© 2021 AGBMBackground and Objective: As is known, point clouds representing the objects are frequently used in object registration. Although the objects can be registered by using all the points in the corresponding point clouds of the objects, the registration process can also be achieved with a smaller number of the landmark points selected from the entire point clouds of the objects. This paper introduces a research study focusing on the fast and accurate rigid registration of the bilateral proximal femurs in bilateral hip joint images by using the random sub-sample points. For this purpose, Random Point Sub-sampling (RPS) was analyzed and the reduced point sets were used for an accurate registration of the bilateral proximal femurs in coronal hip joint magnetic resonance imaging (MRI) slices. Methods: In registration, bilateral proximal femurs in MRI slices were registered rigidly by performing a process consisting of three main phases named as MR image preprocessing, proximal femur registration over the random sub-sample points and MR image postprocessing. In the stage of the MR image preprocessing, segmentation maps of the bilateral proximal femurs are obtained as region of interest (RoI) images from the entire MRI slices and then, the edge maps of the segmented proximal femurs are extracted. In the registration phase, the edge maps describing the proximal femur surfaces are represented as point clouds initially. Thereafter, the RPS is performed on the proximal femur point clouds and the number of points representing the proximal femurs is reduced at different ratios. For the registration of the point clouds, the Iterative Closest Point (ICP) algorithm is performed on the reduced sets of points. Finally, the registration procedures are completed by performing MR image postprocessing on the registered proximal femur images. Results: In performance evaluation tests performed on healthy and pathological proximal femurs in 13 bilateral coronal hip joint MRI slices of 13 Legg-Calve-Perthes disease (LCPD) patients, bilateral proximal femurs were successfully registered with very small error rates by using the reduced set of points obtained via the RPS and promising results were achieved. The minimum error rate was observed at RPS rate of 30% as the value of 0.41 (±0.31)% on all over the bilateral proximal femurs evaluated. When the range of RPS rate of 20-30% is considered as the reference, the elapsed time in registration can be reduced by almost 30-40% compared to the case where all the proximal femur points were included in registration. Additionally, it was observed that the RPS rate should be selected as at least 25% to achieve a successful registration with an error rate below 1%. Conclusion: It was concluded from the observed results that a more successful and faster registration can be accomplished by selecting fewer points randomly from the point sets of proximal femurs instead of using all the points describing the proximal femurs. Not only an accurate registration with low error rates was performed, but also a faster registration process was performed by means of the limited number of points that are sub-sampled randomly from the whole point sets.