Traditional Interpolation Research Articles

High Feed Stability Control Strategies for Pulse Driving Systems

The feed motion stability of pulse driving systems is directly affected by characters of driving pulse sequences generated by CNC interpolators.The motion stability and control strategies are investigated by theoretical analysis,modeling simulation and experimental verification.Based on the mathematical model of interpolator output,the motion stability is discussed in both time-domain and frequency-domain.For traditional interpolation mode,an approach of improving motion stability is given according to the inter-restricted relation among machining accuracy,efficiency and motion stability.Furthermore,breaking through the traditional control mode,a new interpolating control strategy —an adaptive separated-axis interpolator with random period—is proposed to achieve high motion quality by varying interpolation period and synchronization of multi-axes.The results of simulations and machining experiments show the proposed strategies are effective.The efforts described provide new ways to improve the motion stability theoretically and practically.

Research of Aviation Image Multiplication Based on the Fractal Interpolation Algorithm

The resolution of aerial images was low, because the aviation aerospace camera was far from the scenery when shooting. In order to see the object of the aviation images clearly,the aviation images should be enlarged to improve the resolution . As the complexity and irregularity of the aerial images, the texture features is lost and considerable error is caused by using the traditional methods. In this article, the fractal interpolation has been used to enlarge the images, which can not only overcome the shortcoming of the linear interpolation, but also maintain the fine texture features of the original images, which is helpful to obtain higher accuracy than the traditional interpolation.

The look-ahead function-based interpolation algorithm for continuous micro-line trajectories

Continuous micro-line segments having micron magnitude are also used to approach complicated trajectories in computer numerical control (CNC) machining. Traditional linear interpolation processes micro-line segments separately. The rather small lengths of the segments result in low machining efficiency, and the frequent acceleration and deceleration also reduce the lifetime of the motor. To solve the problems, in this paper, we present an interpolation algorithm that is based on the look-ahead function. The look-ahead-based feedrate planning is elaborated from the aspects of trajectory feedrate description, feedrate preplanning, and feedrate planning. With the function of feedrate planning, CNC systems can predict the variation of the curvature of the coming trajectory so that adaptively determining whether accelerates interpolation feedrate to enhance machining efficiency or decelerates the feedrate to guarantee the machining precision. In addition, the trajectory interpolation for micro-line segment trajectories is analyzed as well, which realizes the generalization of the coordinates for each interpolation step. The implementation of the proposed algorithm in our CNC system is also studied. Finally, two machining experiments are provided to verify the accuracy and efficiency of the proposed interpolation algorithm.

Non-local MRI upsampling

In Magnetic Resonance Imaging, image resolution is limited by several factors such as hardware or time constraints. In many cases, the acquired images have to be upsampled to match a specific resolution. In such cases, image interpolation techniques have been traditionally applied. However, traditional interpolation techniques are not able to recover high frequency information of the underlying high resolution data. In this paper, a new upsampling method is proposed to recover some of this high frequency information by using a data-adaptive patch-based reconstruction in combination with a subsampling coherence constraint. The proposed method has been evaluated on synthetic and real clinical cases and compared with traditional interpolation methods. The proposed method is shown to outperform classical interpolation methods compared in terms of quantitative measures and visual observation.

Research and implementation of high-precision biaxial tracking control system based on NURBS interpolator

Many factors affect machining quality such as feedrate fluctuations, chord errors, machining time, machine characteristics, and unreasonable planning. Compared with traditional interpolations, parametric interpolations perform better at reducing feedrate fluctuations, chord errors, and it can save interpolation time. Reasonable feedrate planning and dynamic motion control are also necessary for precision improving. In this paper, NURBS interpolation is employed and feedrate is planned on basis of curve geometry and machine dynamic characters. Furthermore, a synthesized control algorithm is applied in control system to refine following accuracy. Simulation and experimental results demonstrate that the proposed approach can significantly reduce the machining error for biaxial following task.

Implementation of a novel interpolating method to epicardial potential mapping for atrial fibrillation study

Epicardial potential mapping is an efficient way to visualize the potential distribution on the epicardial surface. We found in our previous study, that the traditional linear interpolation used for the epicardial mapping may cause errors and distortions in reconstruction of the electric activities on the epicardial surface especially during the atrial fibrillation. In this study, we devoted on the implementation of a 3D interpolating method, and verified it in comparison with another interpolating method as well as studying of the mechanism of vagal atrial fibrillation (AF). In case studying, we analyzed the epicardial data from seven canine cardiac models using this method and found the macro-re-entry during the sustainable AF is more likely due to the dispersion of refractoriness in the myocardium and does not demonstrated the focal patterns at the beginning of AF. This indicated that the electrophysiological characteristics of myocardium might have been changed during the paroxysmal atrial fibrillation (PAF).

A Computationally Efficient Super-Resolution Reconstruction Algorithm Based On The Hybird Interpolation

In order to release the limitations on the computational complexity and the detail missing of the traditional interpolation algorithm, this paper proposes a double channel hybrid interpolation algorithm for super-resolution reconstruction that can not only reduce the complexity effectively but also keep the details of the image sufficiently. The improved algorithm involves following methods: first, the parallel processing is used in this project; second, the cubic B-spline linear interpolation is introduced in the low frequency domain; third, the edge interpolation algorithm is applied in the high frequency details. The simulation and experiments both indicate that this algorithm is able to process the image in real time with details preserved.

Trace Interpolation Algorithm Based on Intersection Vehicle Movement Modeling

Real vehicle tracking data play an important role in the research of routing in vehicle sensor networks. Most of the vehicle tracking data, however, were collected periodically and could not meet the requirements of real-time by many applications. Most of the existing trace interpolation algorithms use uniform interpolation methods and have low accuracy problem. From our observation, intersection vehicle status is critical to the vehicle movement. In this paper, we proposed a novel trace interpolation algorithm. Our algorithm used intersection vehicle movement modeling (IVMM) and velocity data mining (VDM) to assist the interpolation process. The algorithm is evaluated with real vehicle GPS data. Results show that our algorithm has much higher accuracy than traditional trace interpolation algorithms.

HASM-AD algorithm based on the sequential least squares

The HASM (high accuracy surface modeling) technique is based on the fundamental theory of surfaces, which has been proved to improve the interpolation accuracy in surface fitting. However, the integral iterative solution in previous studies resulted in high temporal complexity in computation and huge memory usage so that it became difficult to put the technique into application, especially for large-scale datasets. In the study, an innovative model (HASM-AD) is developed according to the sequential least squares on the basis of data adjustment theory. Sequential division is adopted in the technique, so that linear equations can be divided into groups to be processed in sequence with the temporal complexity reduced greatly in computation. The experiment indicates that the HASM-AD technique surpasses the traditional spatial interpolation methods in accuracy. Also, the cross-validation result proves the same conclusion for the spatial interpolation of soil PH property with the data sampled in Jiangxi province. Moreover, it is demonstrated in the study that the HASM-AD technique significantly reduces the computational complexity and lessens memory usage in computation.

Image Interpolation Using Edge-Directed Smoothness Measure Filter

This paper proposes a novel adaptive image interpolation method using an edge-directed smoothness filter. Adaptive image interpolation methods tend to create higher visual quality images than traditional interpolation methods such as bicubic interpolation. These methods, however, often suffer from high computational costs and production of inadequate interpolated pixels. We propose a novel method to overcome these problems. Our approach is to estimate the enlarged image from the original image based on an observation model. Obtaining an image with edge-directed smoothness, we constrain the estimated image to have many edge-directed smooth pixels which are measured by using the edge-directed smoothness filter introduced in this paper. Additionally, we also propose a simplification of our algorithm to run with lower computational complexity and smaller memory. Simulation results show that the proposal method produces images with high visual quality and performs well on PSNR and computational times.

Real-Time NURBS Interpolator with an Optimal Feed for High-Speed Machining

NURBS interpolation has many advantages over the traditional linear or circular interpolation in high-speed machining. The existing work in this regard focuses on adaptive feed interpolation considering the chord error constraints and tangent acceleration limits. However, regardless of the dynamic characteristics of individual axis, performance will inevitably suffer when the system is called upon to execute a complex trajectory beyond the range of its capabilities. The intent of the present work is to provide an optimal feed interpolation method respecting both the chord error constraint and the drive constraint of each axis. A look-ahead scheme is applied with a moving window to augment the calculation efficiency for real-time application. Simulations are performed to verify the resulting feedrate, acc/dec profiles and the real-time performance of the proposed interpolator.

NUFFT-Based Iterative Reconstruction Algorithm for Synthetic Aperture Imaging Radiometers

Synthetic aperture imaging radiometers (SAIRs) are powerful sensors for high-resolution observation of the Earth at low microwave frequencies. However, the future application of this new technology is limited by its large number of element antennas and receiving channels. In order to further reduce the complexity of the whole system, the circular and rotating array configurations have been proposed. Their disadvantages lie primarily in more complicated image reconstruction, because the conventional fast Fourier transform (FFT) method could not be used directly for image reconstruction. This letter introduces an iterative method for the reconstruction of radiometric brightness temperature maps from nonuniform visibility function samples. This method combines the conjugate gradient algorithm with min-max nonuniform FFT approach, which has been shown to provide considerably improved image quality relative to the traditional gridding method. Simulations for SAIRs were performed and showed better image quality in comparison to the traditional frequency interpolation method.

An application of artificial neural network models to estimate air temperature data in areas with sparse network of meteorological stations

In this work artificial neural network (ANN) models are developed to estimate meteorological data values in areas with sparse meteorological stations. A more traditional interpolation model (multiple regression model, MLR) is also used to compare model results and performance. The application site is a canyon in a National Forest located in southern Greece. Four meteorological stations were established in the canyon; the models were then applied to estimate air temperature values as a function of the corresponding values of one or more reference stations. The evaluation of the ANN model results showed that fair to very good air temperature estimations may be achieved depending on the number of the meteorological stations used as reference stations. In addition, the ANN model was found to have better performance than the MLR model: mean absolute error values were found to be in the range 0.82–1.72°C and 0.90–1.81°C, for the ANN and the MLR models, respectively. These results indicate that ANN models may provide advantages over more traditional models or methods for temperature and other data estimations in areas where meteorological stations are sparse; they may be adopted, therefore, as an important component in various environmental modeling and management studies.

Robust reconstruction of low-resolution document images by exploiting repetitive character behaviour

In this paper, we present a new approach for reconstructing low-resolution document images. Unlike other conventional reconstruction methods, the unknown pixel values are not estimated based on their local surrounding neighbourhood, but on the whole image. In particular, we exploit the multiple occurrence of characters in the scanned document. In order to take advantage of this repetitive behaviour, we divide the image into character segments and match similar character segments to filter relevant information before the reconstruction. A great advantage of our proposed approach over conventional approaches is that we have more information at our disposal, which leads to a better reconstruction of the high-resolution (HR) image. Experimental results confirm the effectiveness of our proposed method, which is expressed in a better optical character recognition (OCR) accuracy and visual superiority to other traditional interpolation and restoration methods.

Using neural networks as a support tool in the decision making for insurance industry

Under the pressure of market competition, property and casualty insurance companies normally use price competition as a means to enlarge their market share. Traditionally, the fire insurance underwriters use the interpolation method to estimate in-between risks (the classification of exposure falling between two risk levels). This interpolation method gives the underwriter more discretion in pricing to compete in the market. However, problems such as cutthroat competition or adverse selections also play a role, because the interpolation method cannot provide the correct price reflecting these in-between risks. This paper proposes the back propagation neural network (BPNN) model as a tool for the underwriter to determine the proper premium rate of in-between risks. A detailed explanation of how the BPNN model solves problems caused by traditional interpolation method is provided.

Seismic Data Reconstruction with Fractal Interpolation

AbstractIn order to improve the accuracy of reconstructed seismic data, this paper makes a detailed investigation into the fractal interpolation method on the basis of the previous work, and analyzes theoretically a special kind of fractal interpolation function. The explicit presentation of the fractal interpolation function is applied and the locally explicit expression for the vertical scaling factors is put forward. At the same time the interpolating accuracy is investigated from the point of accordingly seismic traces. The influence of the vertical scaling factors to the precision of the fractal interpolation is investigated. The numerical experiments demonstrate that the interpolating residual is in proportion to the exponent function with increasing vertical scaling factors. This explicit fractal interpolation method avoids the iteration that is inevitable in the traditional interpolation method, and then it improves the computational efficiency. By analyzing the theoretical seismograms and the reconstructed seismograms and the differences between them, the numerical results demonstrate that the fractal interpolation method put forward here has high accuracy and efficiency, the largest node error is no more than 3% with respect to the numerical computation. The method not only makes the local information obvious but also preserves the overall characteristics well of the data investigated.

Exact location of extrema for empirical mode decomposition

A novel algorithm to locate the extrema through the sample sequence is investigated. The algorithm is based on computing rather than traditional interpolation and searching in order to provide better precision. Numerical examples are included to corroborate the theoretical development.

Fuzzy Weighted Approach to Improve Visual Quality of Edge-Based Filtering

A new algorithm for the deinterlacing of interlaced scanned video sequences is presented in this paper. The ultimate goal of the proposed algorithm is to exactly determine the unknown pixel value while preserving the edges and details of the image. Traditional edge direction-based interpolation algorithms usually introduce artifacts in the case of non-clear edges. In order to solve the above issues, we adopted fuzzy concepts to design a weight-evaluating technique. The weights were considered to be multiplied by the candidate deinterlaced pixels. Experimental results demonstrated that the resulting frames contained less errors and sharper edges than frames generated using common approaches such as median filtering and edge direction-based linear interpolation.

Denoising by coupled partial differential equations and extracting phase by backpropagation neural networks for electronic speckle pattern interferometry

We extend and refine previous work [Appl. Opt. 46, 2907 (2007)]. Combining the coupled nonlinear partial differential equations (PDEs) denoising model with the ordinary differential equations enhancement method, we propose the new denoising and enhancing model for electronic speckle pattern interferometry (ESPI) fringe patterns. Meanwhile, we propose the backpropagation neural networks (BPNN) method to obtain unwrapped phase values based on a skeleton map instead of traditional interpolations. We test the introduced methods on the computer-simulated speckle ESPI fringe patterns and experimentally obtained fringe pattern, respectively. The experimental results show that the coupled nonlinear PDEs denoising model is capable of effectively removing noise, and the unwrapped phase values obtained by the BPNN method are much more accurate than those obtained by the well-known traditional interpolation. In addition, the accuracy of the BPNN method is adjustable by changing the parameters of networks such as the number of neurons.

Asynchronous multirate multisensor information fusion algorithm

This paper is concerned with the optimal dynamic information fusion problem for asynchronous multirate multisensors. By establishing the state space models at each scale, a novel algorithm is developed to recursively fuse the data from multisensors, where the ratio between the sampling rates of different sensors is allowed to be any positive integer. Without using the traditional interpolation or augmentation approaches for states or measurements, the state estimate is obtained based on global measurements, and the obtained state estimate is then proven to be the optimal in the sense of linear minimum variance. It is shown that our main results improve and extend the existing information fusion algorithms for which the sampling rate ratio of different sensors is restricted to one or a power of two. Finally, the feasibility and efficiency of the proposed algorithm is illustrated by a numerical simulation example.