Traditional Interpolation Research Articles

Food Vehicle Frame Topology Optimization Based on Bi-directional Interpolation Model

Bi-Directional Interpolation Model (BDIM) decided by a threshold is presented in this study to treat intermediate food vehicle frame density elements. Based on BDIM a mathematical model of food vehicle frame topology optimizing is established by integrating the analysis of the traditional interpolation model, only acting on sensitivity with BDIM and acting on sensitivity and rigidity with BDIM under the Gradient Projection Method. And it is exposed that the only acting on sensitivity with BDIM can get a global convergence and boundaries clear optimization results, which provides a new method to resolve the difficult problem of intermediate density elements. This study discusses its application in the field of food transportation vehicle frame.

A Multivariate Geostatistical Methodology to Delineate Areas of Potential Interest for Future Sedimentary Gold Exploration

This paper describes a multivariate geostatistical methodology to delineate areas of potential interest for future sedimentary gold exploration, with an application to an abandoned sedimentary gold mining region in Portugal. The main challenge was the existence of only a dozen gold measurements confined to the grounds of the old gold mines, which precluded the application of traditional interpolation techniques, such as cokriging. The analysis could, however, capitalize on 376 stream sediment samples that were analyzed for twenty two elements. Gold (Au) was first predicted at all 376 locations using linear regression (R2=0.798) and four metals (Fe, As, Sn and W), which are known to be mostly associated with the local gold's paragenesis. One hundred realizations of the spatial distribution of gold content were generated using sequential indicator simulation and a soft indicator coding of regression estimates, to supplement the hard indicator coding of gold measurements. Each simulated map then underwent a local cluster analysis to identify significant aggregates of low or high values. The one hundred classified maps were processed to derive the most likely classification of each simulated node and the associated probability of occurrence. Examining the distribution of the hot-spots and cold-spots reveals a clear enrichment in Au along the Erges River downstream from the old sedimentary mineralization.

Noise-induced bias for convolution-based interpolation in digital image correlation.

In digital image correlation (DIC), the noise-induced bias is significant if the noise level is high or the contrast of the image is low. However, existing methods for the estimation of the noise-induced bias are merely applicable to traditional interpolation methods such as linear and cubic interpolation, but are not applicable to generalized interpolation methods such as BSpline and OMOMS. Both traditional interpolation and generalized interpolation belong to convolution-based interpolation. Considering the widely use of generalized interpolation, this paper presents a theoretical analysis of noise-induced bias for convolution-based interpolation. A sinusoidal approximate formula for noise-induced bias is derived; this formula motivates an estimating strategy which is with speed, ease, and accuracy; furthermore, based on this formula, the mechanism of sophisticated interpolation methods generally reducing noise-induced bias is revealed. The validity of the theoretical analysis is established by both numerical simulations and actual subpixel translation experiment. Compared to existing methods, formulae provided by this paper are simpler, briefer, and more general. In addition, a more intuitionistic explanation of the cause of noise-induced bias is provided by quantitatively characterized the position-dependence of noise variability in the spatial domain.

Compressed Sensing, Pseudodictionary-Based, Superresolution Reconstruction

The spatial resolution of digital images is the critical factor that affects photogrammetry precision. Single-frame, superresolution, image reconstruction is a typical underdetermined, inverse problem. To solve this type of problem, a compressive, sensing, pseudodictionary-based, superresolution reconstruction method is proposed in this study. The proposed method achieves pseudodictionary learning with an available low-resolution image and uses theK-SVD algorithm, which is based on the sparse characteristics of the digital image. Then, the sparse representation coefficient of the low-resolution image is obtained by solving the norm ofl0minimization problem, and the sparse coefficient and high-resolution pseudodictionary are used to reconstruct image tiles with high resolution. Finally, single-frame-image superresolution reconstruction is achieved. The proposed method is applied to photogrammetric images, and the experimental results indicate that the proposed method effectively increase image resolution, increase image information content, and achieve superresolution reconstruction. The reconstructed results are better than those obtained from traditional interpolation methods in aspect of visual effects and quantitative indicators.

On the prediction of extreme flood quantiles at ungauged locations with spatial copula

The present study investigates the use of the spatial copula approach for predicting flood quantiles at ungauged basins. Spatial copulas are the formalization of traditional geostatistics by copulas. In regional flood frequency analysis (RFFA), the regression of flood quantiles is often carried out at the logarithmic scale. Consequently, traditional interpolation methods introduce a bias and provide suboptimal predictions. In this study, the copula framework is examined for offering proper corrections in this framework. Moreover, copula techniques separate the regional distribution of flood quantiles from spatial dependence. This provides a full probabilistic model that represents a more flexible framework where proper combinations of regional distribution and dependence can be adapted to various situations that are encountered in RFFA. The adequacy of the investigated methodology is evaluated on a real world case study involving hydrometric stations from southern Quebec, Canada. Results show that the spatial copula framework is able to deal with the problem of bias, is robust to the presence of problematic stations and may improve the quality of quantile predictions while reducing the level of complexity of the models used in RFFA.

3D Sound applied to the design of Assisted Navigation Devices for the Visually Impaired

This work presents an approach to generate 3D sound by using a set of artificial neural networks (ANNs). The proposed method is capable to reconstruct the Head Related Impulse Responses (HRIRs) by means of spatial interpolation. In order to cover the whole reception auditory space, without increasing the network complexity, a structure of multiple networks (set), each one modeling a specific area was adopted. The three main factors that influence the model accuracy --- the network's architecture, the reception area's aperture angles and the HRIR's time shifts --- are investigated and an optimal setup is presented. The computational effort to process the ANN is shown to be slightly smaller than traditional interpolation methods and all error calculation reached very low levels, validating the method to be used in the design of a 3D sound emitter capable of provide navigation aid for the visually impaired. Two approaches are presented in order to detect obstacles, one which makes use of computational vision techniques and other with laser proximity sensors.

Compressed Sensing Doppler Ultrasound Reconstruction Using Block Sparse Bayesian Learning.

In this paper we propose a framework for using duplex Doppler ultrasound systems. These type of systems need to interleave the acquisition and display of a B-mode image and of the pulsed Doppler spectrogram. In a recent study (Richy , 2013), we have shown that compressed sensing-based reconstruction of Doppler signal allowed reducing the number of Doppler emissions and yielded better results than traditional interpolation and at least equivalent or even better depending on the configuration than the study estimating the signal from sparse data sets given in Jensen, 2006. We propose here to improve over this study by using a novel framework for randomly interleaving Doppler and US emissions. The proposed method reconstructs the Doppler signal segment by segment using a block sparse Bayesian learning (BSBL) algorithm based CS reconstruction. The interest of using such framework in the context of duplex Doppler is linked to the unique ability of BSBL to exploit block-correlated signals and to recover non-sparse signals. The performance of the technique is evaluated from simulated data as well as experimental in vivo data and compared to the recent results in Richy , 2013.

Nonlocal similarity based DEM super resolution

This paper discusses a new topic, DEM super resolution, to improve the resolution of an original DEM based on its partial new measurements obtained with high resolution. A nonlocal algorithm is introduced to perform this task. The original DEM was first divided into overlapping patches, which were classified either as “test” or “learning” data depending on whether or not they are related to high resolution measurements. For each test patch, the similar patches in the learning dataset were identified via template matching. Finally, the high resolution DEM of the test patch was restored by the weighted sum of similar patches under the condition that the reconstruction weights were the same in different resolution cases. A key assumption of this strategy is that there are some repeated or similar modes in the original DEM, which is quite common. Experiments were done to demonstrate that we can restore a DEM by preserving the details without introducing artifacts. Statistic analysis was also conducted to show that this method can obtain higher accuracy than traditional interpolation methods.

An Effective Interpolation Method for MODIS Land Surface Temperature on the Qinghai–Tibet Plateau

Land surface temperature (LST) is a key parameter in the processes of energy and water exchange between land and atmosphere. However, the MODIS LST products are often obscured by clouds and other atmospheric disturbances, resulting in severe data loss. Traditional interpolation methods cannot be effectively applied when there is large area of missing data. Thus, in this study, an effective LST interpolation method is developed to address this issue and is used to interpolate MODIS/Terra LST data on the Qinghai–Tibet Plateau in 2005. This method assumes that some pixels with spatially valid LSTs may follow a change trend over time similar to the null pixels, and the focus thus becomes to locate those similar pixels to interpolate each null pixel. First, LST images with a small amount of missing data, chosen as the reference images, were interpolated using a traditional interpolation method. Then, for each null pixel, other pixels with similar temporal changes of LST were identified by a similarity function. Finally, a transfer function for each null pixel was established based on those pixels most similar to it in the interpolated image and the corresponding reference image. The results were found to be much superior to those interpolated by traditional methods, such as regression Kriging, ordinary Kriging, and IDW. A specially designed experiment on an area that had ample valid LSTs confirmed that the proposed method can produce more favorable results than the other methods, and performed especially well when there was a significant lack of data.

Spatial resolution enhancement of hyperspectral images based on redundant dictionaries

Spatial resolution enhancement of hyperspectral images is one of the key and difficult topics in the field of imaging spectrometry. The redundant dictionary based sparse representation theory is introduced, and a spatial resolution enhancement algorithm is proposed. In this algorithm, a pixel curve instead of a pixel patch is taken as the unit of processing. A pair of low- and high-resolution respective redundant dictionaries are joint trained, with the constraint that a pair of high- and low-resolution corresponded pixel curves can be sparse represented by same coefficients according to the respected dictionaries. In the process of super-resolution restoration, the low-resolution hyperspectral image is first sparse decomposed based on the low-resolution redundant dictionary and then the obtained coefficients are used to reconstruct the corresponding high-resolution image with respect to the high-resolution dictionary. The maximum a posteriori based constrained optimization is performed to further improve the quality of the reconstructed high-frequency information. Experimental results show that the pixel curve based sparse representation is more suitable for a hyperspectral image; the highly spectral correlations are better used for resolution enhancement. In comparison with the traditional bilinear interpolation method and other referenced super-resolution algorithms, the proposed algorithm is superior in both objective and subjective results.

An improved ANUDEM method combining topographic correction and DEM interpolation

Void filling and anomaly replacement in conjunction with auxiliary sources of data have been widely used to improve the quality of existing problematic high-resolution digital elevation models. However, the traditional interpolation methods used for this purpose have always failed to eliminate the discrepancies between different data-sets. In this paper, an improved ANUDEM method is presented for DEM interpolation, which incorporates the idea of topographic correction using high correlation of topological structure between contour lines (CLs) from multi-scale digital elevation models (DEM). Firstly, the terrain topological structure is extracted from the CLs of a low-resolution DEM. The topographic surface correction is then undertaken based on the extracted structure, which recovers the topographic information of the sharp depressions and eminences to fit the high-resolution representation. Finally, the breaklines of the terrain surface are distilled and integrated into the denser DEM generation. The experiments undertaken confirmed the superiority of the proposed method over the other DEM interpolation methods. It is shown that the proposed method can provide results with a higher accuracy, as well as a better visual quality.

Space cutter compensation method for five-axis nonuniform rational basis spline machining

In view of the good machining performance of traditional three-axis nonuniform rational basis spline interpolation and the space cutter compensation issue in multi-axis machining, this article presents a triple nonuniform rational basis spline five-axis interpolation method, which uses three nonuniform rational basis spline curves to describe cutter center location, cutter axis vector, and cutter contact point trajectory, respectively. The relative position of the cutter and workpiece is calculated under the workpiece coordinate system, and the cutter machining trajectory can be described precisely and smoothly using this method. The three nonuniform rational basis spline curves are transformed into a 12-dimentional Bézier curve to carry out discretization during the discrete process. With the cutter contact point trajectory as the precision control condition, the discretization is fast. As for different cutters and corners, the complete description method of space cutter compensation vector is presented in this article. Finally, the five-axis nonuniform rational basis spline machining method is further verified in a two-turntable five-axis machine.

Using a Dynamic Interval Type-2 Fuzzy Interpolation Method to Improve Modeless Robots Calibrations

This paper is an extended research for a novel technique for the position error compensations of the robot and manipulator calibration process based on an IT2FEI (interval type-2 fuzzy error interpolation) method. Traditional robots calibration implements either model or modeless method. The compensation of position error in modeless method is to move the robot's end-effector to a target position in the robot workspace, and to find the target position error based on the measured neighboring 4-point errors around the target position. A camera or other measurement device is attached on the robot's end-effector to find and measure the neighboring position errors, and compensate the target position with the error interpolation results. By using the IT2FEI technique provided in this paper, the accuracy of the position error compensation can be greatly improved, which has been confirmed by the simulation results given in this paper. Compared with some other popular traditional interpolation methods, this IT2FEI technique is a better choice. The simulation results show that more accurate compensation result can be achieved using this technique compared with the type-1 fuzzy interpolation method.

Mapping diversity indices: not a trivial issue

Summary Mapping diversity indices, that is estimating values in all locations of a given area from some sampled locations, is central to numerous research and applied fields in ecology. Two approaches are used to map diversity indices without including abiotic or biotic variables: (i) the indirect approach, which consists in estimating each individual species distribution over the area, then stacking the distributions of all species to estimate and map a posteriori the diversity index, (ii) the direct approach, which relies on computing a diversity index in each sampled locations and then to interpolate these values to all locations of the studied area for mapping. For both approaches, we document drawbacks from theoretical and practical viewpoints and argue about the need for adequate interpolation methods. First, we point out that the indirect approach is problematic because of the high proportion of rare species in natural communities. This leads to zero‐inflated distributions, which cannot be interpolated using standard statistical approaches. Secondly, the direct approach is inaccurate because diversity indices are not spatially additive, that is the diversity of a studied area (e.g. region) is not the sum of the local diversities. Therefore, the arithmetic variance and some of its derivatives, such as the variogram, are not appropriate to ecologically measure variation in diversity indices. For the direct approach, we propose to consider the β‐diversity, which quantifies diversity variations between locations, by the mean of a β‐gram within the interpolation procedure. We applied this method, as well as the traditional interpolation methods for comparison purposes on different faunistic and floristic data sets collected from scientific surveys. We considered two common diversity indices, the species richness and the Rao's quadratic entropy, knowing that the above issues are true for complementary species diversity indices as well as those dealing with other biodiversity levels such as genetic diversity. We conclude that none of the approaches provided an accurate mapping of diversity indices and that further methodological developments are still needed. We finally discuss lines of research that may resolve this key issue, dealing with conditional simulations and models taking into account biotic and abiotic explanatory variables.

Performance of Sparse Recovery Algorithms for the Reconstruction of Radar Images From Incomplete RCS Data

In this letter, we compare the performances of sparse recovery algorithms (SRAs) for the reconstruction of a 2-D inverse synthetic aperture radar (ISAR) image from incomplete radar-cross-section (RCS) data. The three methods considered for the SRA include the basis pursuit (BP), the BP denoising, and the orthogonal matching pursuit methods. The performances of the methods in terms of the reconstruction accuracy of the ISAR image are compared using the incomplete RCS data. In addition, traditional interpolation methods such as nearest-neighbor interpolation, linear interpolation, and spline interpolation are applied to the incomplete RCS data to reconstruct ISAR images, and their performances are compared to that of the SRAs.

A New Ray Tracing Method Based on Linear Travel-Time Interpolation

In the application of industrial flaw detection, the materials to be detected are often a collection of a background area and a small amount of defect areas. In traditional linear travel-time interpolation (LTI) method, the assumption of travel-time linearity will lead to error accumulation when the rays go through multiple cells. In order to reduce the cumulative error in this application, a new ray tracing method is proposed based on linear travel-time interpolation. In our method, calculation points are located on the boundaries between different areas to determine the angle of refraction. Moreover, the minimum travel-time of each point is computed by multidirectional loop strategy, which will make the traced ray path conforms to the condition of minimum travel-time when ray transports from the reverse direction. The simulation results show that using the proposed method to calculate travel-times and paths of tracing rays, it is more rapid and accurate than traditional LTI method and cross-scanning LTI method.

Hybrid fusion and interpolation algorithm with near-infrared image

Silicon-based digital cameras can record visible and near-infrared (NIR) information, in which the full color visible image (RGB) must be restored from color filter array (CFA) interpolation. In this paper, we propose a unified framework for CFA interpolation and visible/NIR image combination. To obtain a high quality color image, the traditional color interpolation from raw CFA data is improved at each pixel, which is constrained by the corresponding monochromatic NIR image in gradient difference. The experiments indicate the effectiveness of this hybrid scheme to acquire joint color and NIR information in real-time, and show that this hybrid process can generate a better color image when compared to treating interpolation and fusion separately.

Application of Multi-Gene Genetic Programming in Kriging Interpolation

A key stage for Kriging interpolation is the estimating of variogram model, which characterizes the spatial behavior of the variables of interest. But most traditional kriging interpolation has finite types of empirical variogram model, and sometimes, the optimal type of variogram model can not be find, which result in decreasing interpolation accuracy. In this paper, we explore the use of Multi-Gene Genetic Programming (MGGP) to automatically find an empirical variogram model that fits on an experimental variogram. Empirical variogram estimation based on MGGP, in contrast with traditional method need not select type of basic variogram model and can directly get both the functional type as well as the coefficients of the optimal variogram. The results of case study show that the proposed method can avoid the subjectivity in choosing the type of variogram models and can adaptively fit variogram according to the real data structure, which improves the interpolation accuracy of kriging significantly.

Method of establishing an underwater digital elevation terrain based on kriging interpolation

A high-precision underwater digital elevation model (DEM) is the premise of terrain-aided navigation. This study introduces the establishment of such a model. The process includes the construction and optimization of a triangular irregular network, selection of interpolation data based on terrain roughness degree, kriging interpolation, and error corrections. Results show that the established interpolation data selection method based on terrain roughness degree is better than other traditional interpolation methods in terms of accuracy. The proposed kriging interpolation method and error corrections exhibit excellent performance.

The Wind Power Forecast Model Based on Improved EMD and SVM

In order to improve the predictive accuracy of short-term wind power, a prediction model based on improved empirical mode decomposition (EMD) and support vector machine (SVM) is constructed. As to the problems of basic EMD, it is proposed to use the steady point meaning sifting method instead of spline envelope meaning sifting method, to improve the overshoots/undershoots caused by traditional cubic spline interpolation. Wind power series can be decomposed into different series by improved EMD, and then SVM is used to forecast power by each component. The total wind power prediction result is obtained through reconstructing at last. Case study shows that the predictive accuracy has significantly been improved by comparing with other models.