Efficient And High-precision Geometric Registration

With the rapid development of depth acquisition equipment,more and more researchers use the acquired 3D data for objects or scene reconstruction,tracking,mobile robot positioning,SLAM,VR/AR,and other tasks.Compared with 2D data,3D data can provide richer information,so that these tasks can be completed more efficiently and accurately.Among these tasks,the geometric registration of 3D data is a key technique.By effectively aligning multiple 3D data,the relative position transformation between the data or more complete 3D information can be obtained.However,the 3D data collected by depth sensors usually have low accuracy and contain a lot of noise and outliers.Moreover,there may be only partial overlap between the two data,and for dynamic objects,there may also be large non-rigid deformations,which greatly increase the difficulty of the geometric registration problem.In addition,some tasks also have real-time requirements,such as SLAM,reconstruction,etc.,so the running speed of the registration algorithm is also a factor that is often considered.In response to these problems,this paper proposes three improved algorithms for registration techniques,aiming at improving the accuracy or efficiency of registration algorithms.Details are as follows:Efficient and robust rigid registration algorithm:In this paper,a robust rigid registration model is proposed,using the Welsch function to measure the point-wise distance between corresponding point pairs.On the one hand,it can make more reliable points play a more important role in the optimization model by reducing the influence of corresponding point pairs with far distances;on the other hand,we can find a quadratic surrogate function for this objective function,and use the Majorization-Minimization algorithm for an iterative solution.At the same time,in order to further speed up the convergence speed,we also adopted the Anderson acceleration technology.Our proposed method greatly improves the accuracy of the registration problem and has a clear speed advantage over other robust registration methods.Efficient non-rigid registration algorithm based on deformation graph:In related tasks of dynamic scenes,such as tracking,reconstruction,etc.,non-rigid registration techniques are often used.The non-rigid deformation will be more challenging than the rigid registration problem due to its more complex form.In this paper,the deformation graph is adopted to model non-rigid deformation fields,which can express deformations in lower dimensions and have high flexibility.Moreover,this paper proposes an efficient improvement strategy to build uniform deformation graphs for poor-quality input models in less time.In addition,this paper also improves the non-rigid registration algorithm by combining robust metrics and efficient solving algorithms.Experiments show that our proposed algorithm greatly improves the solution speed and accuracy of non-rigid registration problems.Non-rigid registration algorithm based on symmetric error metric:The first two methods use a robust metric to reduce the impact of erroneous point pairs between surfaces.They use point-to-point distances or point-to-plane distances to approximate the distance between surfaces.However,the alignment effect of these two approximate distances is limited,and some information,such as the normal of the source surface,is not effectively applied.Therefore,we combine the normal information of the source surface and use the symmetric point-to-plane distance to approximate the distance between surfaces to complete the non-rigid registration task.In order to better model the problem and make the model easy to solve,we also incorporate deformation constraints such as being as rigid as possible.Experiments show that using the symmetric point-toplane distance measure greatly improves the solution accuracy of non-rigid registration problems compared with other distances.In summary,this paper designs three efficient algorithms that improve the robustness or running speed of conventional optimization-based rigid and non-rigid registration techniques.The metrics proposed in this paper can also be applied in deep learningbased methods to improve the generalization of the model.In addition,the methods in this paper can also be easily applied to downstream tasks such as SLAM and 3D reconstruction to promote their developments.