## 4 Registration Algorithms Based on Feature
### Feature Matching  
Feature matching is also a process of transformation estimation. After extracting the feature points, the transformation matrix can be obtained by the corresponding relationship between feature points. The registration problem turns into a convex problem if it has the corresponding. There are several methods to gain transformation matrix, including SVD (singular value decomposition), least squares method, etc. In contrast to the ICP-like procedure, only one coarse transformation is required in this case, therefore accuracy is not the most crucial factor. Instead, the accurate correspondence might offer a suitable initial value for the subsequent fine registration. The brute force matching method is the most fundamental. Assuming that there exist \(n\) features in each of the two-point clouds, it may take up to n6 related feature points needed to detect the rigid transformation between two sets of points, only a tiny portion of which can identify the proper transformation matrix. Direct feature extracting is feasible in the case of a few points in the point cloud. However, it will be a highly time-consuming operation if there are many point clouds. It is possible to develop some search strategies using information from feature extraction that ought to make a substantial speedup in feature matching and a significant reduction in computational cost. [PERSON] and [PERSON] [122] designed a transformation matrix that can be determined between two pairs of line features. Those features that do not satisfy the ratio of line length to plane size are filtered by threshold and then other features are verified to discover the best match iteratively. [PERSON] et al. [123] proposed using the branch-and-bound method for key point matching to convert the coordinate root mean square error verification into the distance root mean square error, thus verifying the quality of key point matching without computing the transformation matrix. The approach is resistant to outliers, noise, and occlusion, but it has strict constraints for the retrieved feature points. [PERSON] et al. [124] introduced constraints on the polar geometry in determining the matching relationship. They looked for feature matching based on RANSAC that made the majority of feature points adhere to the polar geometry requirements. [PERSON] et al. [125] estimated the transformation matrix using a triplet of face features, but first they computed and ordered the triple product of the triples. The translation error is reduced and iterations are terminated when the same transformation happens a set number of times respectively, the greater the triple product being the reason for this. [PERSON] et al. [126] applied a game-theoretic framework to match key points, where matches that satisfy mutually stiff requirements are allowed to persist and all other correspondences are eliminated via a natural selection process. [PERSON] et al. [127] integrated the resulting semantic line features into triangular pairs, created analogous triangular pairs by combining three constraints on line features, removed some erroneous correspondences with geometric consistency tests and calculated the transformation matrix with the remaining correspondences. [PERSON] et al. [128] used the CTNC (closest to next closest) technique: for each feature, the most similar and second-similar features meet a certain ratio requirement to be deemed as the correct matching feature. [PERSON] et al. [129] created two-dimensional synthetic images with a variety of views using three-dimensional point clouds. He then scaled images to produce them at various resolutions, which produced a huge number of repeated feature-matching relationships. Finally, the most repetitions were voted as feature match. [PERSON] et al. [130] took planes as features of K-4 PCS and designed feature matching with angle rather than distance as a metric. [PERSON] et al. [131] used weights to determine the distance between features by weighing color and spatial characteristics.