A Two-Stage Registration Method for Dental Volumetric Data and Mesh Data

Dental computed tomography (CT) images and optical surface scan data are widely used in dental computer-aided design systems. Registration is essential if they are used in software systems. Existing automatic registration methods are either time-consuming or rough, and interactive registration methods are experience-dependent and tedious because of a great deal of purely manual interactions. For overcoming these disadvantages, a two-stage registration method is proposed. In the rough registration stage, the rough translation and rotation matrices are obtained by applying unit quaternion based method on the points interactively selected from the two types of data. In the precise registration stage, the stridden sampling is used to reduce computational complexity and the proposed registration algorithm with scale transformation is used for precise registration. The proposed method offers a good trade-off between precision and time cost. The experimental results demonstrate that the proposed method provides faster convergence and smaller registration errors than existing methods.

fastSW: Efficient Piecewise Linear Approximation of Quaternion-Based Orientation Sensor Signals for Motion Capturing with Wearable IMUs

In the past decade, inertial measurement sensors have found their way into many wearable devices where they are used in a broad range of applications, including fitness tracking, step counting, navigation, activity recognition, or motion capturing. One of their key features that is widely used in motion capturing applications is their capability of estimating the orientation of the device and, thus, the orientation of the limb it is attached to. However, tracking a human’s motion at reasonable sampling rates comes with the drawback that a substantial amount of data needs to be transmitted between devices or to an end point where all device data is fused into the overall body pose. The communication typically happens wirelessly, which severely drains battery capacity and limits the use time. In this paper, we introduce fastSW, a novel piecewise linear approximation technique that efficiently reduces the amount of data required to be transmitted between devices. It takes advantage of the fact that, during motion, not all limbs are being moved at the same time or at the same speed, and only those devices need to transmit data that actually are being moved or that exceed a certain approximation error threshold. Our technique is efficient in computation time and memory utilization on embedded platforms, with a maximum of 210 instructions on an ARM Cortex-M4 microcontroller. Furthermore, in contrast to similar techniques, our algorithm does not affect the device orientation estimates to deviate from a unit quaternion. In our experiments on a publicly available dataset, our technique is able to compress the data to 10% of its original size, while achieving an average angular deviation of approximately 2° and a maximum angular deviation below 9°.

Unit Quaternion Description Method for Detecting High-Temperature Geothermal Well Drilling Conditions

When the typically utilized method for detecting the drilling conditions of high-temperature geothermal wells is applied, the detection takes a long time, the detection results are inconsistent with the actual conditions, and there are problems such as low detection efficiency and large detection deviation. Therefore, a method for detecting the drilling conditions of high-temperature geothermal wells described by a unit quaternion is proposed. Based on quaternion theory, the quaternion model of the position and attitude is constructed to obtain the drilling attitude. According to the analysis results and the basic principle of kernel principal component analysis, a model is built to realize the detection of high-temperature geothermal well drilling conditions. The experimental results show that in many iterations, the time required is stable and lower than that of other comparison methods, and the detection errors are all lower than 10%. The proposed method has high detection efficiency and low detection errors.

Attention-Based 3D Human Pose Sequence Refinement Network

Three-dimensional human mesh reconstruction from a single video has made much progress in recent years due to the advances in deep learning. However, previous methods still often reconstruct temporally noisy pose and mesh sequences given in-the-wild video data. To address this problem, we propose a human pose refinement network (HPR-Net) based on a non-local attention mechanism. The pipeline of the proposed framework consists of a weight-regression module, a weighted-averaging module, and a skinned multi-person linear (SMPL) module. First, the weight-regression module creates pose affinity weights from a 3D human pose sequence represented in a unit quaternion form. Next, the weighted-averaging module generates a refined 3D pose sequence by performing temporal weighted averaging using the generated affinity weights. Finally, the refined pose sequence is converted into a human mesh sequence using the SMPL module. HPR-Net is a simple but effective post-processing network that can substantially improve the accuracy and temporal smoothness of 3D human mesh sequences obtained from an input video by existing human mesh reconstruction methods. Our experiments show that the noisy results of the existing methods are consistently improved using the proposed method on various real datasets. Notably, our proposed method reduces the pose and acceleration errors of VIBE, the existing state-of-the-art human mesh reconstruction method, by 1.4% and 66.5%, respectively, on the 3DPW dataset.

A Lie Group-Based Iterative Algorithm Framework for Numerically Solving Forward Kinematics of Gough–Stewart Platform

In this work, we began to take forward kinematics of the Gough–Stewart (G-S) platform as an unconstrained optimization problem on the Lie group-structured manifold SE(3) instead of simply relaxing its intrinsic orthogonal constraint when algorithms are updated on six-dimensional local flat Euclidean space or adding extra unit norm constraint when orientation parts are parametrized by a unit quaternion. With this thought in mind, we construct two kinds of iterative problem-solving algorithms (Gauss–Newton (G-N) and Levenberg–Marquardt (L-M)) with mathematical tools from the Lie group and Lie algebra. Finally, a case study for a general G-S platform was carried out to compare these two kinds of algorithms on SE(3) with corresponding algorithms that updated on six-dimensional flat Euclidean space or seven-dimensional quaternion-based parametrization Euclidean space. Experiment results demonstrate that those algorithms on SE(3) behave better than others in convergence performance especially when the initial guess selection is near to branch solutions.

Relativistic Combination of Non-Collinear 3-Velocities Using Quaternions

Quaternions have an (over a century-old) extensive and quite complicated interaction with special relativity. Since quaternions are intrinsically 4-dimensional, and do such a good job of handling 3-dimensional rotations, the hope has always been that the use of quaternions would simplify some of the algebra of the Lorentz transformations. Herein we report a new and relatively nice result for the relativistic combination of non-collinear 3-velocities. We work with the relativistic half-velocities w defined by v=2w1+w2, so that w=v1+1−v2=v2+O(v3), and promote them to quaternions using w=wn^, where n^ is a unit quaternion. We shall first show that the composition of relativistic half-velocities is given by w1⊕2≡w1⊕w2≡(1−w1w2)−1(w1+w2), and then show that this is also equivalent to w1⊕2=(w1+w2)(1−w2w1)−1. Here as usual we adopt units where the speed of light is set to unity. Note that all of the complicated angular dependence for relativistic combination of non-collinear 3-velocities is now encoded in the quaternion multiplication of w1 with w2. This result can furthermore be extended to obtain novel elegant and compact formulae for both the associated Wigner angle Ω and the direction of the combined velocities: eΩ=eΩΩ^=(1−w1w2)−1(1−w2w1), and w^1⊕2=eΩ/2w1+w2|w1+w2|. Finally, we use this formalism to investigate the conditions under which the relativistic composition of 3-velocities is associative. Thus, we would argue, many key results that are ultimately due to the non-commutativity of non-collinear boosts can be easily rephrased in terms of the non-commutative algebra of quaternions.

Forward and Backward Visual Fusion Approach to Motion Estimation with High Robustness and Low Cost

We present a novel low-cost visual odometry method of estimating the ego-motion (self-motion) for ground vehicles by detecting the changes that motion induces on the images. Different from traditional localization methods that use differential global positioning system (GPS), precise inertial measurement unit (IMU) or 3D Lidar, the proposed method only leverage data from inexpensive visual sensors of forward and backward onboard cameras. Starting with the spatial-temporal synchronization, the scale factor of backward monocular visual odometry was estimated based on the MSE optimization method in a sliding window. Then, in trajectory estimation, an improved two-layers Kalman filter was proposed including orientation fusion and position fusion . Where, in the orientation fusion step, we utilized the trajectory error space represented by unit quaternion as the state of the filter. The resulting system enables high-accuracy, low-cost ego-pose estimation, along with providing robustness capability of handing camera module degradation by automatic reduce the confidence of failed sensor in the fusion pipeline. Therefore, it can operate in the presence of complex and highly dynamic motion such as enter-in-and-out tunnel entrance, texture-less, illumination change environments, bumpy road and even one of the cameras fails. The experiments carried out in this paper have proved that our algorithm can achieve the best performance on evaluation indexes of average in distance (AED), average in X direction (AEX), average in Y direction (AEY), and root mean square error (RMSE) compared to other state-of-the-art algorithms, which indicates that the output results of our approach is superior to other methods.