Interpolation Process Research Articles

Dealing with small sample size problems in process industry using virtual sample generation: a Kriging-based approach

The operational data of advanced process systems have met with explosive growth, but its fluctuations are so slight that the number of the extracted representative samples is quite limited, making it difficult to reflect the nature of the process and to establish prediction models. In this study, inspired by the process of fisherman repairing nets, a Kriging-based virtual sample generation (VSG) named Kriging-VSG is proposed to generate feasible virtual samples in data sparse regions. Then, the accuracy of prediction models is further enhanced by applying the generated virtual samples. In order to reasonably find data sparse regions, a distance-based criterion is imposed on each dimension to identify important samples with large information gaps. Similar to the process of fisherman repairing nets, a certain dimension is initially fixed at different quantiles. A dimension-wise interpolation process using Kriging is then performed on the center between important samples with large information gaps. To validate the performance of the proposed Kriging-VSG, two numerical simulations and a real-world application from a cascade reaction process for high-density polyethylene are carried out. The results indicate that the proposed Kriging-VSG outperforms other methods.

The Use of Lidar Data and VHR Imagery to Estimate the Effects of Tree Roots on Shallow Landslides Assessment

The study of geo-hazards has been benefited from the technological advances in the field of Remote Sensing (RS) techniques as the ALS (Airborne Laser Scanners) Systems with Very High Resolution (VHR) cameras. Recently, the LiDAR (Light Detection and Ranging) is an active sensor technique used for a variety of geoscientific applications including slope monitoring to retrieve ground surface displacements at high spatial resolution. Additionally, LiDAR has been widely used in order to collect high-resolution information on forests structure for the determination and characterization of vegetation cover due its ability to capture multiple returns and to reach the ground, even in forested areas, allowing the generation of Digital Terrain Models (DTMs) for the estimation of forest variables. In this paper, a LiDAR dataset and VHR imagery from aerial survey was used in the southwest zone of Medellín City-Colombia where the most frequent landslides are shallow and triggered by rainfall. Slopes with gradients up to 30% on residual soils characterize the study area, having about of 30% of forest cover consisting predominantly of Eucalyptus and Coniferous forests. For the estimation of the tree roots effects on the shallow landslides assessment on a natural slope, interpolation processes were developed from the LiDAR 3D point cloud, obtaining DTMs of 1 m-pixel. Additionally, orthophotos with the same spatial resolution were acquired in the aerial campaign. The proposed workflow was implemented on a GIS platform, and considers the extraction of the tree heights by generating a Canopy Height Model (CHM), while for the delineation of the tree crown a process of image segmentation was developed. Once the vegetation has been characterized using LiDAR products and dendrometric relationships, the Limit Equilibrium Method (LEM) was used to evaluate slope stability considering the effect of vegetation (trees). The results indicate that the proposed workflow allows to obtain adequate stability indicators for the estimation of tree roots contribution and additionally, this RS technique allows saving resources in this kind of analysis.

SPATIAL DEPENDENCE DEGREE AND SAMPLING NEIGHBORHOOD INFLUENCE ON INTERPOLATION PROCESS FOR FERTILIZER PRESCRIPTION MAPS

Data interpolation is widely required in precision agriculture. However, its effectiveness is a function of the characteristics of the dataset, being necessary for the evaluation of several parameters. This study aimed to identify how the spatial interpolators, Kriging, and Inverse Distance Weighting, are influenced by the degree of spatial dependence of the variables analyzed and the number of neighbors considered in the interpolation process (sampling neighborhood). Soil samples were collected from three sugarcane fields. By the optimization process, we verified that the sampling neighborhood influences the accuracy of interpolations, but there is not a standard recommendation to follow. Thus, the best sampling neighborhood must ever be optimized for each case when preparing fertilizer prescription maps. Evaluating the performance of interpolations is always important to infer the reliability of the prescription maps, since no index that measures the degree of spatial dependence is effective. Because high prediction errors can occur when spatial dependence is poorly modeled, one cannot expect crop response with the continuous application of fertilizers in variable rates. Thus, work with homogeneous soil zones can be an interesting palliative approach. This study guides precision agriculture practitioners on some points that should be carefully considered in the data interpolation process for generating fertilizer prescription maps.

Strong clutter suppression in non‐uniform PRF radar: techniques based on interpolation and adaptive processing

Standard Doppler processing techniques are not capable of controlling strong clutter sidelobes when non-uniform pulse repetition frequency (PRF) radar waveforms are utilised. In this study, the authors propose a weighted bandlimited interpolation (WBI)-based Doppler processing technique, which generates a spectrum similar to that of uniform PRF waveform processing, successfully suppressing undesired spectral sidelobes. Three versions of WBI are introduced: WBI windowed, WBI adaptive, and WBI-principal components inverse (WBI-PCI), and their detection performance is quantified by generating receiver operating characteristics and estimating associated signal-to-noise ratio (SNR) losses. The performance of the algorithms is also analysed in terms of computational complexity. The superiority of the proposed WBI techniques compared to existing techniques is also demonstrated. WBI-PCI is an attractive choice for non-uniform PRF waveform processing, given its low SNR loss, low complexity, and low training requirement.

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.

Semivariogram fitting based on SVM and GPR for DEM interpolation

DEM (Digital Elevation Model) as a digital model of the earth’s surface elevation could be generated from remote sensing technology such as stereo imaging for various applications. To generate DEM from stereo imagery, interpolation or approximation process stage is required. Stochastic interpolation e.g. ordinary kriging uses semivariogram fitting to calculate weights of interpolation values based on known points. This research is applying regression types of machine learning for semivariogram fitting to interpolate DEM. Previous research conducted was LS-SVM (Least Square-Support Vector Machine) and SVR (Support Vector Regression) for semivariogram fitting process. Types of SVM and GPR (Gaussian Process Regression) are adopted for semivariogram fitting for ordinary kriging interpolation in this experiment. The result showed that in general SVM types could predict accuracy better than other types of regression, and GPR types produce better DEM accuracy based on the experiment.

Nonuniform sampling pitch acquisition method in myocardial single-photon emission computed tomography.

Single-photon emission computed tomography is a tomographic imaging method that acquires a projection image by rotating a gamma camera around by 380° or 180°. For myocardial single-photon emission computed tomography, 180° acquisition is common, but it has limitations including an incomplete reconstruction, which can distort the resulting image. It is possible to produce a complete reconstruction using 360° acquisition, but the testing time is long and is burdensome to patients. The nonuniform sampling pitch acquisition (NUSPA) method devised in this study involves reducing the total sampling count using NUSPA that reduces the sampling pitch in the range in which the gamma cameras are closer to the myocardium (RAO45-LPO45) and increases it elsewhere. The NUSPA-1 method based on a 6° sampling pitch had 20 views fewer than 360° acquisition. In addition, the NUSPA-2 method based on a 3.75° sampling pitch had 60 views fewer than 360° acquisition, considerably reducing the testing time. The acquired sinograms from the NUSPA methods were subjected to nonuniform rational B-spline surface interpolation processing, producing data with a uniform sampling pitch, after which image reconstruction was performed. The images after nonuniform rational B-spline interpolation for both the line sources and heart-liver phantom investigated in this study were not found to have the distortion observed from 180° acquisition or a count decrease at the center, resulting in image quality nearly equivalent to 360° acquisition. This method enabled a reduction in testing time without impacting image quality.

Assessing radiomic feature robustness to interpolation in 18F-FDG PET imaging

Radiomic studies link quantitative imaging features to patient outcomes in an effort to personalise treatment in oncology. To be clinically useful, a radiomic feature must be robust to image processing steps, which has made robustness testing a necessity for many technical aspects of feature extraction. We assessed the stability of radiomic features to interpolation processing and categorised features based on stable, systematic, or unstable responses. Here, 18F-fluorodeoxyglucose (18F-FDG) PET images for 441 oesophageal cancer patients (split: testing = 353, validation = 88) were resampled to 6 isotropic voxel sizes (1.5 mm, 1.8 mm, 2.0 mm, 2.2 mm, 2.5 mm, 2.7 mm) and 141 features were extracted from each volume of interest (VOI). Features were categorised into four groups with two statistical tests. Feature reliability was analysed using an intraclass correlation coefficient (ICC) and patient ranking consistency was assessed using a Spearman’s rank correlation coefficient (ρ). We categorised 93 features robust and 6 limited robustness (stable responses), 34 potentially correctable (systematic responses), and 8 not robust (unstable responses). We developed a correction technique for features with potential systematic variation that used surface fits to link voxel size and percentage change in feature value. Twenty-nine potentially correctable features were re-categorised to robust for the validation dataset, after applying corrections defined by surface fits generated on the testing dataset. Furthermore, we found the choice of interpolation algorithm alone (spline vs trilinear) resulted in large variation in values for a number of features but the response categorisations remained constant. This study attempted to quantify the diverse response of radiomics features commonly found in 18F-FDG PET clinical modelling to isotropic voxel size interpolation.

Fast Hue-Division-Based Selective Color Transfer

This paper introduces a new concept, selective color transfer (SCT), to allow for color experimentation and visualization on a selected object within an image, without affecting any other image content or color. To implement this new concept, this paper proposes a new fast SCT-I algorithm for image input data and a new SCT-V algorithm for video input data. For the SCT-I algorithm, its fundamental novelties include: 1) utilizing a new hue-division-based color region segmentation (HCR) based on defining a new nonlinear and circular property of the hue spectrum; 2) developing two new color artifact suppression strategies, including color region integration and circular statistical calculation; and 3) applying a new truncated color transfer equation to solve the problem of mismatches in the data range. The SCT-V algorithm utilizes: 1) object tracking to locate the target of interest (TOI) within each video frame; 2) the SCT-I algorithm to update the original color within TOIs; and 3) an expected color interpolation process to support different special color animation effects. The experimental results demonstrate: 1) there are no residual color artifacts introduced; 2) the approaches have tremendous flexibility for modifying an object's color; and 3) these algorithms have a low computational cost. Furthermore, these algorithms require minimal manual intervention for the easy use of ordinary users. The performance analysis demonstrates the potential of these two methods for various applications, including creating special effects in videos, making histology images much clearer for medical inspection, and enabling low-cost experimentation of manufacturing the design of a product.

Geospatial modeling of surface soil texture of agricultural land using fuzzy logic, geostatistics and GIS techniques

ABSTRACTSoil texture is a key controlling factor of soil properties and its functions include water and nutrient holding capacity, retention of pollutants, root development, soil biodiversity, and biogeochemical cycling. From the geotechnical standpoint, it is interesting to analyze the soil texture in regions due to its relation with the infiltration and runoff processes and, consequently, the effect on erosion processes. The purpose of this study is to present a methodology that provides the soil texture spatial variation by using Fuzzy logic theory and geostatistical technique in Geographic Information System (GIS) platform. A total of 140 soil samples were taken from topsoil (0–30 cm) in the study area located in the north of Guilan Province, the southern coast of Caspian Sea, Northern Iran. The soil textural classes were converted to numerical values (fuzzy values) using the fuzzy logic concept. The fuzzy values were spatially interpolated by ordinary kriging method such that the fitted model on experimental semi-variogram was exponential with moderate structure. The results showed the accuracy of soil texture predictive map was acceptable according to the values of normalized root-mean-square error for train data set (0.182) and test data set (0.179). The knowledge of the spatial variability of soil properties such as the soil texture can be an important tool for land-use planning in order to reduce the potential soil losses during rainy seasons. The results indicated that the integration of fuzzy logic, geostatistics, and GIS can improve the interpolation process.

Linear fuzzy rule base interpolation using fuzzy geometry

Fuzzy Rule Interpolation (FRI) provides an interpretable decision in sparse fuzzy rule based system. The objective of this work is to establish a mathematical demonstration of the pattern of existing fuzzy rule base using fuzzy geometry. Though several authors contributed on fuzzy rule base interpolation but there is a need to generate closed mathematical form of interpolating pattern. The present work is an initiative to demonstrate the same. First part of this paper presents some spatial geometrical transformation of a fuzzy point. In the second part of this paper, a new FRI scheme is suggested using fuzzy geometry with above mentioned transformation. The proposed method operates in two different steps. In the first step, all the fuzzy rules are converted into fuzzy sets or mostly fuzzy points in higher dimension by using mathematical operator on the individual of antecedent and consequent parts. All rules or fuzzy points are then joined with a class of fuzzy line segments (FLS). Second step considers the identification of mathematical pattern of the interpolated piecewise linear fuzzy polynomial which is able to compute the desired conclusion of a given observation. The presented method not only associates the FRI technique to classical interpolation technique, but also promises to provide the geometrical visualization of the behaviour of fuzzy sets during the interpolation process.

Phylin 2.0: Extending the phylogeographical interpolation method to include uncertainty and user-defined distance metrics.

Estimating geographical ranges of intra-specific evolutionary lineages is crucial to the fields of biogeography, evolution, and biodiversity conservation. Models of isolation mechanisms often consider multiple distances in order to explain genetic divergence. Yet, the available methods to estimate the geographical ranges of lineages are based on direct geographical distances, neglecting other distance metrics that can better explain the spatial genetic structure. We extended the phylogeographical interpolation method (phylin) in order to accommodate user-defined distance metrics and to incorporate the uncertainty associated with genetic distance calculation. These new features were tested with simulated and empirical data sets. Multiple distance matrices were generated including geographical, resistance, and environmental distances to derive maps of lineage occurrence. The new additions to this method improved the ability to predict lineage occurrence, even with low sample size. We used a regression framework to quantify the relationship between the genetic divergence and competing distance matrices representing potential isolation processes that are subsequently used in the interpolation process. Including uncertainty in tree topology and the different distance matrices improved the robustness of the variograms, allowing a better fit of the theoretical model of spatial dependence. The improvements to the method increase its potential application in other fields. Accurately mapping genetic divergence can help to locate potential contact zones between lineages as well as barriers to gene flow, which has a broad interest in biogeographical and evolutionary studies. Additionally, conservation efforts could benefit from the integration of genetic variation and landscape features in a spatially explicit framework.

Smooth switching method for asynchronous multiple viewpoint videos using frame interpolation

This research proposes a method that generates viewpoint smooth switching by reducing the flickering artefacts that are observed at bullet-times generated from asynchronous multi-view videos using frame interpolation processing. When we asynchronously capture multi-view videos of an object moving at a high velocity, deviations occur in the observed position at the bullet-times. We apply a frame interpolation technique to smooth this problem. By selecting suitable interpolated images that produce the smallest movement of the subject’s observed position, we smoothly generate a viewpoint-switched bullet-time video.In this paper, we examine the subjective evaluation of the video generated by the proposed method. And we also examine objective evaluation. Therefore, the effectiveness of the proposed method is shown. Furthermore, reproducibility was improved by considering the application conditions of the proposed method.

A Loewner Interpolation Method for Power System Identification and Order Reduction

An accurate framework for power system identification and model order reduction based on the Loewner matrix method is proposed. In this approach, frequency responses corresponding to non-symmetrical non-square MIMO transfer functions are introduced as tangential data in the Loewner interpolation process. Such responses can be either computed efficiently when explicit large sparse models are available or measured when only black-box models are at disposal. Numerical results are discussed for a couple of well-reported multi-machine test systems. The accuracy of the produced models and comparison against other state-of-the-art techniques are then discussed.

Lagrange interpolation at Pollaczek–Laguerre zeros on the real semiaxis

In order to approximate functions defined on the real semiaxis, which can grow exponentially both at 0 and at +∞, we introduce a suitable Lagrange operator based on the zeros of orthogonal polynomials with respect to the weight w(x)=xγe−x−α−xβ. We prove that this interpolation process has Lebesgue constant with order logm in weighted uniform metric and converges with the order of the best approximation in a large subset of weighted Lp-spaces, 1<p<∞, with proper assumptions.

Ceramic materials and energy—Extended Coble’s model and fractal nature

The new frontiers open different directions within the higher and deeper knowledge structure using unemployed nano sizes domains. The BaTiO3 and other ceramic materials have fractal configuration nature based on three phenomena. First, ceramic grains have fractal shape looking as a contour in cross section or as a surface. Second, there is the so-called “negative space” made of pores and intergranular space. Third, there is fractal Brownian motion (fBm) within the material, during and after sintering, in the form of microparticle flow: ions, atoms, and electrons. Here, we took upon ourselves the task of extending Coble’s model, with already generalized Euclidean geometries, by fractal nature correction. These triple factors make the very peculiar microelectronic environment electro-static/dynamic combination. The stress is here set on inter-granular micro-capacity in function of higher energy harvesting and storage. Constructive fractal theory allows identifying micro-capacitors with fractal electrodes. The method is based on the iterative process of interpolation which is compatible with the grain model itself. Inter-granular permeability is taken as the fundamental thermodynamic parameter function of temperature and enthalpy (Gibbs free energy), which are very important for a structure-energy relation.

The validity of RFID badges measuring face-to-face interactions

Face-to-face interactions are important for a variety of individual behaviors and outcomes. In recent years, a number of human sensor technologies have been proposed to incorporate direct observations in behavioral studies of face-to-face interactions. One of the most promising emerging technologies is the application of active Radio Frequency Identification (RFID) badges. They are increasingly applied in behavioral studies because of their low costs, straightforward applicability, and moderate ethical concerns. However, despite the attention that RFID badges have recently received, there is a lack of systematic tests on how valid RFID badges are in measuring face-to-face interactions. With two studies, we aim to fill this gap. Study 1 (N = 11) compares how data assessed with RFID badges correspond with video data of the same interactions (construct validity) and how this fit can be improved using straightforward data processing strategies. The analyses show that the RFID badges have a sensitivity of 50%, which can be enhanced to 65% when flickering signals with gaps of less than 75 s are interpolated. The specificity is relatively less affected by this interpolation process (before interpolation 97%, after interpolation 94.7%)—resulting in an improved accuracy of the measurement. In Study 2 (N = 73) we show that self-report data of social interactions correspond highly with data gathered with the RFID badges (criterion validity).

Orebody Modeling from Non-Parallel Cross Sections with Geometry Constraints

In this paper, we present an improved approach to the surface reconstruction of orebody from sets of interpreted cross sections that allows for shape control with geometry constraints. The soft and hard constraint rules based on adaptive sampling are proposed. As only the internal and external position relations of sections are calculated, it is unnecessary to estimate the normal directions of sections. Our key contribution is proposing an iterative closest point correction algorithm. It can be used for iterative correction of the distance field based on the constraint rules and the internal and external position relations of the model. We develop a rich variety of geometry constraints to dynamically control the shape trend of orebody for structural geologists. As both of the processes of interpolation and iso-surface extraction are improved, the performance of this method is excellent. Combined with the interactive tools of constraint rules, our approach is shown to be effective on non-trivial sparse sections. We show the reconstruction results with real geological datasets and compare the method with the existing reconstruction methods.

Convergence of spline interpolation processes and conditionality of systems of equations for spline construction

This study is a continuation of research on the convergence of interpolation processes with classical polynomial splines of odd degree. It is proved that the problem of good conditionality of a system of equations for interpolation spline construction via coefficients of the expansion of the th derivative in -splines is equivalent to the problem of convergence of the interpolation process for the th spline derivative in the class of functions with continuous th derivatives. It is established that for interpolation with splines of degree , the conditions that the projectors corresponding to the derivatives of orders and be bounded are equivalent. Bibliography: 26 titles.

Agile maneuvering with a small fixed-wing unmanned aerial vehicle

This paper presents a general and systematic approach to automating a variety of agile maneuvers with a small fixed-wing unmanned aerial vehicle. The methodology begins by numerically solving optimal control problems off-line to generate a small set of reference trajectories and feedforward control inputs for maneuvers. A dynamic time warping-based interpolation process parametrizes these solutions, adding robustness to the maneuver, whilst allowing the on-board library of state and control time histories to remain compact. To handle errors, inaccuracies, noise, and disturbances that are not accounted for by feedforward control, feedback control laws stabilize about the reference trajectories. The work focuses mainly on one agile maneuver: an aggressive turn-around, in which the aircraft undergoes a rapid 180 degree heading reversal, beginning and ending in straight and level flight. To establish the generality of the methodology, it is also applied to transition maneuvers between straight and level flight, and a nose-up hover. The proposed automation scheme is computationally light during flight, consisting of a simple feedforward/feedback controller coupled to a compact library of maneuvers that are optimized over the full flight envelope. The methodology is validated in simulations and flight tests. The automation scheme is implemented successfully on a small fixed-wing unmanned aerial vehicle.