As the line laser sensor can be only installed beside rails during dynamic inspection, it cannot ensure the intersection line of line laser measurement plane and wheel surface to be through wheel center, which causes the affine distortion of large number of wheel profiles and makes it difficult to use the traditional iterative closest point (ICP) algorithm to register the measured profile and to ensure the accuracy and robustness of measurement. In this paper, an algorithm of reweighted scaling iterative closest point based on region of interest (ROI-RSICP) is proposed to achieve accurate registration of worn wheel profiles with affine distortion. First, according to the wear characteristics of wheel profiles and a large number of worn wheel profile data, the PointNet deep learning network is adopted to divide the collected wheel profile point sets into two parts: wear region of interest (ROI) and non-wear part. Then, the ROI-RSICP method is proposed by assigning different values of weight to ROI and non-wear part to achieve accurate registration of the worn wheel profiles with affine distortion and the standard wheel profiles. Finally, the Hausdorff distance algorithm is used to visualize the wheel profile wear. The results of ICP algorithm, scaling ICP algorithm, ROI-RSICP algorithm and the 4th kind of inspector are compared in the experiment, which verifies the superiority of the proposed algorithm for dynamic inspection of worn wheel profiles with affine distortion.