Rigid Body Transformation Research Articles

Dual X-Ray Image under Neural Network Adopted in Comparison of Efficacy and Safety of Deep Hydrolyzed Protein Milk Powder and Parenteral Nutrition in Intervention of Neonatal Noninfectious Abdominal Distension

Objective. The aim of this study was to explore the application value of double X-ray image based on neural network in comparison of the efficacy and safety of deep-water proteolytic milk powder and parenteral nutrition in the intervention of neonatal noninfectious abdominal distention. Methods. Clinical data of 58 neonates diagnosed with noninfectious abdominal distention were retrospectively analyzed. 2D-3D registration was simplified into two steps by decomposing spatial rigid-body transformation parameters into two planes, including 2D-2D approximate rigid-body registration and single-parameter 2D-3D rigid-body registration. Then, the convolution neural network was used to fit the nonlinear mapping relationship between the residual of X-ray images and the corresponding attitude differences of children, and the residual regression spatial rigid-body transformation parameters of the X-DRR image pairs were obtained. Noninfectious abdominal distention was diagnosed in all neonates, of which 28 neonates were treated with deep hydrolyzed protein milk powder. Another 30 neonates who received parenteral nutrition support were set as control group. All newborns received two weeks of treatment. The total effective rate, birth weight recovery, weight growth rate, intestinal feeding recovery time, and incidence of feeding intolerance were compared between the two groups. Results. Spatial coordinate decomposition using double X-ray can simplify the mapping relationship between spatial coordinate transformation and X-DRR residual image. Compared with the gray level iterative optimization registration algorithm, the registration accuracy and speed were significantly improved. The total effective rate in the treatment group (92.86%) was significantly higher than that in the control group (9%). The recovery time of birth weight, intestinal feeding recovery time, and meconium excretion time were significantly shorter than those in the control group, and the body weight in the treatment group increased faster than that in the control group ( P < 0.05 ). In addition, the incidence of feeding intolerance was 3.57% (1/28) in the treatment group and 36.36% (8/22) in the control group, which was significantly lower than that in the treatment group ( P < 0.05 ). Conclusion. After data training, the network can complete accurate double ray registration in 0.04 s. Deep hydrolyzed protein milk powder had remarkable therapeutic effect on neonates, with no infective abdominal distention, fast recovery, and low incidence of feeding intolerance, which was safe and reliable in clinical application.

Correcting whole-body motion capture data using rigid body transformation.

Using motion capture data as a part of mobile brain-body imaging (MoBI) recording has been increasing. With minimal linear algebra background, this paper explains how the rigid body transformation can be a useful preprocessing step for denoising and missing marker recovery. Such a transformation can provide insight and necessary-and-sufficient solutions requiring no assumption other than the minimum number of markers present. First, a simulation test using the empirical datasets from the AudioMaze project published from this journal's same volume demonstrates theoretical accuracy. The simulation results show that the rigid-body method perfectly recovers missing markers on a rigid body if a minimum of three marker positions is available. Second, the same transformation is applied to the empirical dataset. Before preprocessing, the raw data show that 15-80% of data frames had all markers present for rigid-body defined body parts. After using the rigid-body correction, most body parts recovered full markers in 90-95% of the data frames. The result also suggests the necessity for performing across-trial corrections for within-participant (42% missing detected in one of the body parts) and across-participants (11% missing). The discussion section introduces a solution and a performance summary for non-rigid-body marker correction using a neural network. Data support that the rigid body transformation is an intuitive and powerful correction method necessary for preprocessing motion capture data for neurocognitive experiments. The supporting information section contains a URL link to Matlab code and example data.

MPCR-Net: Multiple Partial Point Clouds Registration Network Using a Global Template

With advancements in photoelectric technology and computer image processing technology, the visual measurement method based on point clouds is gradually being applied to the 3D measurement of large workpieces. Point cloud registration is a key step in 3D measurement, and its registration accuracy directly affects the accuracy of 3D measurements. In this study, we designed a novel MPCR-Net for multiple partial point cloud registration networks. First, an ideal point cloud was extracted from the CAD model of the workpiece and used as the global template. Next, a deep neural network was used to search for the corresponding point groups between each partial point cloud and the global template point cloud. Then, the rigid body transformation matrix was learned according to these correspondence point groups to realize the registration of each partial point cloud. Finally, the iterative closest point algorithm was used to optimize the registration results to obtain the final point cloud model of the workpiece. We conducted point cloud registration experiments on untrained models and actual workpieces, and by comparing them with existing point cloud registration methods, we verified that the MPCR-Net could improve the accuracy and robustness of the 3D point cloud registration.

On Bundle Adjustment for Multiview Point Cloud Registration

Multiview registration is used to estimate Rigid Body Transformations (RBTs) from multiple frames and reconstruct a scene with corresponding scans. Despite the success of pairwise registration and pose synchronization, the concept of Bundle Adjustment (BA) has been proven to better maintain global consistency. So in this work, we make the multiview point-cloud registration more tractable from a different perspective in resolving range-based BA. We first analyse the optimal condition of the objective function of BA that unifies some previous approaches. Based on this analysis, we propose an objective function that takes both measurement noises and computational cost into account. For the feature parameter update, instead of calculating the global distribution parameters from the raw measurements, we aggregate the local distributions in a frame-wise fashion at each iteration. The computational cost of feature update is then only dependent on the number of scans. Finally, we develop a multiview registration system using voxel-based quantization that can be applied in real-world scenarios. The experimental results demonstrate our superiority over the baselines in terms of both accuracy and speed. Moreover, the results also show that our average positioning errors achieve the centimeter level. Related materials are available at our project page https://hyhuang1995.github.io/bareg/.

A mortar formulation for frictionless line-to-line beam contact

This paper describes the quasi-static formulation of frictionless line contact between flexible beams by employing the mortar finite element approach. Contact constraints are enforced in a weak sense along the contact region using Lagrange multipliers. A simple projection appropriate for thin beams with circular cross-sections is proposed for the computation of contact regions. It is combined with the geometrically exact beam formalism on the Lie group SE(3). Interestingly, this framework leads to a constraint gradient and a tangent stiffness invariant under rigid body transformations. The formulation is tested in some numerical examples.

Robust [formula omitted] kinematic control of manipulator robots using dual quaternion algebra

This paper proposes a robust dual-quaternion based H∞ task-space kinematic controller for robot manipulators. To address the manipulator liability to modeling errors, uncertainties, exogenous disturbances, and their influence upon the kinematics of the end-effector pose, we adapt H∞ techniques – suitable only for additive noises – to unit dual quaternions. The noise to error attenuation within the H∞ framework has the additional advantage of casting aside requirements concerning noise distributions, which are significantly hard to characterize within the group of rigid body transformations. Using dual quaternion algebra, we provide a connection between performance effects over the end-effector trajectory and different sources of uncertainties and disturbances while satisfying attenuation requirements with minimum instantaneous control effort. The result is an easy-to-implement closed form H∞ control design criterion. The performance of the proposed strategy is evaluated within different realistic simulated scenarios and validated through real experiments.

Spherical convolutions on molecular graphs for protein model quality assessment

Processing information on three-dimensional (3D) objects requires methods stable to rigid-body transformations, in particular rotations, of the input data. In image processing tasks, convolutional neural networks achieve this property using rotation-equivariant operations. However, contrary to images, graphs generally have irregular topology. This makes it challenging to define a rotation-equivariant convolution operation on these structures. In this work, we propose spherical graph convolutional network that processes 3D models of proteins represented as molecular graphs. In a protein molecule, individual amino acids have common topological elements. This allows us to unambiguously associate each amino acid with a local coordinate system and construct rotation-equivariant spherical filters that operate on angular information between graph nodes. Within the framework of the protein model quality assessment problem, we demonstrate that the proposed spherical convolution method significantly improves the quality of model assessment compared to the standard message-passing approach. It is also comparable to state-of-the-art methods, as we demonstrate on critical assessment of structure prediction benchmarks. The proposed technique operates only on geometric features of protein 3D models. This makes it universal and applicable to any other geometric-learning task where the graph structure allows constructing local coordinate systems. The method is available at https://team.inria.fr/nano-d/software/s-gcn/.

A nonlocal operator method for finite deformation higher-order gradient elasticity

We present a general finite deformation higher-order gradient elasticity theory. The governing equations of the higher-order gradient solid along with boundary conditions of various orders are derived from a variational principle using integration by parts on the surface. The objectivity of the energy functional is achieved by carefully selecting the invariants under rigid-body transformation. The third-order gradient solid theory includes more than 10.000 material parameters. However, under certain simplifications, the material parameters can be greatly reduced; down to 3. With this simplified formulation, we develop a nonlocal operator method and apply it to several numerical examples. The numerical analysis shows that the high gradient solid theory exhibits a stiffer response compared to a ’conventional’ hyperelastic solid. The numerical tests also demonstrate the capability of the nonlocal operator method in solving higher-order physical problems.

A novel deep-learning-based approach for automatic reorientation of 3D cardiac SPECT images.

Reconstructed transaxial cardiac SPECT images need to be reoriented into standard short-axis slices for subsequent accurate processing and analysis. We proposed a novel deep-learning-based method for fully automatic reorientation of cardiac SPECT images and evaluated its performance on data from two clinical centers. We used a convolutional neural network to predict the 6 rigid-body transformation parameters and a spatial transformation network was then implemented to apply these parameters on the input images for image reorientation. A novel compound loss function which balanced the parametric similarity and penalized discrepancy of the prediction and training dataset was utilized in the training stage. Data from a set of 322 patients underwent data augmentation to 6440 groups of images for the network training, and a dataset of 52 patients from the same center and 23 patients from another center were used for evaluation. Similarity of the 6 parameters was analyzed between the proposed and the manual methods. Polar maps were generated from the output images and the averaged count values of the 17 segments were computed from polar maps to evaluate the quantitative accuracy of the proposed method. All the testing patients achieved automatic reorientation successfully. Linear regression results showed the 6 predicted rigid parameters and the average count value of the 17 segments having good agreement with the reference manual method. No significant difference by paired t-test was noticed between the rigid parameters of our method and the manual method (p > 0.05). Average count values of the 17 segments show a smaller difference of the proposed and manual methods than those between the existing and manual methods. The results strongly indicate the feasibility of our method in accurate automatic cardiac SPECT reorientation. This deep-learning-based reorientation method has great promise for clinical application and warrants further investigation.

Total Least-Squares Determination of Body Segment Attitude.

To examine segment and joint attitudes when using image-based motion capture, it is necessary to determine the rigid body transformation parameters from an inertial reference frame to a reference frame fixed in a body segment. Determine the rigid body transformation parameters must account for errors in the coordinates measured in both reference frames, a total least-squares problem. This study presents a new derivation that shows that a singular value decomposition-based method provides a total least-squares estimate of rigid body transformation parameters. The total least-squares method was compared with an algebraic method for determining rigid body attitude (TRIAD method). Two cases were examined: case 1 where the positions of a marker cluster contained noise after the transformation, and case 2 where the positions of a marker cluster contained noise both before and after the transformation. The white noise added to position data had a standard deviation from zero to 0.002 m, with 101 noise levels examined. For each noise level, 10 000 criterion attitude matrices were generated. Errors in estimating rigid body attitude were quantified by computing the angle, error angle, required to align the estimated rigid body attitude with the actual rigid body attitude. For both methods and cases, as the noise level increased the error angle increased, with errors larger for case 2 compared with case 1. The singular value decomposition (SVD)-based method was superior to the TRIAD algorithm for all noise levels and both cases, and provided a total least-squares estimate of body attitude.

Improved Point Cloud Registration with Scale Invariant Feature Extracted

The efficiency and accuracy of point set registration is always a challenge to deal with. In this paper, we propose an improved algorithm using a scale invariant feature extracted. The larger transformation scale and rotation angle cause lower registration accuracy. The initial corresponding point set can be obtained using a scale invariant feature transform (SIFT) operator. In addition, the geometric features of the points are combined to remove the wrong points. The unit quaternion algorithm is used to estimate the best rigid body transformation matrix for precise registration. The experiments show that the registration accuracy increases by 7.99%, while the time consumption decreased by 6.24% in a typical indoor scene.

Robust wavefront segment registration based on a parallel approach.

This paper presents a robust registration algorithm for wavefront reconstruction from multiple partial measurements. Wavefronts exceeding the dynamic range or size of the Shack-Hartmann sensor can be measured as a set of segments. The wavefront is reconstructed by parallel registration of these wavefront segments, enabling compensation for sensor misalignment as well as for phase differences. For registration, a global mismatch metric is minimized by rigid body transformations and propagation of the wavefront segments. Apart from the description of the algorithm, a simulation-based evaluation and comparison to the iterative closest point (ICP) algorithm is performed. It is shown that in the case of a noisy data set, the parallel approach enables reconstruction errors that are a factor of 10 smaller than the result obtained with the ICP algorithm.

Thermomechanical modeling of nonlinear internal hysteresis due to incomplete phase transformation in pseudoelastic shape memory alloys

This paper presents a thermomechanical model for pseudoelastic shape memory alloys (SMAs) accounting for internal hysteresis effect due to incomplete phase transformation. The model is developed within the finite-strain framework, wherein the deformation gradient is multiplicatively decomposed into thermal dilation, rigid body rotation, elastic and transformation parts. Helmholtz free energy density comprises three components: the reversible thermodynamic process , the irreversible thermodynamic process and the physical constraints of both. In order to capture the multiple internal hysteresis loops in SMA, two internal variables representing the transition points of the forward and reverse phase transformation, $$\phi _s^f$$ and $$\phi _s^r$$ , are introduced to describe the incomplete phase transformation process. Evolution equations of the internal variables are derived and linked to the phase transformation. Numerical implementation of the model features an Euler discretization and a cutting-plane algorithm. After validation of the model against the experimental data, numerical examples are presented, involving a SMA-based vibration system and a crack SMA specimen subjected to partial loading–unloading case. Simulation results well demonstrate the internal hysteresis and free vibration behavior of SMA.

Technical Note: Extended field-of-view (FOV) MRI distortion determination through multi-positional phantom imaging.

Comprehensive characterization of geometric distortions for MRI simulators and MRI‐guided treatment delivery systems is typically performed with large phantoms that are costly and unwieldy to handle. Here we propose an easily implementable methodology for MR distortion determination of the entire imaging space of the scanner through the use of a compact commercially available distortion phantom. The MagphanRT phantom was scanned at several locations within a MR scanner. From each scan, an approximate location of the phantom was determined from a subset of the fiducial spheres. The fiducial displacements were determined, and a displacement field was fitted to the displacement data using the entire multi‐scan data set. An orthogonal polynomial expansion fitting function was used that had been augmented to include independent rigid‐body transformations for each scan. The rigid‐body portions of the displacement field were thereafter discarded, and the resultant fit then represented the distortion field. Multi‐positional scans of the phantom were used successfully to determine the distortion field with extended coverage. A single scan of the phantom covered 20 cm in its smallest dimension. By stitching together overlapping scans we extended the distortion measurements to 30 cm. No information about the absolute location or orientation of each scan was required. The method, termed the Multi‐Scan Expansion (MSE) method, can be easily applied for larger field‐of‐views (FOVs) by using a combination of larger phantom displacements and more scans. The implementation of the MSE method allows for distortion determination beyond the physical limitations of the phantom. The method is scalable to the user’s needs and does not require any specialized equipment. This approach could open up for easier determination of the distortion magnitude at distances further from the scanner’s isocenter. This is especially important in the newly proposed methodologies of MR‐only simulation in RT and in adaptive replanning in MR linac systems.

Calibration routine for a telecentric stereo vision system considering affine mirror ambiguity

A robust calibration approach for a telecentric stereo camera system for three-dimensional (3-D) surface measurements is presented, considering the effect of affine mirror ambiguity. By optimizing the parameters of a rigid body transformation between two marker planes and transforming the two-dimensional (2-D) data into one coordinate frame, a 3-D calibration object is obtained, avoiding high manufacturing costs. Based on the recent contributions in the literature, the calibration routine consists of an initial parameter estimation by affine reconstruction to provide good start values for a subsequent nonlinear stereo refinement based on a Levenberg–Marquardt optimization. To this end, the coordinates of the calibration target are reconstructed in 3-D using the Tomasi–Kanade factorization algorithm for affine cameras with Euclidean upgrade. The reconstructed result is not properly scaled and not unique due to affine ambiguity. In order to correct the erroneous scaling, the similarity transformation between one of the 2-D calibration plane points and the corresponding 3-D points is estimated. The resulting scaling factor is used to rescale the 3-D point data, which then allows in combination with the 2-D calibration plane data for a determination of the start values for the subsequent nonlinear stereo refinement. As the rigid body transformation between the 2-D calibration planes is also obtained, a possible affine mirror ambiguity in the affine reconstruction result can be robustly corrected. The calibration routine is validated by an experimental calibration and various plausibility tests. Due to the usage of a calibration object with metric information, the determined camera projection matrices allow for a triangulation of correctly scaled metric 3-D points without the need for an individual camera magnification determination.

Maximal Disjoint Ball Decompositions for shape modeling and analysis

A large number of geometric representations have been proposed to address the needs of specific engineering applications. This, in turn, exacerbates the inherent challenges associated with system interoperability for downstream engineering applications.In this paper, we define the Maximal Disjoint Ball Decomposition (MDBD) as the location of the largest d-dimensional closed balls recursively placed in the interior of a d-dimensional domain and show that the proposed decomposition can be used to provide an underlying common analysis framework for geometric models using different representation schemes. Importantly, our decomposition only relies on the ability of an existing geometric representation to compute distances, which must be supported by any valid geometric representation scheme, and does not require an explicit representation conversion. Moreover, MDBD is unique for a given domain up to rigid body transformation, reflection, as well as uniform scaling, and its formulation suggests appealing stability and robustness properties against small boundary modifications.Furthermore, we show that MDBD can be used as a universal shape descriptor to perform shape similarity of models coming from various geometric representation schemes. A salient attribute of this decomposition is that it provides adequate support for key downstream applications for models coming from disparate geometric representations. For example, MDBD can be naturally used to carry out meshless solutions to boundary value problems; efficient collision detection; and 3D mesh generation of models that use any valid geometric representation scheme. Finally, our hierarchical formulation of the proposed Maximal Disjoint Ball Decomposition allows for a choice of model complexity at run-time to match the available computational resources.

Fractional derivative for interpolation in [formula omitted] and SO(n) applications in functionally graded materials and rigid body transformations

An integration of fractional calculus, data interpolation, and Lie group leads to new treatments of interpolation problems. A local and centered fractional derivative is introduced, which enables the fractional interpolant to create a Cα-smooth (α∈R+) curve by extending integer order cost functions to fractional ones. The fractional interpolant fills the gaps between the traditional linear interpolating segments, cubic splines, and higher-order splines. Interpolating rigid body transformations has enormous applications in mechanics, computer graphics, and robotics. Previous approaches have provided the re-parametrization methods, the recursive methods (e.g., de Casteljau’s algorithm), and the gradient methods. To approximate the correct interpolating curve on SO(3), a closed-form model that merges the tangent spaces of knots is proposed. The model first constructs a family of candidate curves and then combines them into an improved approximation. Applications in modeling functionally graded materials and rigid body transformations are discussed.

3D Nasal Magnetic Resonance Image Registration by Maximization of Mutual Information

The magnetic resonance image (MRI) is widely used in medical treatment, which is harmless for human body. However, more noise than the CT image sometimes can be a problem when doctor focus on details of some narrow structure of human body such as nasal. It is necessary to process the MRI like image fusion before using it. Subjects have to move head during a few MR scans. Image registration can help all corresponding points find their own correct position, so that it can be processed and give us more information from not only one time scan. Mutual information is a good mathematics tool in statistics and information theory. It can describe the relationship between input signal and output signal. In this paper, they are reference image data set and float image data set, and the process between them are some little bit head move and some other influence during scanning. The rigid body transformation is used to reduce the impact of head move because the nasal consisting of bones almost don’t changes shape during scan. Registered images from another scan and reference image can get together to be used in image fusion and reconstruction.

Research on the Method of Multi-point Pressing Adjustment of Space Mechanism Driven by Measurement

In order to solve the problems of difficult assembly and adjustment and poor operation accessibility in the assembly process of multi-point pressure-type large-scale equipment on spacecraft, this paper presents a method of multi-point compact assembly of space mechanism driven by measurement. The method establishes the geometric constraint mathematical model of the equipment pressing mechanism, proposes the assembly coordinate system based on the mounting hole and the compensation method based on the rigid body transformation, and develops the relevant software according to the method. This method has been verified during the installation of the equipment and has achieved good results, which can be used as a reference for other digital assembly methods of aerospace equipment.

Matching Method of Cultural Relic Fragments Constrained by Thickness and Contour Feature

The virtual restoration of cultural relics by adopting computer technology is the trend of cultural relics protection and value mining. In order to solve the problem of large error in the existing matching methods of non-thin-walled cultural relic fragments, in this paper, a matching method of cultural relic fragments is proposed, when the thickness feature and the contour feature are combined, and the strategy of coarse matching followed by fine matching is adopted. Firstly, the broken contour of cultural relic fragments is extracted, and the upper and lower contour lines are identified; secondly, the thickness feature is calculated and the thickness histogram is constructed. After that, the initial matching of fragments is completed according to the similarity of the histogram. Thirdly, the fracture contour is segmented, and the fragments of the mismatching relationship in the initial matching are also eliminated by the modified Hausdorff distance to optimize the coarse matching results. Finally, the SVD method is adopted to solve the rigid body transformation parameters, and the ICP algorithm is employed to accurately align the fine matching. The experimental results show that with the method in this paper, excellent matching results have been obtained regarding the fragments of the Terracotta Warriors. Compared with matching methods of other cultural relic fragments, the accuracy and algorithm cost of this method are better.