Point-pair registration in a real scene remains a challenging task, due to the complexity of solving three transformations (scale, rotation, and displacement) simultaneously, and the influence of noise and outliers. Aimed at this problem, a registration algorithm based on histogram and vector operations is proposed in this paper. This approach converts point-based operations into vector-based operations, thereby decomposing the registration process into three independent steps solving for scale transformation factors, rotation matrices, and displacement vectors, which reduces the complexity of the solution and avoids the effects of scaling in the other two processes. The influence of outliers on the global transformation matrix is simultaneously eliminated using a histogram-based approach. Algorithm performance was evaluated through a comparison with the most commonly used SVD method in a series of validation experiments, with results showing that our methodology was superior to SVD in the cases with scaling transformation or outliers.