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Miniature air vehicles (MAVs) are often used for low altitude flights where unknown obstacles might be encountered. Path planning and obstacle avoidance for MAVs involve planning a feasible path from an initial state to a goal state while avoiding obstacles in the environment. This paper presents a vision-based local multi-resolution mapping and path planning technique for MAVs using a forward-looking onboard camera. A depth map, which represents the time-to-collision (TTC) and bearing information of the obstacles, is obtained by computer vision algorithms. To account for measurement uncertainties introduced by the camera, a multi-resolution map in the body frame of the MAV is created in polar coordinates. Using the depth map, the locations of the obstacles are determined in the multi-resolution map. Dijkstra's algorithm is employed to find a collision-free path in the body frame. The simulation and flight test results show that the proposed technique is successful in solving path planning and multiple obstacles avoidance problems for MAVs.