Existing point-to-point registration methods often suffer from inaccuracies caused by erroneous matches and noisy correspondences, leading to significant decreases in registration accuracy and efficiency. To address these challenges, this paper presents a new coarse registration method based on a geometric constraint and a matrix evaluation. Compared to traditional registration methods that require a minimum of three correspondences to complete the registration, the proposed method only requires two correspondences to generate a transformation matrix. Additionally, by using geometric constraints to select out high-quality correspondences and evaluating the matrix, we greatly increase the likelihood of finding the optimal result. In the proposed method, we first employ a combination of descriptors and keypoint detection techniques to generate initial correspondences. Next, we utilize the nearest neighbor similarity ratio (NNSR) to select high-quality correspondences. Subsequently, we evaluate the quality of these correspondences using rigidity constraints and salient points' distance constraints, favoring higher-scoring correspondences. For each selected correspondence pair, we compute the rotation and translation matrix based on their centroids and local reference frames. With the transformation matrices of the source and target point clouds known, we deduce the transformation matrix of the source point cloud in reverse. To identify the best-transformed point cloud, we propose an evaluation method based on the overlap ratio and inliers points. Through parameter experiments, we investigate the performance of the proposed method under various parameter settings. By conducting comparative experiments, we verified that the proposed method's geometric constraints, evaluation methods, and transformation matrix computation consistently outperformed other methods in terms of root mean square error (RMSE) values. Additionally, we validated that our chosen combination for generating initial correspondences outperforms other descriptor and keypoint detection combinations in terms of the registration result accuracy. Furthermore, we compared our method with several feature-matching registration methods, and the results demonstrate the superior accuracy of our approach. Ultimately, by testing the proposed method on various types of point cloud datasets, we convincingly established its effectiveness. Based on the evaluation and selection of correspondences and the registration result's quality, our proposed method offers a solution with fewer iterations and higher accuracy.
Keywords: evaluation of registration; geometric constraint; point cloud registration; transformation estimation.