Research On Registration Algorithm Of The Three-dimensional Point Cloud Data

In recent years, reverse engineering technology has been more and more applied to theshape of the new product design and development, and become one of the most importantdesign and manufacturing technology. Currently, reverse engineering has become a researchhot spot of the computer aided design technology, and reverse engineering technology whichcan produce digital model via an object physical model is obtained more and more widelyused as a result of its own unique characteristics, and at the same time, with the developmentof the science and technology new, the hardware equipment are also increasingly perfect, italso provides more than enough technical support for the operation of the digital model.Via scan sampling to obtain the two groups of the point cloud data which have repeatregions, are aligned and merged in a single coordinate system by determining an appropriatecoordinate transformation, this process is called point cloud registration. Thus we obtain acomplete data model of the measured object. Point cloud registration can be divided intoautomatic registration, registration of the instrument-dependent and manual registration. Wesaid in the general case of point cloud registration refers an automatic registration.The purpose of point cloud registration is to determine transformation relation betweentwo sets of points and to recover the transformation that maps one point set to the other. Thekey of achieving the two point clouds registration is to establish a one-to-one mappingrelationship between the two point clouds. Assuming the two point clouds sets are representedas X and Y. Thus, the problem is transformed to how to obtain the coordinatetransformation T (Y, θ), which makes the distance between transformed TY and X minimum,and where θ is a set of the transformation parameters. Depending on the set oftransformation parameters, we can divide the point cloud registration into two categories:rigid registration and non-rigid registration. A rigid transformation only allows for translation,rotation, and scaling, however, the non-rigid transformation is relatively complex. Thesimplest non-rigid transformation is affine, which also allows anisotropic scaling and skews.Simplistic approximations of the true non-rigid transformation, including piecewise affine andpolynomial models, are often inadequate for correct alignment and can produce erroneous correspondences. Thus the true underlying nonrigid transformation model is often unknownand challenging to model.This paper respectively researches from the rigid registration and nonrigid registration ofpoint cloud registration theory. The alignment of two point sets is viewed as a probabilitydensity estimation problem. We regard one of the point sets as the centroids of the Gaussianmixture model (GMM) and regard another point as data points by the maximum likelihood.Based on this idea we fit the centroids of the Gaussian mixture model to the data points, andin view of the existence of noise points (outliers), this paper respectively expounds the rigidpoint cloud registration and non-rigid point cloud registration theory.First, in the rigid case, transforming the minimum of the distance between the two pointcloud sets into the problem of maximum trace of matrix tr(ATR), thus we can obtain onlyoptimal rotation matrix R which makes tr(ATR)maximize, where the A is real matrixwhich is given and R is unknown rotation matrix.Second, in the non-rigid case, we impose the coherence constraint by regularizing thedisplacement field and using the variational calculus to derive the optimal transformation, andSo that we make the centroid of the Gaussian mixture model coherently move to the datapoint and complete alignment.At last, this paper proposed a fast algorithm which combined the FGT algorithm with thelow-rank matrix approximation, respectively, for the rigid and non-rigid registrationaccelerated algorithm, and this accelerated algorithm reduces the method computationcomplexity to linear. Currently, due to the inherent flaws of the registration algorithm, thealgorithm proposed in this paper has not achieved an accurate and fast desired result, butcompromise on accuracy and speed. In fact, the point cloud registration requirement foraccuracy is much higher than the speed of the registration, the next problem will be solved is:how in an acceptable time limit of registration, to further enhance the accuracy of theregistration algorithm.