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This paper introduces a novel approach named the point-to-line metric based iterative closest point (ICP) with bounded scale algorithm, which integrates a scale with boundaries into the traditional point-to-line metric-based ICP algorithm. It converges quadratically, requires few number of iterations and is not sensitive to large initial displacement errors. Based on the analysis of the error function being minimized, a efficient solution is proposed to reduce the computational cost. The proposed technique is fit for both laser scan data sets and other 2D m-D point sets, and yields more satisfying robust results than the traditional point-to-line ICP method. Further more, it provides a method to calculate the covariance of registration results. Experimental results illustrate the feasibility of the proposed theory and algorithms.