Global localization is a key problem that needs to be solved for single-line LiDAR based robot navigation since it will directly affect the estimation accuracy of the robot's initial pose and the success rate of recovering the robot's state when it loses its local pose. Existing studies to deal with this problem usually extract feature points from laser beams and then resort to fast retrieval and registration methods to further determine the robot's pose. Although these methods have achieved good results in specific scenes, they often fail to perform well when the robot is far away from the map-building trajectory. It is therefore highly desirable to develop more robust techniques for this problem. In this work, we propose a novel solution which is based on “Dense 2D Signature and 1D Registration”, D2S1R for short. By establishing a dense signature database for 2D locations and combining with the fast retrieval technology, the 2D search space is extremely compressed. Furthermore, fast yaw angle determination is achieved by converting scan points to 1D space and measuring the difference of scan contours based on relative entropy. Experimental results on several complex indoor scenes show that D2S1R can complete global localization within 0.03s on an ordinary CPU in an area of nearly 4,000m <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> . Besides, on the premise of achieving a location accuracy of 0.08±0.04m and an orientation accuracy of 0.72±0.60°, it can achieve an average success rate of 95% on all test datasets.