B-spline Interpolation Method Research Articles

A novel approach for estimating lung tumor motion based on dynamic features in 4D-CT

Due to the high expenses involved, 4D-CT data for certain patients may only include five respiratory phases (0%, 20%, 40%, 60%, and 80%). This limitation can affect the subsequent planning of radiotherapy due to the absence of lung tumor information for the remaining five respiratory phases (10%, 30%, 50%, 70%, and 90%). This study aims to develop an interpolation method that can automatically derive tumor boundary contours for the five omitted phases using the available 5-phase 4D-CT data. The dynamic mode decomposition (DMD) method is a data-driven and model-free technique that can extract dynamic information from high-dimensional data. It enables the reconstruction of long-term dynamic patterns using only a limited number of time snapshots. The quasi-periodic motion of a deformable lung tumor caused by respiratory motion makes it suitable for treatment using DMD. The direct application of the DMD method to analyze the respiratory motion of the tumor is impractical because the tumor is three-dimensional and spans multiple CT slices. To predict the respiratory movement of lung tumors, a method called uniform angular interval (UAI) sampling was developed to generate snapshot vectors of equal length, which are suitable for DMD analysis. The effectiveness of this approach was confirmed by applying the UAI-DMD method to the 4D-CT data of ten patients with lung cancer. The results indicate that the UAI-DMD method effectively approximates the lung tumor’s deformable boundary surface and nonlinear motion trajectories. The estimated tumor centroid is within 2 mm of the manually delineated centroid, a smaller margin of error compared to the traditional BSpline interpolation method, which has a margin of 3 mm. This methodology has the potential to be extended to reconstruct the 20-phase respiratory movement of a lung tumor based on dynamic features from 10-phase 4D-CT data, thereby enabling more accurate estimation of the planned target volume (PTV).

A Certified Cubic B-Spline Interpolation Method with Tangential Direction Constraints

A Certified Cubic B-Spline Interpolation Method with Tangential Direction Constraints

Improved Collision Avoidance Algorithm of Autonomous Rice Transplanter Based on Virtual Goal Point

To ensure the operation safety and efficiency of an autonomous rice transplanter, a path planning method of obstacle avoidance based on the improved artificial potential field is proposed. Firstly, the obstacles are divided into circular or elliptic obstacles according to the difference between the length and width of an obstacle as well as the angle between the vehicle’s forward direction and the length direction of the obstacle. Secondly, improved repulsive fields for circular and elliptic models are developed. To escape the local minimum and goal inaccessibility of the traditional artificial potential field as well as meet the requirements of agronomy and vehicle kinematics constraints, the adaptive setting and adjusting strategy for virtual goal points is proposed according to relative azimuth between obstacle and vehicle. The path smoothing method based on the B-spline interpolation method is presented. Finally, the intelligent obstacle avoidance algorithm is designed, and the path evaluation rule is given to obtain the low-cost, non-collision, smooth and shortest obstacle avoidance path. To verify the effectiveness of the proposed obstacle avoidance algorithm, simulation and field experiments are conducted. Simulation and experimental results demonstrate that the proposed improved collision avoidance algorithm is highly effective and realizable.

Quad-Rotor Unmanned Aerial Vehicle Path Planning Based on the Target Bias Extension and Dynamic Step Size RRT* Algorithm

For the path planning of quad-rotor UAVs, the traditional RRT* algorithm has weak exploration ability, low planning efficiency, and a poor planning effect. A TD-RRT* algorithm based on target bias expansion and dynamic step size is proposed herein. First, random-tree expansion is combined with the target bias strategy to remove the blindness of the random tree, and we assign different weights to the sampling point and the target point so that the target point can be quickly approached and the search speed can be improved. Then, the dynamic step size is introduced to speed up the search speed, effectively solving the problem of invalid expansion in the process of trajectory generation. We then adjust the step length required for the expansion tree and obstacles in real time, solve the opposition between smoothness and real time in path planning, and improve the algorithm’s search efficiency. Finally, the cubic B-spline interpolation method is used to modify the local inflection point of the path of the improved RRT* algorithm to smooth the path. The simulation results show that compared with the traditional RRT* algorithm, the number of iterations of path planning of the TD-RRT* algorithm is reduced, the travel distance from the starting position to the end position is shortened, the time consumption is reduced, the path route is smoother, and the path optimization effect is better. The TD-RRT* algorithm based on target bias expansion and dynamic step size significantly improves the planning efficiency and planning effect of quad-rotor UAVs in a three-dimensional-space environment.

B-spline convected particle domain interpolation method

The B-spline material point method (BSMPM) has been shown to be a promising approach to effectively mitigate the cell-crossing instability by using high-order B-spline basis functions. However, the BSMPM still suffers from the quadrature error, another well-known source of inaccuracy in the material point methods. On the other hand, the convected particle domain interpolation (CPDI) method effectively reduces the quadrature error by using alternative basis functions. The B-spline basis functions can be naturally used within the CPDI formulation, here called the BSCPDI method. The BSCPDI may be prone to the cell-crossing instability since the alternative basis functions in the BSCPDI are always C0-continuous despite the high-continuity of the B-spline basis functions used as the original grid basis functions. In this paper, the reproducibility of the BSCPDI effective basis function gradients and the susceptibility of the method to the cell-crossing instability are investigated analytically and numerically. The effectiveness of the BSCPDI in mitigating the quadrature error is also investigated through numerical simulations.

Research on Three-Dimensional Shape Curve Reconstruction Technology for a Scraper Conveyor on an Intelligent Working Face.

"Three straight and two flat" is the inevitable demand when realizing the intelligent mining of a fully mechanized mining face. To address the crucial technical issue of lacking accurate perception of the shape of the scraper conveyor during intelligent coal mining, a three-dimensional curvature sensor involving fiber Bragg grating (FBG) is used as a perceptive tool to conduct curve reconstruction research based on different local motion frames and to reconstruct the shape of the scraper conveyor. Firstly, the formation process of the 'S'-shaped bending section of the scraper conveyor during the pushing process is determined. Based on the FBG sensing principle, a mathematical model between the variation in the central wavelength and the strain and curvature is established, and the cubic B-spline interpolation method is employed to continuously process the obtained discrete curvature. Secondly, based on differential geometry, a spatial curve reconstruction algorithm based on the Frenet moving frame is derived, and the shape curve prediction interpolation model is built based on a gated recurrent unit (GRU) model, which reduces the impact of the decrease in curve reconstruction accuracy caused by damage to some grating measuring points. Finally, an experimental platform was designed and built, and sensors with curvature radii of 6 m, 7 m, and 8 m were tested. The experimental results showed that the reconstructed curve was essentially consistent with the actual shape, and the absolute error at the end was about 2 mm. The feasibility of this reconstruction algorithm in engineering has been proven, and this is of great significance in achieving shape curve perception and straightness control for scraper conveyors.

Multi-objective Optimal Motion Planning of Heavy-duty Assembly Robot for Large Spacecraft Entering Cabin

The space inside the space capsule such as the space station sky and the core module is narrow, the size of the depth is large, and the bearing points are scattered and weak, there are some difficulties in loading, large size, different shape, complicated interface, scattered position, difficult position and pose adjustment, high assembly risk, etc.. To solve these problems, a six-DOF heavy-duty assembly robot is proposed in this paper. The robot adopts the combination of linear drive and rotating joint to increase the working space and bearing capacity of the robot. The kinematics and dynamics analysis model of the robot is established, and the path planning is carried out by means of quintic non-uniform B-spline interpolation method, considering fully the space constraints of the assembled equipment, a multi-objective trajectory optimization model based on NSGA2 algorithm is established to obtain the Pareto optimal solution set with time, impact and energy consumption as optimization objectives, prove that the equipment can be efficient and smooth. Reliable installation, with less impact and less power consumption under multi-objective optimization analysis.

Fully automatic DOM generation method based on optical flow field dense image matching

ABSTRACT Automatic Digital Orthophoto Map (DOM) generation plays an important role in many downstream works such as land use and cover detection, urban planning, and disaster assessment. Existing DOM generation methods can generate promising results but always need ground object filtered DEM generation before otho-rectification; this can consume much time and produce building facade contained results. To address this problem, a pixel-by-pixel digital differential rectification-based automatic DOM generation method is proposed in this paper. Firstly, 3D point clouds with texture are generated by dense image matching based on an optical flow field for a stereo pair of images, respectively. Then, the grayscale of the digital differential rectification image is extracted directly from the point clouds element by element according to the nearest neighbor method for matched points. Subsequently, the elevation is repaired grid-by-grid using the multi-layer Locally Refined B-spline (LR-B) interpolation method with triangular mesh constraint for the point clouds void area, and the grayscale is obtained by the indirect scheme of digital differential rectification to generate the pixel-by-pixel digital differentially rectified image of a single image slice. Finally, a seamline network is automatically searched using a disparity map optimization algorithm, and DOM is smartly mosaicked. The qualitative and quantitative experimental results on three datasets were produced and evaluated, which confirmed the feasibility of the proposed method, and the DOM accuracy can reach 1 Ground Sample Distance (GSD) level. The comparison experiment with the state-of-the-art commercial softwares showed that the proposed method generated DOM has a better visual effect on building boundaries and roof completeness with comparable accuracy and computational efficiency.

Super-Resolution Reconstruction of Speckle Images of Engineered Bamboo Based on an Attention-Dense Residual Network.

With the global population surge, the consumption of nonrenewable resources and pollution emissions have reached an alarming level. Engineered bamboo is widely used in construction, mechanical and electrical product packaging, and other industries. Its main damage is the material fracture caused by the expansion of initial cracks. In order to accurately detect the length of crack propagation, digital image correlation technology can be used for calculation. At present, the traditional interpolation method is still used in the reconstruction of engineered bamboo speckle images for digital correlation technology, and the performance is relatively lagging. Therefore, this paper proposes a super-resolution reconstruction method of engineering-bamboo speckle images based on an attention-dense residual network. In this study, the residual network is improved by removing the BN layer, using the loss function, introducing the attention model, and designing an attention-intensive residual block. An image super-resolution model based on the attention-dense residual network is proposed. Finally, the objective evaluation indexes PSNR and SSIM and subjective evaluation index MOS were used to evaluate the performance of the model. The ADRN method was 29.19 dB, 0.938, and 3.19 points in PSNR, SSIM, and MOS values. Compared to the traditional BICUBIC B-spline interpolation method, the speckle images reconstructed by this model increased by 8.55 dB, 0.323, and 1.43 points, respectively. Compared to the SRResNet method, the speckle images reconstructed by this model were increased by 4.53 dB, 0.111, and 0.14 points, respectively. The reconstructed speckle images of engineered bamboo were clearer, and the image features were more obvious, which could better identify the tip crack position of the engineered bamboo. The results show that the super-resolution reconstruction effect of engineered-bamboo speckle images can be effectively improved by adding the attention mechanism to the residual network. This method has great application value.

Error Compensation Trajectory Planning Method of Brake Disc Shaft Hole Assembly considering Robot Accumulated Error

Aiming at the problem of alignment deviation between shaft and hole caused by accumulated error in the assembly process of brake disc shaft hole, a trajectory planning method for compensating accumulated error is proposed. First, the path before the error is planned, and then the second compensation path is planned between the error position and the actual target point, so as to realize the accurate assembly of the brake disc. In this paper, the IRB 1410 robot is taken as the research object, and its kinematic model is established by using the improved D-H parameter method. The joint space quintic B-spline interpolation method was used to carry out trajectory planning, and the improved particle swarm optimization algorithm was introduced to solve the optimization. The optimal time and smooth trajectory were expected to be obtained. Then, using MATLAB software to simulate, compared with the nonoptimized trajectory, not only is the trajectory running time reduced from 8.6 s to 6.7 s but also the maximum joint change angle of each joint is reduced, which proves that the algorithm has optimization effect on trajectory running time and stability. Finally, the accuracy verification experiment of the algorithm is carried out, and the error between simulation and experiment is less than 6%, which shows the effectiveness of the method. This research provides a theoretical basis for improving the responsiveness and stability of brake disc assembly.

Spatiotemporal Calibration of Camera-LiDAR Using Nonlinear Angular Constraints on Multiplanar Target

The combinations of data captured from diverse sensors can yield reliable geometric and semantic information. However, calibration process must be preceded to make use of combined data. Calibration methods are classified by the adjusted parameters. Spatial calibration, which merges data to a single spatial reference frame, adjusts spatial parameters. Moreover, temporal offset parameter must be adjusted for sensors to acquire data under dynamic conditions, which is known as temporal calibration. In this study, a novel constraint adjustment method was proposed for spatiotemporal calibration, which combines mobile light detection and ranging (LiDAR) sensor with visual camera. It estimates seven parameters–three lever arm parameters, three bore-sight parameters, and temporal offset parameter–simultaneously. A nearly orthogonal multiplanar chessboard target was built for nonlinear angular constraints. B-spline interpolation method was employed to interpolate the plane parameters obtained from the camera and facilitate estimation of the temporal offset. Additionally, the calibration results were evaluated using correlation values and standard errors of the estimated parameters. The sequential quadratic programming method, which yields robust results for nonlinear optimization problem, was used to optimize a point-to-plane distance model subjected to nonlinear angular constraints. Assorted experiments with different sensor motions were conducted to evaluate the effects of the nonlinear angular constraints. Compared to the results of nonconstrained calibration methods, the results of the proposed method indicate lower correlation values between the calibration parameters, reduced standard errors, and fewer iterations in the optimization process, which validates the superiority of the proposed calibration method.

An Isogeometric analysis based method for frictional elastic contact problems with randomly rough surfaces

The problem addressed in this paper concerns the frictional contact between an elastomer and a rigid body with randomly rough surfaces. The work is accomplished on the basis of two crucial elements: a framework for generating random geometries and a robust frictional contact algorithm, both of which are realised in the approach of Isogeometric analysis (IGA) for its high accuracy and robustness. For the former, a new Isogeometric framework for random geometry modelling is proposed, which combines the random field generation based on Karhunen–Loève expansion theory with Non-Uniform Rational B-Spline (NURBS) interpolation method. For the latter, a mortar-based frictional contact algorithm in 2D large deformation regime is adopted incorporating a modified closest point projection method for detection of contact. Numerical experiments are conducted with several settings such as ‘rough–smooth’, ‘smooth–rough’ and ‘rough–rough’ contact, depending on which side of the contact pair the randomly rough surface belongs to. The ratio of the global coefficient of friction to the prescribed local one and the ratio of true contact area to the nominal contact area are characterised under these settings, and factors like the root mean square roughness and correlation length of the random surface and the external traction are discovered to have a significant influence on the two ratios.

Path planning of the fruit tree pruning manipulator based on improved RRT-Connect algorithm

Aiming to realize the obstacle avoidance of the fruit tree pruning manipulator in unstructured complex natural environment, an improved bidirectional fast extended random tree (RRT-Connect) algorithm was presented in this study. The manipulator and obstacles were properly simplified based on their geometrical characteristics to build collision detection models taking account of the obstacles, ground, and manipulator itself and to carry out the obstacle avoidance path planning. Goal-biased strategy and adaptive step size adjustment principle were introduced to accelerate the path search speed. Bidirectional pruning optimal strategy and cubic non-uniform B-spline interpolation method were adopted to optimize the path generated by RRT-Connect. The simulation path planning experiment was carried out in the simulation system of the fruit tree pruning manipulator and the practical obstacle avoidance path planning experiment was carried out on the real fruit tree pruning manipulator path planning experiment platform. The results showed that the path planning time and the path length of the improved RRT-Connect algorithm reduced by about 55% and 60% respectively compared with the basic RRT-Connect algorithm. The path planning success rate of the improved RRT-Connect algorithm was 100%, and the planned path was smooth, continual and executable, which could effectively guide the manipulator to avoid obstacles and lead the end effector of the manipulator to the goal point. The proposed improved algorithm not only has certain application value for obstacle avoidance of the fruit tree pruning manipulator in fruit tree pruning environment, but also has theoretical reference value for path planning of other types of robots. Keywords: manipulator, path planning, RRT-Connect, jujube pruning, obstacle avoidance, non-uniform B-spline DOI: 10.25165/j.ijabe.20221502.6249 Citation: Chen Y Y, Fu Y X, Zhang B, Fu W, Shen C J. Path planning of the fruit tree pruning manipulator based on improved RRT-Connect algorithm. Int J Agric & Biol Eng, 2022; 15(2): 177–188.

Construction of fine resolution bioclimatic variables for Central Highlands and Southern Central Coast of Vietnam

In this study, 19 surface bioclimatic variables of high spatial resolution 0.00226o (~ 250 m) are generated in a Geographic Information System by the combination of (1) the raster dataset of monthly temperature and precipitation obtained from the global WorldClim database at 0.00833o spatial resolution for the period of 1960–2000; and (2) the climate data (temperature and precipitation) of the Central Highlands and Southern Central Coast collected from the 31 temperature and 97 precipitation recording sites for the period of 1991–2015. The statistical downscaling method is applied, using multiple linear regression analysis, in which elevation, geographic coordinates, and distance from the coast are treated as independent variables, to estimate the distribution of temperature; and the B-Spline interpolation method combined with multiple linear regression analysis is employed on precipitation over the study area. The outcomes of the two main analyses are computed to create 19 high spatial resolution bioclimatic variables. While using only local climate data on analyzing the regression models results in high fluctuation of estimated temperature, the combination of the two datasets is more informative. The spatial distribution of our interpolated precipitation is similar to the WorldClim data but has a smaller difference in the mean annual precipitation. The results, which shows higher spatial resolution and are closer to the observed data than those from the WorldClim, could be better applied for predicting species distribution in the region.

UAV Path Planning of Combining Ant Colony and Beetle Antennae Algorithm Using Intelligent Wireless Communication

In order to settle the problem of UAV path planning under mountain, an algorithm which based on the combination of ant colony algorithm and beetle antennae algorithm is proposed. Three dimensional environment model is established and objective function is constructed. It used ant colony algorithm to initialize the search path and the particle coordinates of all the next steps are updated by the beetle antennae algorithm. The improved algorithm adopted a new step update rule to speed up the convergence of the algorithm and used third-order B-spline interpolation method to smooth the path. Simulation results show that improved fusion algorithm has faster convergence speed and high stability by comparing with other algorithms under the same conditions, which verifies its effectiveness.

Dual Memory LSTM with Dual Attention Neural Network for Spatiotemporal Prediction.

Spatiotemporal prediction is challenging due to extracting representations being inefficient and the lack of rich contextual dependences. A novel approach is proposed for spatiotemporal prediction using a dual memory LSTM with dual attention neural network (DMANet). A new dual memory LSTM (DMLSTM) unit is proposed to extract the representations by leveraging differencing operations between the consecutive images and adopting dual memory transition mechanism. To make full use of historical representations, a dual attention mechanism is designed to capture long-term spatiotemporal dependences by computing the correlations between the current hidden representations and the historical hidden representations from temporal and spatial dimensions, respectively. Then, the dual attention is embedded into DMLSTM unit to construct a DMANet, which enables the model with greater modeling power for short-term dynamics and long-term contextual representations. An apparent resistivity map (AR Map) dataset is proposed in this paper. The B-spline interpolation method is utilized to enhance AR Map dataset and makes apparent resistivity trend curve continuous derivative in the time dimension. The experimental results demonstrate that the developed method has excellent prediction performance by comparisons with some state-of-the-art methods.

New Cubic B-Spline Approximation for Solving Linear Two-Point Boundary-Value Problems

In this study, we introduce a new cubic B-spline (CBS) approximation method to solve linear two-point boundary value problems (BVPs). This method is based on cubic B-spline basis functions with a new approximation for the second-order derivative. The theoretical new approximation for a second-order derivative and the error analysis have been successfully derived. We found that the second-order new approximation was O(h3) accurate. By using this new second-order approximation, the proposed method was O(h5) accurate. Four numerical problems consisting of linear ordinary differential equations and trigonometric equations with different step sizes were performed to validate the accuracy of the proposed methods. The numerical results were compared with the least squares method, finite difference method, finite element method, finite volume method, B-spline interpolation method, extended cubic B-spline interpolation method and the exact solutions. By finding the maximum errors, the results consistently showed that the proposed method gave the best approximations among the existing methods. We also found that our proposed method involved simple implementation and straightforward computations. Hence, based on the results and the efficiency of our method, we can say that our method is reliable and a promising method for solving linear two-point BVPs.

Interpolation Algorithm for Motion Vector Field of CTA Image and Accelerated Implementation Based on Uniform Grid and Multi-level B-spline

In order to solve the problems of slow operation speed and low registration accuracy of thin plate spline (TPS) interpolation method for motion vector field in coronary computed tomography angiography (CTA), a multi-level B-spline interpolation method (MBS) with uniform grid is proposed. On the one hand, the interpolation method used local B-spline to refine the sparse mesh layer by layer in a multiscale way to improve the accuracy of registration. On the other hand, it used the splitting matrix method to interpolate the motion vector field, greatly reducing the operation time of interpolation. The experimental results show that the proposed method can be used for CTA image registration efficiently.

Continuous body 3-D reconstruction of limbless animals.

Limbless animals such as snakes, limbless lizards, worms, eels and lampreys move their slender, long bodies in three dimensions to traverse diverse environments. Accurately quantifying their continuous body's 3-D shape and motion is important for understanding body-environment interactions in complex terrain, but this is difficult to achieve (especially for local orientation and rotation). Here, we describe an interpolation method to quantify continuous body 3-D position and orientation. We simplify the body as an elastic rod and apply a backbone optimization method to interpolate continuous body shape between end constraints imposed by tracked markers. Despite over-simplifying the biomechanics, our method achieves a higher interpolation accuracy (∼50% error) in both 3-D position and orientation compared with the widely used cubic B-spline interpolation method. Beyond snakes traversing large obstacles as demonstrated, our method applies to other long, slender, limbless animals and continuum robots. We provide codes and demo files for easy application of our method.

Adaptive Physics-Based Non-Rigid Registration for Immersive Image-Guided Neuronavigation Systems.

Objective: In image-guided neurosurgery, co-registered preoperative anatomical, functional, and diffusion tensor imaging can be used to facilitate a safe resection of brain tumors in eloquent areas of the brain. However, the brain deforms during surgery, particularly in the presence of tumor resection. Non-Rigid Registration (NRR) of the preoperative image data can be used to create a registered image that captures the deformation in the intraoperative image while maintaining the quality of the preoperative image. Using clinical data, this paper reports the results of a comparison of the accuracy and performance among several non-rigid registration methods for handling brain deformation. A new adaptive method that automatically removes mesh elements in the area of the resected tumor, thereby handling deformation in the presence of resection is presented. To improve the user experience, we also present a new way of using mixed reality with ultrasound, MRI, and CT.Materials and methods: This study focuses on 30 glioma surgeries performed at two different hospitals, many of which involved the resection of significant tumor volumes. An Adaptive Physics-Based Non-Rigid Registration method (A-PBNRR) registers preoperative and intraoperative MRI for each patient. The results are compared with three other readily available registration methods: a rigid registration implemented in 3D Slicer v4.4.0; a B-Spline non-rigid registration implemented in 3D Slicer v4.4.0; and PBNRR implemented in ITKv4.7.0, upon which A-PBNRR was based. Three measures were employed to facilitate a comprehensive evaluation of the registration accuracy: (i) visual assessment, (ii) a Hausdorff Distance-based metric, and (iii) a landmark-based approach using anatomical points identified by a neurosurgeon.Results: The A-PBNRR using multi-tissue mesh adaptation improved the accuracy of deformable registration by more than five times compared to rigid and traditional physics based non-rigid registration, and four times compared to B-Spline interpolation methods which are part of ITK and 3D Slicer. Performance analysis showed that A-PBNRR could be applied, on average, in <2 min, achieving desirable speed for use in a clinical setting.Conclusions: The A-PBNRR method performed significantly better than other readily available registration methods at modeling deformation in the presence of resection. Both the registration accuracy and performance proved sufficient to be of clinical value in the operating room. A-PBNRR, coupled with the mixed reality system, presents a powerful and affordable solution compared to current neuronavigation systems.