is paramount for mobile robotic platforms such as self-driving cars and unmanned aerial vehicles. This work is devoted to a task that is indispensable for safety yet was largely overlooked in the past -- detecting obstacles that are of very thin structures, such as wires, cables and tree branches. This is a challenging problem, as thin objects can be problematic for active sensors such as lidar and sonar and even for stereo cameras. In this work, we propose to use video sequences for thin obstacle detection. We represent obstacles with edges in the video frames, and reconstruct them in 3D using efficient edge-based visual odometry techniques. We provide both a monocular camera solution and a stereo camera solution. The former incorporates Inertial Measurement Unit (IMU) data to solve scale ambiguity, while the latter enjoys a novel, purely vision-based solution. Experiments demonstrated that the proposed methods are fast and able to detect thin obstacles robustly and accurately under various conditions.