Adaptive Interpolation Research Articles

Fuzzy Noise-Induced Codimension-Two Bifurcations Captured by Fuzzy Generalized Cell Mapping with Adaptive Interpolation

In this paper, the Fuzzy Generalized Cell Mapping (FGCM) method is developed with the help of the Adaptive Interpolation (AI) in the space of fuzzy parameters. The adaptive interpolation on the set-valued fuzzy parameter is introduced in computing the one-step transition membership matrix to enhance the efficiency of the FGCM. For each of initial points in the state space, a coarse database is constructed at first, and then interpolation nodes are inserted into the database iteratively each time errors are examined with the explicit formula of interpolation error until the maximal errors are just under the error bound. With such an adaptively expanded database on hand, interpolating calculations assure the required accuracy with maximum efficiency gains. The new method is termed as Fuzzy Generalized Cell Mapping with Adaptive Interpolation (FGCM with AI), and is used to investigate codimension-two bifurcations in two-dimensional and three-dimensional nonlinear dynamical systems with fuzzy noise. It is found that global changes in fuzzy dynamics are dominated by the underlying deterministic counterparts, and the fuzzy attractor expands along the unstable manifold leading to a collision with a saddle when a bifurcation occurs. The examples show that the FGCM with AI has a thirtyfold to fiftyfold efficiency over the traditional FGCM to achieve the same analyzing accuracy.

A Novel Adaptive GA-based B-spline Curve Interpolation Method

Background: Curve interpolation is very important in engineering such as computer aided design, image analysis and NC machining. Many patents on curve interpolation have been invented. Objective: Since different knot vector configuration and data point parameterization can generate different shapes of an interpolated B-spline curve, the goal of this paper is to propose a novel adaptive genetic algorithm (GA) based interpolation method of B-spline curve. Method: Relying on geometric features owned by the data points and the idea of genetic algorithm which liberalizes the knots of B-spline curve and the data point parameters, a new interpolation method of B-spline curve is proposed. In addition, the constraint of a tangent vector is also added to ensure that the obtained B-spline curve can approximately satisfy the tangential constraint while ensuring strict interpolation. Results: Compared with the traditional method, this method realizes the adaptive knot vector selection and data point parameterization. Therefore, the interpolation result was better than the traditional method to some extent, and the obtained curve was more natural. Conclusion: The proposed method is effective for the curve reconstruction of any scanned data point set under tangent constraints. Meanwhile, this paper put forward a kind of tangent calculation method of discrete data points, where users can also set the tangent of each data point in order to get more perfect interpolation results.

FPGA Implementation of Adaptive Multiplier-Based Linear Image Interpolation

This work provides an image interpolation for multimedia applications by utilizing an adaptive multiplier-based stepwise linear interpolation with clam filter. Image interpolation is also termed as image up-scaling. Generally, while enlarging an image some vacant bit positions are introduced and due to this empty pixel positions, the quality of the image is decreased. Therefore to maintain the quality of the image, new pixels are introduced and those pixels are used to fill the vacant bit positions by using interpolation techniques. In the adaptive interpolation techniques, edge pixels are identified and filtered at prior to the interpolation process. This will improve the quality of the interpolated image. However, the adaptive interpolation scheme increases the complexity of the system. To reduce the complexity, this work uses low complexity stepwise linear interpolation and to maintain the quality it uses multiplier-based linear stepwise (MBLSI) and edge enhancement technique. The experimental results demonstrate that the complexity of the proposed work is less as compared with other related work as well as the quality is also maintained. The proposed work utilizes 275 LUTs to provide the average peak signal to noise ratio (PSNR) of 20.44 dB and structural similarity index (SSIM) as 0.8250. This proposed work increases the PSNR by 0.89 dB from the conventional multiplier-based stepwise linear interpolation. Further the proposed interpolation algorithm utilizes less number of resources in field programmable gate array (FPGA) by comparing with other related interpolation techniques.

A New Adaptive Image Interpolation Method to Define the Shoreline at Sub-Pixel Level

This paper presents a new methodological process for detecting the instantaneous land-water border at sub-pixel level from mid-resolution satellite images (30 m/pixel) that are freely available worldwide. The new method is based on using an iterative procedure to compute Laplacian roots of a polynomial surface that represents the radiometric response of a set of pixels. The method uses a first approximation of the shoreline at pixel level (initial pixels) and selects a set of neighbouring pixels to be part of the analysis window. This adaptive window collects those stencils in which the maximum radiometric variations are found by using the information given by divided differences. Therefore, the land-water surface is computed by a piecewise interpolating polynomial that models the strong radiometric changes between both interfaces. The assessment is tested on two coastal areas to analyse how their inherent differences may affect the method. A total of 17 Landsat 7 and 8 images (L7 and L8) were used to extract the shorelines and compare them against other highly accurate lines that act as references. Accurate quantitative coastal data from the satellite images is obtained with a mean horizontal error of 4.38 ± 5.66 m and 1.79 ± 2.78 m, respectively, for L7 and L8. Prior methodologies to reach the sub-pixel shoreline are analysed and the results verify the solvency of the one proposed.

Optimization of the multidimensional signal interpolator in a lower dimensional space

Adaptive multidimensional signal interpolators are developed. These interpolators take into account the presence and direction of boundaries of flat signal regions in each local neighborhood based on the automatic selection of the interpolating function for each signal sample. The selection of the interpolating function is performed by a parameterized rule, which is optimized in a parametric lower dimensional space. The dimension reduction is performed using rank filtering of local differences in the neighborhood of each signal sample. The interpolating functions of adaptive interpolators are written for the multidimensional, three-dimensional and two-dimensional cases. The use of adaptive interpolators in the problem of compression of multidimensional signals is also considered. Results of an experimental study of adaptive interpolators for real multidimensional signals of various types are presented.

Fast Green Function Evaluation for Method of Moment

In this letter, an approach to accelerate the matrix filling in method of moment (MOM) is presented. Based on the fact that the Green function is dependent on the Euclidean distance between the source and the observation points, we constructed an efficient adaptive one-dimensional interpolation approach to fast calculate the $Exp$ type function values. In the proposed method, several adaptive interpolation tables are constructed based on the maximum and minimum distance between any two integration points with local refinement near zero function values to minimize the relative error. An efficient approach to obtain the sampling points used in the interpolation phase is carefully designed. Then, any function values can be efficiently calculated through a linear interpolation method for Exp and a Lagrange polynomial interpolation method for the Green function. In addition, the error bound of the proposed method is rigorously investigated. The proposed method can be quite easily integrated into the available MOM codes for different integration equation (IE) formulations with few efforts. Comprehensive numerical experiments validate its accuracy and efficiency through several IE formulations. Results show that over 20% efficiency improvement can be achieved without sacrificing the accuracy.

Improved Fast Adaptive IDW Interpolation Algorithm based on the Borehole Data Sample Characteristic and Its Application

The inverse distance weighted algorithm (IDW) is one of the most widely used algorithms in geoscience calculation based on its university and simple theory. However, in the practical application based on borehole sampling data, the distance between boreholes is further than the sampling distance along the bedding direction of one borehole, and it needs to search all the near points through a large number of distance calculation, and the process is very slow, so this lacks practicality in the spatial interpolation of the large amount and non-uniform distribution data. Based on the special features of the borehole sampling data, this paper presents a fast adaptive and improved inverse distance weighted interpolation method. And firstly the sample point position could be indexed by the adaptive cube grid raster, then determine the index grid in the horizontal and vertical directions of the interpolation point, and combine these grids for the finally IDW calculation, which significantly improves the search speed of the adjacent interpolation calculation points. It can improve the engineering applicability of the IDW method, especially the three-dimensional spatial interpolation and computing has a good application prospect.

Adaptive Interpolation Algorithm Based on a kd-Tree for the Problems of Chemical Kinetics with Interval Parameters

The questions of simulating chemical processes with uncertainty in their parameters are considered. A new approach consisting in the construction of a dynamic structured grid based on a kd-tree over the space formed by the interval parameters of a problem is proposed. When the algorithm is executed, a piecewise polynomial function interpolating the dependence of a solution on certain values of interval parameters is built at every step of integrating the initial system of ordinary differential equations. The results of testing the algorithm on the problems of chemical kinetics, including the combustion processes, demonstrate its efficiency and broad range of applications.

The adaptive interpolation method for proving replica formulas. Applications to the Curie–Weiss and Wigner spike models

In this contribution we give a pedagogic introduction to the newly introduced adaptive interpolation method to prove in a simple and unified way replica formulas for Bayesian optimal inference problems. Many aspects of this method can already be explained at the level of the simple Curie–Weiss spin system. This provides a new method of solution for this model which does not appear to be known. We then generalize this analysis to a paradigmatic inference problem, namely rank-one matrix estimation, also refered to as the Wigner spike model in statistics. We give many pointers to the recent literature where the method has been succesfully applied.

Study on reflectivity data interpolation and mosaics for multiple Doppler weather radars

Multiple weather radars’ joint detection can enlarge the radar detection range and can improve the detection accuracy, which has become an important method to monitor large-scale weather effectively. In this paper, the methods of interpolating reflectivity volume scan data onto the grids in the Cartesian coordinate system and three-dimensional mosaic for gridded reflectivity data of several radars are studied. In order to retain the physical characteristics of the raw data, the smoothing parameters of adaptive Barnes interpolation are improved which based on the space structure of the raw reflectivity data. Through comparison of constant altitude plan position indication (CAPPI) images obtained by the commonly used interpolation schemes and the improved Adaptive Barnes interpolation, it was found that the latter can provide consecutive reflectivity fields and retain high-resolution structure comparable to the raw data. The mean deviation filter filtering erroneous grid data and the data are fused by various fusion methods. Result shows that Exponential Weighting is an excellent method which can provide continuous three-dimensional reflectivity mosaic data.

An Adaptive Image Registration Technique to Remove Atmospheric Turbulence

Turbulence/Heat Scintillations is the change that arises in the refraction index of air with the temperature. The distortion created by the atmospheric turbulence is proportional to the distance between object and camera. In last few years, several approaches have been proposed to estimate and eliminate geometric distortion and blur. In this paper, a novel technique is proposed that improves the visual quality of video sequences affected by atmospheric turbulence. The proposed method is based on adaptive control grid interpolation (CGI). CGI approximates accurate motion vectors to generate a geometrically correct frame using certain reference frames. For high scintillation sequences, CGI doesn’t mitigate scintillations completely. The new methodology is proposed with updated trajectory estimation. The proposed method can effectively reduce the influence even for high atmospheric turbulence. Experimental results also prove that proposed approach is time efficient compared to traditional CGI.

A parameter extraction algorithm for microwave filter based on adaptive interpolation fitting

This article proposes a parameter extraction algorithm based on adaptive interpolation fitting. By adaptively inserting interpolation points within a given interval, the number of the sampling points in the extraction process can be greatly reduced, which makes the calculation more efficient. Furthermore, the effect of noise can be eliminated with the multipath characteristic of the algorithm. The specific algorithm flow is given in detail. And two microwave filter design examples verified the feasibility and effectiveness of the proposed algorithm.

Semi-supervised learning using autodidactic interpolation on sparse representation-based multiple one-dimensional embedding

In this paper, we present a novel semi-supervised classification method based on sparse representation (SR) and multiple one-dimensional embedding-based adaptive interpolation (M1DEI). The main idea of M1DEI is to embed the data into multiple one-dimensional (1D) manifolds satisfying that the connected samples have shortest distance. In this way, the problem of high-dimensional data classification is transformed into a 1D classification problem. By alternating interpolation and averaging on the multiple 1D manifolds, the labeled sample set of the data can enlarge gradually. Obviously, proper metric facilitates more accurate embedding and further helps improve the classification performance. We develop a SR-based metric, which measures the affinity between samples more accurately than the common Euclidean distance. The experimental results on several databases show the effectiveness of the improvement.

Parametric Space Dimensionality Reduction in Multidimensional Signal Interpolation

The reduction of the dimensionality of a parametric space is done in the adaptive interpolation of a multidimensional signal. A hybrid adaptive interpolator underlies the dimensionality reduction. The multidimensional hybrid interpolator uses structurally different algorithms to interpolate multidirectional sections of the signal. The approximation of some sections of the signal by other sections underlies the interrelations between signal sections. The adaptive parametric interpolation of intra-sectional readings accounts for intra-sectional interrelations between signal readings. Computational experiments on real multidimensional signals prove the efficiency of the hybrid adaptive interpolator.

Adaptive weighted fuzzy rule interpolation based on ranking values and similarity measures of rough-fuzzy sets

In real-world applications, the performances of traditional fuzzy interpolation methods are not good enough because they may produce inconsistent fuzzy interpolation results when contradictory fuzzy interpolated results are obtained after fuzzy interpolation processes. In recent years, several adaptive fuzzy rule interpolation (AFRI) methods have been proposed for identification and correction of the contradictory fuzzy interpolated results. In this paper, we propose a new adaptive weighted fuzzy rule interpolation (AWFRI) method based on ranking values and similarity measures of rough-fuzzy sets (RFSs). If the degree of similarity obtained between the fuzzy interpolation results is less than a predefined threshold value, the proposed AWFRI method applies the proposed transformation and modification techniques to solve the contradiction between fuzzy interpolation results. The experimental results show that the proposed AWFRI method can overcome the drawbacks of the existing AFRI methods because it obtains higher consistency degrees between fuzzy interpolation results and it deals with AWFRI based on RFSs rather than type-1 fuzzy sets or interval type-2 fuzzy sets.

Remote Sensing Image Compression Based on Adaptive Directional Wavelet Transform With Content-Dependent Binary Tree Codec

Remote sensing images provide a wealth of information for a variety of applications, but it is at the expense of huge data. In this paper, we present a novel compression method based on optimum adaptive directional lifting (OADL) with content-dependent binary tree codec. First, the OADL model is designed, which calculates the optimal prediction direction of each image block and performs the weighted directional adaptive interpolation during the process of lifting. The former aims to reduce the edge and texture energy of the non-horizontal and non-vertical directions in the high-frequency subbands, and the latter focuses on preserving the directional characteristics of remote sensing images as much as possible. Second, a binary tree codec with content-based adaptive scanning is introduced, which can provide different scanning orders and scanning manners among and within subbands, respectively. In addition, it can encode more significant coefficients at the same bit rate. Experimental results show that, compared with other scan-based compression methods, the proposed compression method can always provide better coding performance in terms of some evaluation indexes.

A Fast Calibration Method for Photonic Mixer Device Solid-State Array Lidars.

The photonic mixer device (PMD) solid-state array lidar, as a three-dimensional imaging technology, has attracted research attention in recent years because of its low cost, high frame rate, and high reliability. To address the disadvantages of traditional PMD solid-state array lidar calibration methods, including low calibration efficiency and accuracy, and serious human error factors, this paper first proposes a calibration method for an array complementary metal–oxide–semiconductor photodetector using a black-box calibration device and an electrical analog delay method; it then proposes a modular lens distortion correction method based on checkerboard calibration and pixel point adaptive interpolation optimization. Specifically, the ranging error source is analyzed based on the PMD solid-state array lidar imaging mechanism; the black-box calibration device is specifically designed for the calibration requirements of anti-ambient light and an echo reflection route; a dynamic distance simulation system integrating the laser emission unit, laser receiving unit, and delay control unit is designed to calibrate the photodetector echo demodulation; the checkerboard calibration method is used to correct external lens distortion in grayscale mode; and the pixel adaptive interpolation strategy is used to reduce distortion of distance images. Through analysis of the calibration process and results, the proposed method effectively reduces the calibration scene requirements and human factors, meets the needs of different users of the lens, and improves both calibration efficiency and measurement accuracy.

Fast Radio Map Construction by using Adaptive Path Loss Model Interpolation in Large-Scale Building.

The radio map construction is usually time-consuming and labor-sensitive in indoor fingerprinting localization. We propose a fast construction method by using an adaptive path loss model interpolation. Received signal strength (RSS) fingerprints are collected at sparse reference points by using multiple smartphones based on crowdsourcing. Then, the path loss model of an access point (AP) can be built with several reference points by the least squares method in a small area. Afterwards, the RSS value can be calculated based on the constructed model and corresponding AP’s location. In the small area, all models of detectable APs can be built. The corresponding RSS values can be estimated at each interpolated point for forming the interpolated fingerprints considering RSS loss, RSS noise and RSS threshold. Through combining all interpolated and sparse reference fingerprints, the radio map of the whole area can be obtained. Experiments are conducted in corridors with a length of 211 m. To evaluate the performance of RSS estimation and positioning accuracy, inverse distance weighted and Kriging interpolation methods are introduced for comparing with the proposed method. Experimental results show that our proposed method can achieve the same positioning accuracy as complete manual radio map even with the interval of 9.6 m, reducing 85% efforts and time of construction.

Resolution and quality enhancement of images using interpolation and contrast limited adaptive histogram equalization

In this paper, hybrid models for image quality enhancement are presented comprising both Contrast Limited Adaptive Histogram Equalization (CLAHE) and image interpolation. Adaptive histogram equalization is employed for contrast enhancement, while image interpolation is employed for resolution enhancement. Both the CLAHE and image interpolation are used interchangeably to check the most suitable model for quality enhancement of Low-Resolution (LR) images. The utilized interpolation techniques throughout this paper are polynomial and inverse techniques. Simulation results prove that the application of the CLAHE after interpolation gives the best image quality, especially with regularized inverse interpolation.

Bi-dimensional empirical mode decomposition (BEMD) algorithm based on particle swarm optimization-fractal interpolation

The performance of interpolation algorithm used in bi-dimensional empirical mode decomposition directly affects its popularization and application. Therefore, the research on interpolation algorithm is more reasonable, accurate and fast. So far, in the interpolation algorithm adopted by the bi-dimensional empirical mode decomposition, an adaptive interpolation algorithm can be proposed according to the image characteristics. In view of this, this paper proposes an image interpolation algorithm based on the particle swarm and fractal. Its procedure includes: to analyze the given image by using the fractal brown function, to pick up the feature quantity from the image, and then to operate the adaptive image interpolation in terms of the obtained feature quantity. The parameters involved in the interpolation process are optimized by particle swarm optimization algorithm, and the optimal parameters are obtained, which can solve the problem of low efficiency and low precision of interpolation algorithm used in bi-dimensional empirical mode decomposition. It solves the problem that the image cannot be decomposed to obtain accurate and reliable bi-dimensional intrinsic modal function, and realize the fast decomposition of the image. It lays the foundation for the further popularization and application of the bi-dimensional empirical mode decomposition algorithm.