Invariant features and the registration of rigid bodies

Abstract

This paper investigates the use of Euclidean invariants in the iterative closest point registration of range images. Invariants are used in a modified distance function for the selection of point correspondences. Theoretical results show that under ideal conditions, using invariants can only improve the chance of a making correct correspondences. In addition, monotonic convergence to a local minimum is preserved. Experimental results show that using invariant features accelerates the registration and decreases the probability of being trapped in a local minimum.

Automatic registration of overlapping 3D point clouds using closest points

“…While the row normalisation is relatively easy to implement, the column normalisation needs special attention: even though a row has just two columns, we have to process them into n 2 columns, corresponding to each point in the second view. Comparing either the SoftICP or WeightICP algorithm with the existing improved ICP algorithms described in the introduction, the former has a clear advantage of easy implementation and is of general use, since they do not require any feature extraction [20,44,54], parameter estimation [31,27,41] necessary for the elimination of false correspondences, or any structural information from data points [14,51].…”

“…In the last two decades, a large number of algorithms have been proposed to tackle the difficult and challenging 3D free form shape registration problem based on techniques, such as scatter matrix [25], iterative closest point (ICP) [3,4,57], improved ICP algorithm [11,18,20,22,[28][29][30]41,44,54], interactive method [52], geometric histogram [1], graduated assignment algorithm [5,7,10,[15][16][17] among many others. Among these methods, the ideas of the ICP algorithm and the graduated assignment algorithm are most attractive and their brief analysis is thus given below.…”

“…As a result, the key to successfully applying the ICP algorithm for 3D free form shape registration lies in eliminating the correspondences with relatively lower qualities. For this purpose, the following techniques have been proposed: † Increase the dimensionality of points from 3D [3,4] to higher dimensions by incorporating other geometric or optical features, such as normal vectors [12], invariants [44], curvature [55], laser reflectance strength value [35], and colours [22]; † Sample points uniformly [51], in normal space [42], or based on covariance matrix [14]; † Establish correspondences from matching points to matching curves [48,53] to matching 2D images [20,23,54], from matching local structural features to examining motion consistency [28,31,41] to combining both [27]; † Consider the reliability of point correspondences as a function of the cosine of the including angle between vertex normals and their viewing directions [51]; † Eliminate false matches through removing boundary points [42,51], checking interpoint distance consistency [11] or orientation consistency [38,57], examining motion consistency [29][30][31]41], or examining both the motion and structural consistency [28,27]; † Estimate motion parameters from using least squares to using weighted least squares [51], genetic algorithm [45], M-estimator [35] or simulated annealing [33], or from the Euclidean space to the frequency space [32].…”

“…The main reason why the GICP algorithm was chosen is that while most existing algorithms require more or less structural information from images [11,20,22,28,38,44,54], such information is not easy to estimate from point clouds. The GICP algorithm was designed for the registration of unorganised point sets and does not need to extract any structural information from point clouds and thus, also has an advantage of easy implementation.…”

Augmented Reality in Medicine

“…However, the accuracy of fiducial based registration varies depending on the number of fiducials and measurement quality of each fiducial position, as well as their spatial arrangement [2]. To improve registration accuracy, iterative closest point (ICP) based surface matching is often used in combination with point based registration [13][14][15]. However, careful selection and collection of 3D surface data is critical for final accuracy, usually expressed in terms of target registration error (TRE).…”