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This paper presents a vision-based collision avoidance technique for Miniature Air Vehicles (MAVs) using local-level frame mapping and planning in spherical coordinates. To explicitly address the obstacle initialization problem, the maps are parameterized using the inverse time-to-collision (TTC), which is independent of the ground speed of the MAV. Using bearing-only measurements, an extended Kalman Filter (EKF) is employed to estimate the inverse TTC, azimuth, and elevation to obstacles. A nonlinear observability analysis is used to derive conditions for the observability of the system. Based on these conditions, we design a path planning algorithm that minimizes the estimation uncertainties while simultaneously avoiding collisions with obstacles. The behavior of the planning algorithm is analyzed and the characteristics of the environment in which the planning algorithm guarantees collision-free paths for MAVs are described. Numerical results show that the proposed method is successful in solving the path planning problem for MAVs.