B-spline Interpolation Research Articles

Autoencoding low-resolution MRI for semantically smooth interpolation of anisotropic MRI.

High-resolution medical images are beneficial for analysis but their acquisition may not always be feasible. Alternatively, high-resolution images can be created from low-resolution acquisitions using conventional upsampling methods, but such methods cannot exploit high-level contextual information contained in the images. Recently, better performing deep-learning based super-resolution methods have been introduced. However, these methods are limited by their supervised character, i.e. they require high-resolution examples for training. Instead, we propose an unsupervised deep learning semantic interpolation approach that synthesizes new intermediate slices from encoded low-resolution examples. To achieve semantically smooth interpolation in through-plane direction, the method exploits the latent space generated by autoencoders. To generate new intermediate slices, latent space encodings of two spatially adjacent slices are combined using their convex combination. Subsequently, the combined encoding is decoded to an intermediate slice. To constrain the model, a notion of semantic similarity is defined for a given dataset. For this, a new loss is introduced that exploits the spatial relationship between slices of the same volume. During training, an existing in-between slice is generated using a convex combination of its neighboring slice encodings. The method was trained and evaluated using publicly available cardiac cine, neonatal brain and adult brain MRI scans. In all evaluations, the new method produces significantly better results in terms of Structural Similarity Index Measure and Peak Signal-to-Noise Ratio (p<0.001 using one-sided Wilcoxon signed-rank test) than a cubic B-spline interpolation approach. Given the unsupervised nature of the method, high-resolution training data is not required and hence, the method can be readily applied in clinical settings.

Path Optimization of Agricultural Robot Based on Immune Ant Colony: B-Spline Interpolation Algorithm

This study presents a path planning algorithm based on immune ant colony B spline interpolation to eliminate path duplication and corner inflection points, increase the smoothness of the agricultural robot’s path trajectory, and enhance the path planning performance. Firstly, this study improves the convergence speed of the algorithm by introducing an adaptive factor that obeys the normal distribution to optimize the path heuristic function. Secondly, to strengthen the variety of the target path search, an immune algorithm was utilized to perform a global investigation of the appropriate routes and assign the initial pheromones of the ant colony. Then, the adaptive judgment factor is introduced based on the incentive degree function and the pheromone evaporation coefficient, and the update formula are adjusted to promote the algorithm’s flexibility while suppressing the optimal regional problem. Finally, the pathways are processed using a cubic B spline interpolation method to remove the edges and minimize the peak inflection points. To verify the specific optimization performance of the algorithm in this paper, we have selected the same type of improved algorithm as a comparison and tested it in a raster map model. The simulation results demonstrate that the values of the proposed algorithm paths and the standard deviation of the tracks are smaller than the comparison algorithm, which indicates the higher performance of the algorithm in searching the optimal routes and more flexible and accurate search. Compared with the comparison algorithm, the average time-consuming reduction rate of the algorithm in this paper is between 38% and 45% in different grid maps, and the number of turns is reduced by 33% to 58%. It meets the requirements of the actual work on the robot.

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.

Trigonometric tension B-spline collocation approximations for time fractional Burgers’ equation

This manuscript’s aim is to form and examine the numerical simulation of Caputo-time fractional nonlinear Burgers’ equation via collocation approach with trigonometric tension B-splines as base functions. First, L1 discretization formula is utilized for the time fractional derivative and after linearizing the nonlinear term, the trigonometric tension B-spline interpolants are utilized to get a system of simultaneous linear equations that are solved via Gauss elimination method. Thus, numerical approximation at the desired time level is obtained. It is demonstrated via von-Neumann approach that proposed scheme produces stable solutions. The results of six different test examples having their analytical solutions are compared with the results in the literature to validate the accuracy and efficiency of the scheme.

Unsupervised arterial spin labeling image superresolution via multiscale generative adversarial network.

Arterial spin labeling (ASL) magnetic resonance imaging (MRI) is an advanced noninvasive imaging technology that can measure cerebral blood flow (CBF) quantitatively without a contrast agent injection or radiation exposure. However, because of the weak labeling, conventional ASL images usually suffer from low signal-to-noise ratio (SNR), poor spatial resolution, and long acquisition time. Therefore, a method that can simultaneously improve the spatial resolution and SNR isneeded. In this work, we proposed an unsupervised superresolution (SR) method to improve ASL image resolution based on a pyramid of generative adversarial networks (GAN). Through layer-by-layer training, the generators can learn features from the coarsest to the finest. The last layer's generator that contains fine details and textures was used to generate the final SR ASL images. In our proposed framework, the corresponding T1-weighted MR image was supplied as a second-channel input of the generators to provide high-resolution prior information. In addition, a low-pass-filter loss term was included to suppress the noise of the original ASL images. To evaluate the performance of the proposed framework, a simulation study and two real-patient experiments based on the in vivo datasets obtained from three healthy subjects on a 3T MR scanner were conducted, regarding the low-resolution (LR) to normal-resolution (NR) and the NR-to-SR tasks. The proposed method was compared to the nearest neighbor interpolation, trilinear interpolation, third-order B-splines interpolation methods, and deep image prior (DIP) with the peak signal-to-noise ratio (PSNR) and structural similarity index (SSIM) as the quantification metrics. The averaged ASL images acquired with 44 min acquisition time were used as the ground truth for real-patient LR-to-NR study. The ablation studies of low-pass-filter loss term and T1-weighted MR image were performed based on simulation data. For the simulation study, results show that the proposed method achieved significantly higher PSNR ( -value 0.05) and SSIM ( -value 0.05) than the nearest neighbor interpolation, trilinear interpolation, third-order B-splines interpolation, and DIP methods. For the real-patient LR-to-NR experiment, results show that the proposed method can generate high-quality SR ASL images with clearer structure boundaries and low noise levels and has the highest mean PSNR and SSIM. For real-patient NR-to-SR tasks, the structure of the results using the proposed method is sharper and clearer, which are the most similar to the structure of the reference 44 min acquisition image than other methods. The proposed method also shows the ability to remove artifacts in the NR image while superresolution. The ablation study verified that the low-pass-filter loss term and T1-weighted MR image are necessary for the proposedmethod. The proposed unsupervised multiscale GAN framework can simultaneously improve spatial resolution and reduce image noise. Experiment results from simulation data and three healthy subjects show that the proposed method achieves better performance than the nearest neighbor interpolation, the trilinear interpolation, the third-order B-splines interpolation, and DIP methods.

Trajectory planning of transcranial magnetic stimulation manipulator based on time-safety collision optimization

In this study, an optimal time-safety collision trajectory planning method of manipulator is proposed. It optimizes the coupling and contradictory performance indexes of manipulator joint motion time and safety collision coefficient. The trajectory of the manipulator can be transformed into the position and time series in the joint space by Inverse Kinematics (IK). Among the splines, quintic B-spline used commonly for interpolating robotic trajectories is preferred also in this study. Under the constraints of the manipulator, non-dominated sorting genetic algorithms-II (NSGA-II) is used to optimize the objective function. The total optimized running time is shortened by 33.07 s. The main joints damage before and after optimization of safety collision have been reduced more than 49.4%. After quintic B-spline interpolation, the time-safety collision of manipulator trajectory are effectively optimized. In general, the execution efficiency of the manipulator is improved, the collision damage to the human head is reduced, and the motion control performance of TMS manipulator is improved to be widely used in medical clinic.

Design of electronic cam for lower hook mechanism of fishing net-weaving machine based on polynomial fitting

The working efficiency and stability of the double hook-based fishing net-weaving machine is mainly determined by the lower hook mechanism. In this work, a new kind of lower hook mechanism, which is driven by four servo motors, is presented, and the electronic cam curve of the lower hook mechanism is introduced. First, cubic B-spline interpolation is used to get the basic motion path of the lower hook plate, and then the piecewise quintic polynomial fitting method is used to fit the motion path. Finally, self-adaptive mutation-based particle swarm optimization is put forward and used to obtain the optimal parameters of the quintic polynomial, which performs better compared with the other two particle swarm optimization algorithms in this study. Experiments suggest that the electronic cam curve generated by the piecewise quintic polynomial fitting has got 55.91% (horizontal motors) and 60.96% (vertical motors) optimization in maximum motor torque compared with curves generated by cubic B-spline interpolations. In addition, the new lower hook mechanism and its moving curve described in this paper improved the theoretical weaving speed of the fishing net-weaving machine, providing a basis for digital improvement of the knotted net-weaving industry.

Path Planning Based on the Improved RRT* Algorithm for the Mining Truck

Planning a reasonable driving path for trucks in mining areas is a key point to improve mining efficiency. In this paper, a path planning method based on Rapidly-exploring Random Tree Star (RRT*) is proposed, and several optimizations are carried out in the algorithm. Firstly, the selection process of growth target points is optimized. Secondly, the process of selecting the parent node is optimized and a Dubins curve is used to constraint it. Then, the expansion process from tree node to random point is optimized by the gravitational repulsion field method and dynamic step method. In the obstacle detection process, Dubins curve constraint is used, and the bidirectional RRT* algorithm is adopted to speed up the iteration of the algorithm. After that, the obtained paths are smoothed by using the greedy algorithm and cubic B-spline interpolation. In addition, to verify the superiority and correctness of the algorithm, an unmanned mining vehicle kinematic model in the form of front-wheel steering is developed based on the Ackermann steering principle and simulated for CoppeliaSim. In the simulation, the Stanley algorithm is used for path tracking and Reeds-Shepp curve to adjust the final parking attitude of the truck. Finally, the experimental comparison shows that the improved bidirectional RRT* algorithm performs well in the simulation experiment, and outperforms the common RRT* algorithm in various aspects.

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.

Serial Manipulator Time-Jerk Optimal Trajectory Planning Based on Hybrid IWOA-PSO Algorithm

Loading and unloading operations are widely employed in industrial robots and CNC machine tools. In the present study, an effective algorithm is established for optimum time-jerk path planning and reducing the vibration of the serial manipulator, and enhancing the robot efficiency. To this end, the manipulator&#x2019;s trajectory is constructed using quintic B-spline interpolation in the joint space and the optimal objective function is constructed in terms of time and mean jerk. A hybrid improved whale optimization and particle swarm optimization (IWOA-PSO) method is proposed to optimize the objective function. First, WOA is improved by employing adaptive weight and threshold to balance exploration and exploitation of the WOA to prevent falling into the local optimum solution. Then, PSO method and IWOA techniques are combined to enhance the convergence speed of the IWOA. Applying different algorithms to 23 benchmark functions demonstrate superiority of the proposed algorithm to state-of-the-art algorithms. A 6-DOF serial industrial manipulator integrated in CNC machine was taken as a case study and the joint positions are considered the IWOA-PSO inputs. All calculations are performed in the MATLAB 2018b environment. The obtained results demonstrate that the proposed IWOA-PSO can effectively reduce the jerk of the robot while improving its work efficiency.

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.

Improving the performance of sea surface temperature predictions using a revised method

ABSTRACT Sea surface temperature (SST) prediction plays an important role in global and regional ocean-related research. With the rapid development of remote sensing technology, there are plenty of studies for SST prediction with deep learning to pursue better prediction performance and normalization was used for most studies. However, SST always fluctuates widely, so the denormalization scaled up the difference between normalized observed SSTs and normalized predicted SSTs (OnP-DIFF), and it results in a significant decline in the prediction performance. Therefore, a revision method used to revert the scale-up is proposed in this letter. This method uses cube B-spline interpolation to enhance OnP-DIFF, utilizes Long Short Term Memory network (LSTM) to train and predict OnP-DIFF and generate revision tensor (RT), and finally uses RT to revise denormalized predicted SSTs. To our knowledge, it is the first attempt to use the revision method to solve the problem of performance decline for SST prediction because of wide fluctuations of SST. The experiment results indicate that the proposed method can revert the performance back to and even better than the value before denormalization for deep learning models, significantly improving the prediction performance, and is reliable for SST prediction with high performance for a wide time range and large spatial scope.

An interpolation method based on adaptive smooth feedrate scheduling and parameter increment compensation for NURBS curve

Compared with the traditional line/circle interpolation, non-uniform rational B-splines (NURBS) interpolation has more efficient and high-quality advantages in free-form curve/surface modeling. In order to obtain high efficiency and stable interpolation feed motion, a NURBS interpolation method with adaptive smoothing federate scheduling and parameter increment compensation is studied. Firstly, according to the curvature constraint, the adaptive feedrate is obtained and the segmentation of the NURBS curve is completed. Then, in order to avoid the problem of feeding speed overrun, the improved S-shape acceleration/deceleration control is adopted to adjust the jerk. The adjacent segments meeting the combined planning conditions are treated comprehensively. Secondly, aiming at the problem of velocity error in interpolation point parameter calculation, an interpolation parameter calculation method based on parameter increment compensation is proposed to reduce the velocity fluctuation and improve the interpolation point parameter calculation accuracy. Finally, the effectiveness of the proposed method is verified by simulation and experiment. The results show that the algorithm is effective.

Prediction of variable amplitude fatigue crack growth life based on modified grey model

Grey model has been several applications on fatigue crack, with prediction on fatigue crack growth life curve often serving as milestones. A typical difficulty in predicting the fatigue crack growth life curve is the retardation of crack growth caused by the overload effect. Overload retardation, resulting in the lack of experiment data points in the retardation interval and the deflection of crack growth curve, is a long-term challenge for predicting fatigue crack growth. We improve the ability of grey model to predict fatigue crack growth life by second order B-spline interpolation, an interpolation for local data points. It combines the trend of local data point to deal with the retardation interval, and interpolates multiple data points in the retardation interval when there is a lack of local data, and uses a metabolic grey model to construct the prediction formula of crack growth. In the study involving variable amplitude load and multiple overload fatigue crack growth experiments, the proposed method is proved to improve, with statistical significance, the predictive ability on the whole range of experiment data. The method is simple and accurate. Consequently, it is conducive to solve the problem of fatigue crack growth life of engineering structure.

Joint inversion of seismic slopes, traveltimes and gravity anomaly data based on structural similarity

SUMMARY Attention is paid to joint inversion of multiple geophysical data because of its advantages on weakening the non-uniqueness of inversion and further enhancing comprehensive interpretation. Due to the good correlation between rock velocity and density, seismic and gravity data have been widely used in joint inversion. However, the joint inversion of pre-stack seismic reflection and gravity data remains underdeveloped at the exploration scale. Without a quantitive relation between velocity and density, we develop a structure-based joint inversion using seismic reflection traveltimes, slopes and Bouguer gravity anomaly data simultaneously for building both velocity and density models. In our method, cubic B-spline interpolation is used to parametrize the common knots of velocity and density models. Incorporating seismic slopes into the joint inversion framework, we build a composite objective function which minimizes the weighted-sum of seismic/gravity data misfits, regularization and structural constraint terms. By subdividing the knot spacing, a multiscale strategy is alternative to increase the stability of inversion. First, we describe the methodology, followed by three synthetic examples to illustrate the feasibility and benefits of the method. Examination of the convergence curves via inversion suggests that the desired solution is more likely to be obtained with gentle convergence of each term, thus it can be used as an indicator for weight adjustment. Additionally, locations of scattering points and acoustic impedance can be obtained as by-products. Compared with the inversion of the respective data, the joint inversion exhibits the complementary characteristics of seismic and gravity data, improves the distribution and structural features of the resulting physical properties, especially in deep and complex tectonic situations.

Research on the Detection Method of Tunnel Surface Flatness Based on Point Cloud Data

The curved surface of the tunnel is symmetrical. The curved surface of the tunnel can be roughly divided into the left and right arch walls along the direction of the central axis of the tunnel. The symmetry of the tunnel needs to be analyzed when the flatness inspection of the tunnel engineering is carried out. The flatness of the initial support of the tunnel project is an important indicator of the quality inspection and acceptance of the tunnel project. The three-dimensional laser scanner (3DLS) can be used to detect its rapidity effectively. According to the points obtained by the scanner, the surface fitting method based on B-spline interpolation and the SG bar initial support value processing method are used to optimize the tunnel surface to obtain the initial degree calculation reference. Based on the method, a calculation system for the initial flatness of the tunnel based on 3DLS technology is established. At the same time, the calculation method of the overall field of view distance and the development of small blocks is proposed. Through its application and comparison with traditional methods, the analysis shows that the three-dimensional laser scanning technology is feasible in the detection of the initial branch of the tunnel, and achieves a high degree of accuracy requirements.

Structure-guided gravity inversion for layered density modeling with an application in the Chezhen Depression, Bohai Bay Basin

Gravity inversion, as a static potential field inversion, has inherent ambiguity with low vertical resolution. To reduce the nonuniqueness of the inversion, it is necessary to impose the a priori constraints derived by other geophysical inversions, drilling, or geologic modeling. Based on the a priori normalized gradients derived from seismic imaging or reference models, a structure-guided gravity inversion method with a few known point constraints is developed for mapping density with multiple layers. The cubic B-spline interpolation is used to parameterize the forward modeling calculation of the gravity response to smooth density fields. A recently adopted summative gradient is used to maximize the structural similarity between the a priori and inverted models. First, we have determined the methodology, followed by a synthetic fault model example to confirm its validity. Monte Carlo tests and uncertainty tests further examine the stability and practicality of the method. This method is easy to implement; consequently, it produces an interpretable density model with geologic consistency. Finally, we apply this method to the density modeling of the Chezhen Depression in the Bohai Bay Basin. Our work determines the distribution of deep Lower Paleozoic carbonate rocks and Archean buried hills with high-density characteristics. Our results are consistent with the existing formation mechanism of the “upper source-lower reservoir” type oil-gas targets.

B-spline interpolation problem in Hilbert C∗-modules

We introduce the B-spline interpolation problem corresponding to a C∗-valued sesquilinear form on a Hilbert C∗-module and study its basic properties as well as the uniqueness of solution. We first study the problem in the case when the Hilbert C∗-module is self-dual. Passing to the setting of Hilbert W∗-modules, we present our main result by characterizing when the spline interpolation problem for the extended C∗-valued sesquilinear form has a solution. Finally, solutions of the B-spline interpolation problem for Hilbert C∗-modules over C∗-ideals of W∗-algebras are extensively discussed.

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.

Time-optimal trajectory planning of manipulator with simultaneously searching the optimal path

Time-optimal trajectory planning can improve the efficiency of the manipulator, which has a paramount research significance. Nonetheless, almost all the current algorithms have the problem of path limitation — the algorithm constantly searches for the optimal motion time of the manipulator on a specific motion path. To solve this problem, we design a time-optimal trajectory planning method for the manipulator by searching the optimal path simultaneously. We propose using a cubic uniform B-spline interpolation algorithm to derive the motion curve expression of the manipulator joint with unknown path points. Then we use a genetic algorithm to optimize the path point and the motion time of the manipulator at the same time to get the time-optimal motion path of the manipulator. Moreover, we prove that the algorithm proposed in this paper is comparable with similar algorithms with known paths through experiments.