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This article presents a particle filter for pose estimation using unit dual quaternion kinematics. The eight-parameter unit dual quaternion is used for global representation of the pose, whereas the six parameters of the dual modified Rodrigues parameters (MRPs) are used for local pose representation in the state-space model. The dual MRPs enable estimates of the mean and the covariance to be calculated from the particles without violating the algebraic constraint of the unit dual quaternion. For verification of the filter and comparison with state of the art, we consider pose measurements available in the form of unit dual quaternions. Angular velocity and specific force measurements from a body-mounted inertial measurement unit are also considered in the filtering. We show through simulations that the suggested particle filter has comparable accuracy with a previously proposed unscented Kalman filter based on unit dual quaternions. We also consider a practical application where the pose of an arbitrary rigid object is estimated using a sequence of point clouds from a 3-D camera. A model point cloud of the object is displaced with the unit dual quaternion associated with each particle, and a fitting score is calculated between the displaced model point cloud and the measured point cloud from the 3-D camera. The likelihoods of the fitting scores are calculated from an exponential distribution and are used to update the weights of the particles. The system was verified in an experiment where the motion of a swinging payload hanging from a crane was estimated using a 3-D camera.

The number of fragments and the variety of primitive cultural relics unearthed in archaeology, especially the mixed fragments of several dynasties unearthed in Qinglong town, Shanghai, pose a great challenge to the manual splicing. The traditional manual comparison method is easy to cause the second damage to the cultural relics. In this paper, the edge feature is extracted based on removing the noise of point cloud, a bilateral filtering point cloud denoising algorithm based on salient features is proposed. By changing the step size and field of view, the Improved Artificial Fish Swarm Algorithm is used to get the matching strategy, and the point cloud is used to reconstruct 3D model by the Dual Quaternion Transformation method. The pairing of fragments and virtual reconstruction can effectively avoid the secondary damage of cultural relic fragments. It provides a feasible artificial intelligence solution for the protection and restoration of similar archaeological excavations.

In this paper we present a method for representing surfaces using a set of dual quaternion control points, with the goal of fitting to point clouds. Each control point is defined by a position and radius, which specify the area of the surface it affects, and a dual quaternion defining the transformation it applies. A point is mapped using the surface by a weighted sum of the control points, in a similar method to dual quaternion skinning. A surface is then represented as the transformation of an original surface, such as a unit square plane, using the control points. We demonstrate how we may fit surfaces to point clouds using a modified iterative gradient descent algorithm, adding control points to regions of the surface that are most poorly modelled at the current step. These methods are applied to the problem of representing human breathing by fitting surfaces to a subject’s chest as recorded by an RGB-D (image plus depth) camera and parameterizing the breathing using each control point’s parameters. Variations in the breathing pattern are shown before and after exercise.

Since pairwise registration is a necessary step for the seamless fusion of point clouds from neighboring stations, a closed-form solution to planar feature-based registration of LiDAR (Light Detection and Ranging) point clouds is proposed in this paper. Based on the Plücker coordinate-based representation of linear features in three-dimensional space, a quad tuple-based representation of planar features is introduced, which makes it possible to directly determine the difference between any two planar features. Dual quaternions are employed to represent spatial transformation and operations between dual quaternions and the quad tuple-based representation of planar features are given, with which an error norm is constructed. Based on L2-norm-minimization, detailed derivations of the proposed solution are explained step by step. Two experiments were designed in which simulated data and real data were both used to verify the correctness and the feasibility of the proposed solution. With the simulated data, the calculated registration results were consistent with the pre-established parameters, which verifies the correctness of the presented solution. With the real data, the calculated registration results were consistent with the results calculated by iterative methods. Conclusions can be drawn from the two experiments: (1) The proposed solution does not require any initial estimates of the unknown parameters in advance, which assures the stability and robustness of the solution, (2) Using dual quaternions to represent spatial transformation greatly reduces the additional constraints in the estimation process.

This paper presents a method for pose estimation of a rigid body using unit dual quaternions where pose measurements from point clouds are filtered with a multiplicative extended Kalman filter (MEKF). The point clouds come from a 3D camera fixed to the moving rigid body, and then consecutive point clouds are aligned with the Iterative Closest Point (ICP) algorithm to obtain pose measurements. The unit constraint of the dual quaternion is ensured in the filtering process with the Dual Quaternion MEKF (DQ-MEKF), where the measurement updates are performed using the dual quaternion product so that the result is a unit dual quaternion. In addition, we use the Cayley transform for the discrete time propagation of the DQ-MEKF estimate, eliminating the need for normalization and projection of the resulting unit dual quaternion. The ICP algorithm is initialized with the time propagated state of the filter to give faster and more accurate pose measurements. To further improve the accuracy of the initialization, angular velocity measurements from a gyroscope fixed to the camera are included in the filter. The proposed method has been tested in experiments using a Kinect v2 3D camera mounted rigidly on a KUKA KR6 robotic arm, while a customized ICP algorithm was successfully implemented on a Graphical Processing Unit (GPU) system. © 2018 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.

The representation of similarity transformation in three-dimensional (3D) space, especially of orientation, is a crucial issue in navigation, geodesy, photogrammetry, robot arm manipulation, etc. Considering the large amount of computer resources required by iterative algorithms designed for spatial similarity transformation, the high dependence on initial values of unknown parameters, and the instability of solving transformation parameters for large-angle registration, a closed-form solution for pairwise light detection and ranging (LiDAR) point cloud registration is proposed. In this solution, dual-number quaternions are used to represent the 3D rotation. The relationship between the rotation matrix-based representation of similarity transformation and the dual quaternion-based representation is described first. Considering that the same features from two neighboring stations coincide after pairwise registration, a dual quaternion-based error norm, which is associated with the sum of the position errors, is constructed. Based on theory of least squares and by extreme value analysis of the error norm, detailed derivations of the model and the main formulas are obtained. Once the similarities between the same features from the two neighboring LiDAR stations are constructed, the rotation matrix, the scale parameter, and the translation vector are simultaneously derived. Two experiments are conducted to verify the feasibility and effectiveness of the proposed algorithm. The proposed algorithm has the advantages of simplicity and ease of implementation, making it better than the traditional methods that use matrices to describe spatial rotation. Moreover, it solves the transformation parameters without the initial estimates of unknown parameters, making it better than iterative algorithms. Most importantly, in contrast to unit quaternion-based algorithms, the proposed algorithm solves seven unknown parameters simultaneously. Therefore, it effectively avoids the accumulation of introduced error in calculation and the negative impact from the inappropriate choice of initial values.