An active omni-directional raging system using an omni-directional vision with structured light has many advantages compared to the conventional ranging systems: robustness against external illumination noise because of the laser structured light and computational efficiency because of one shot image containing $360^{circ}$ environment information from the omni-directional vision. The omni-directional range data represents a local distance map at a certain position in the workspace. In this paper, we propose a matching algorithm for the local distance map with the given global map database, thereby to localize a mobile robot in the global workspace. Since the global map database consists of line segments representing edges of environment object in general, the matching algorithm is based on relative position and orientation of line segments in the local map and the global map. The effectiveness of the proposed omni-directional ranging system and the matching are verified through experiments.