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Journal articles on the topic 'Spatial interpolation'

Author: Grafiati
Published: 4 June 2021
Last updated: 11 September 2023

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1

Earshia V., Diana, and Sumathi M. "Interpolation of Low-Resolution Images for Improved Accuracy Using an ANN Quadratic Interpolator." International Journal on Recent and Innovation Trends in Computing and Communication 11, no. 4s (April 3, 2023): 135–40. http://dx.doi.org/10.17762/ijritcc.v11i4s.6319.

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The era of digital imaging has transitioned into a new one. Conversion to real-time, high-resolution images is considered vital. Interpolation is employed in order to increase the number of pixels per image, thereby enhancing spatial resolution. Interpolation's real advantage is that it can be deployed on user end devices. Despite raising the number of pixels per inch to enhances the spatial resolution, it may not improve the image's clarity, hence diminishing its quality. This strategy is designed to increase image quality by enhancing image sharpness and spatial resolution simultaneously. Proposed is an Artificial Neural Network (ANN) Quadratic Interpolator for interpolating 3-D images. This method applies Lagrange interpolating polynomial and Lagrange interpolating basis function to the parameter space using a deep neural network. The degree of the polynomial is determined by the frequency of gradient orientation events within the region of interest. By manipulating interpolation coefficients, images can be upscaled and enhanced. By mapping between low- and high-resolution images, the ANN quadratic interpolator optimizes the loss function. ANN Quadratic interpolator does a good work of reducing the amount of image artefacts that occur during the process of interpolation. The weights of the proposed ANN Quadratic interpolator are seeded by transfer learning, and the layers are trained, validated, and evaluated using a standard dataset. The proposed method outperforms a variety of cutting-edge picture interpolation algorithms..
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Etherington, Thomas R. "Discrete natural neighbour interpolation with uncertainty using cross-validation error-distance fields." PeerJ Computer Science 6 (July 13, 2020): e282. http://dx.doi.org/10.7717/peerj-cs.282.

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Interpolation techniques provide a method to convert point data of a geographic phenomenon into a continuous field estimate of that phenomenon, and have become a fundamental geocomputational technique of spatial and geographical analysts. Natural neighbour interpolation is one method of interpolation that has several useful properties: it is an exact interpolator, it creates a smooth surface free of any discontinuities, it is a local method, is spatially adaptive, requires no statistical assumptions, can be applied to small datasets, and is parameter free. However, as with any interpolation method, there will be uncertainty in how well the interpolated field values reflect actual phenomenon values. Using a method based on natural neighbour distance based rates of error calculated for data points via cross-validation, a cross-validation error-distance field can be produced to associate uncertainty with the interpolation. Virtual geography experiments demonstrate that given an appropriate number of data points and spatial-autocorrelation of the phenomenon being interpolated, the natural neighbour interpolation and cross-validation error-distance fields provide reliable estimates of value and error within the convex hull of the data points. While this method does not replace the need for analysts to use sound judgement in their interpolations, for those researchers for whom natural neighbour interpolation is the best interpolation option the method presented provides a way to assess the uncertainty associated with natural neighbour interpolations.
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Stein, A. "Spatial Interpolation." Biometrics 50, no. 2 (June 1994): 592. http://dx.doi.org/10.2307/2533421.

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4

Caloiero, Tommaso, Gaetano Pellicone, Giuseppe Modica, and Ilaria Guagliardi. "Comparative Analysis of Different Spatial Interpolation Methods Applied to Monthly Rainfall as Support for Landscape Management." Applied Sciences 11, no. 20 (October 14, 2021): 9566. http://dx.doi.org/10.3390/app11209566.

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Landscape management requires spatially interpolated data, whose outcomes are strictly related to models and geostatistical parameters adopted. This paper aimed to implement and compare different spatial interpolation algorithms, both geostatistical and deterministic, of rainfall data in New Zealand. The spatial interpolation techniques used to produce finer-scale monthly rainfall maps were inverse distance weighting (IDW), ordinary kriging (OK), kriging with external drift (KED), and ordinary cokriging (COK). Their performance was assessed by the cross-validation and visual examination of the produced maps. The results of the cross-validation clearly evidenced the usefulness of kriging in the spatial interpolation of rainfall data, with geostatistical methods outperforming IDW. Results from the application of different algorithms provided some insights in terms of strengths and weaknesses and the applicability of the deterministic and geostatistical methods to monthly rainfall. Based on the RMSE values, the KED showed the highest values only in April, whereas COK was the most accurate interpolator for the other 11 months. By contrast, considering the MAE, the KED showed the highest values in April, May, June and July, while the highest values have been detected for the COK in the other months. According to these results, COK has been identified as the best method for interpolating rainfall distribution in New Zealand for almost all months. Moreover, the cross-validation highlights how the COK was the interpolator with the best least bias and scatter in the cross-validation test, with the smallest errors.
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Al-husban, Yusra. "Comparison of Spatial Interpolation Methods for Estimating the Annual Rainfall in the Wadi Al-Mujib Basin in Jordan." Jordan Journal of Social Sciences 15, no. 2 (September 29, 2022): 198–208. http://dx.doi.org/10.35516/jjss.v15i2.490.

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Accurate rainfall data are essential for environmental applications in the actual assessment of the geographical distribution of rainfall. Interpolation methods are usually applied to monitor the spatial distribution of the rainfall data. There are many spatial interpolation methods, but none of them can achieve in all cases the best results. In this study, three different interpolation methods were investigated with regard to their suitability for producing a spatial rainfall distribution. Rainfall data from 14 meteorological stations were spatially interpolated using three common interpolation techniques: inverse distance weighting (IDW), ordinary kriging (OK), and kernel smoothing (KS) were compared and assessed against station rainfall data and modeled rainfall. Cross-validation was applied to evaluate the accuracy of interpolation methods in terms of the root-mean-square error (RMSE). The best results were obtained by the lowest RMSE for interpolating the precipitation (RMSE) = 100.86542, while the inverse distance weighting (IDW) performed the worst, and are least efficient with the largest RMSE=103.43; in addition, the kernel smoothing with the least minimum (-) and maximum (+) error is -92.38 mm and 313.33 mm.
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6

DeGaetano, Arthur T., Brian N. Belcher, and William Noon. "Temporal and Spatial Interpolation of the Standardized Precipitation Index for Computational Efficiency in the Dynamic Drought Index Tool." Journal of Applied Meteorology and Climatology 54, no. 4 (April 2015): 795–810. http://dx.doi.org/10.1175/jamc-d-14-0088.1.

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AbstractThe feasibility of interpolating gamma-distribution parameters between different precipitation accumulation intervals (durations) is statistically evaluated. The interpolation of these parameters for a specific accumulation interval, but ending on different dates, is similarly assessed. Such interpolation increases the computational efficiency of drought-monitoring tools that require calculation of the standardized precipitation index (SPI) for any user-specified accumulation period on any given day. Spatial interpolation of the distribution parameters is also assessed. Given a 60-yr period of record, few statistically significant differences were found between gamma-distribution percentiles interpolated between fixed base durations and those computed directly. Shorter interpolation intervals (generally 30 days) were required for the shortest (e.g., 30 days) durations, whereas interpolation over periods of as long as 180 days could be used for the longest (between 360 and 720 days) durations. Interpolating the distribution parameters to different ending dates on the basis of those computed for the end of each month was also appropriate. The spatial interpolation of gamma-distribution parameters, although viable in practice for monitoring large-scale drought conditions, was associated with larger SPI differences than was the spatial interpolation of the SPI index itself or the interpolation of historical precipitation and the subsequent calculation of gamma-distribution parameters on the basis of these values.
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7

Van der Steen, A., B. Heeg, F. De Charro, and BA Van Hout. "PMC10 SPATIAL INTERPOLATION." Value in Health 10, no. 6 (November 2007): A453. http://dx.doi.org/10.1016/s1098-3015(10)65564-7.

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8

Wickramathilaka, Nevil, Uznir Ujang, Suhaibah Azri, and Tan Liat Choon. "Calculation of Road Traffic Noise, Development of Data, and Spatial Interpolations for Traffic Noise Visualization in Three-dimensional Space." Geomatics and Environmental Engineering 17, no. 5 (August 28, 2023): 61–85. http://dx.doi.org/10.7494/geom.2023.17.5.61.

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Road traffic noise visualization is vital in three-dimensional (3D) space. Designing noise observation points (NOPs) and the developments of spatial interpolations are key elements for the visualization of traffic noise in 3D. Moreover, calculating road traffic noise levels by means of a standard noise model is vital. This study elaborates on the developments of data and spatial interpolations in 3D noise visualization. In 3D spatial interpolation, the value is interpolated in both horizontal and vertical directions. Eliminating flat triangles is vital in the vertical direction. Inverse distance weighted (IDW), kriging, and triangular irregular network (TIN) are widely used to interpolate noise levels. Because these interpolations directly support the interpolation of three parameters, the developments of spatial interpolations should be applied to interpolate noise levels in 3D. The TIN noise contours are primed to visualize traffic noise levels while IDW and kriging provide irregular contours. Further, this study has identified that the TIN noise contours fit exactly with NOPs in 3D. Moreover, advanced kriging interpolation such as empirical Bayesian kriging (EBK) also provides irregular shape contours and this study develops a comparison for such contours. The 3D kriging in EBK provides a significant approach to interpolate noise in 3D. The 3D kriging voxels show a higher accurate visualization than TIN noise contours.
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9

Flannigan, M. D., and B. M. Wotton. "A study of interpolation methods for forest fire danger rating in Canada." Canadian Journal of Forest Research 19, no. 8 (August 1, 1989): 1059–66. http://dx.doi.org/10.1139/x89-161.

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Canadian fire control agencies use either simple interpolation methods or none at all in estimating fire danger between weather stations. We compare several methods of interpolation and use the fire weather index in the North Central Region of Ontario as a case study. Our work shows that the second order least square polynomial, the smoothed cubic spline, and the weighted interpolations had the lowest residual sum of squares in our verification scheme. These methods fit the observed data at both high and low fire weather index values. The highly variable nature of the spatial distribution of summer precipitation amount is the biggest problem in interpolating between stations. This factor leads to highly variable fire weather index fields that are the most difficult to interpolate. The use of radar and (or) satellite data could help resolve precipitation patterns with greater precision. These interpolation methods could easily be implemented by fire control agencies to gain a better understanding of fire danger in the region.
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10

Etzel, K. R., and J. M. McCarthy. "Interpolation of Spatial Displacements Using the Clifford Algebra of E4." Journal of Mechanical Design 121, no. 1 (March 1, 1999): 39–44. http://dx.doi.org/10.1115/1.2829427.

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In this paper we show that the Clifford Algebra of four dimensional Euclidean space yields a set of hypercomplex numbers called “double quaternions.” Interpolation formulas developed to generate Bezier-style quaternion curves are shown to be applicable to double quaternions by simply interpolating the components separately. The resulting double quaternion curves are independent of the coordinate frame in which the key frames are specified. Double quaternions represent rotations in E4 which we use to approximate spatial displacements. The result is a spatial motion interpolation methodology that is coordinate frame invariant to a desired degree of accuracy within a bounded region of three dimensional space. Examples demonstrate the application of this theory to computing distances between spatial displacement, determining the mid-point between two displacements, and generating the spatial motion interpolating a set of key frames.
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11

Sekulić, Aleksandar, Milan Kilibarda, Gerard B. M. Heuvelink, Mladen Nikolić, and Branislav Bajat. "Random Forest Spatial Interpolation." Remote Sensing 12, no. 10 (May 25, 2020): 1687. http://dx.doi.org/10.3390/rs12101687.

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For many decades, kriging and deterministic interpolation techniques, such as inverse distance weighting and nearest neighbour interpolation, have been the most popular spatial interpolation techniques. Kriging with external drift and regression kriging have become basic techniques that benefit both from spatial autocorrelation and covariate information. More recently, machine learning techniques, such as random forest and gradient boosting, have become increasingly popular and are now often used for spatial interpolation. Some attempts have been made to explicitly take the spatial component into account in machine learning, but so far, none of these approaches have taken the natural route of incorporating the nearest observations and their distances to the prediction location as covariates. In this research, we explored the value of including observations at the nearest locations and their distances from the prediction location by introducing Random Forest Spatial Interpolation (RFSI). We compared RFSI with deterministic interpolation methods, ordinary kriging, regression kriging, Random Forest and Random Forest for spatial prediction (RFsp) in three case studies. The first case study made use of synthetic data, i.e., simulations from normally distributed stationary random fields with a known semivariogram, for which ordinary kriging is known to be optimal. The second and third case studies evaluated the performance of the various interpolation methods using daily precipitation data for the 2016–2018 period in Catalonia, Spain, and mean daily temperature for the year 2008 in Croatia. Results of the synthetic case study showed that RFSI outperformed most simple deterministic interpolation techniques and had similar performance as inverse distance weighting and RFsp. As expected, kriging was the most accurate technique in the synthetic case study. In the precipitation and temperature case studies, RFSI mostly outperformed regression kriging, inverse distance weighting, random forest, and RFsp. Moreover, RFSI was substantially faster than RFsp, particularly when the training dataset was large and high-resolution prediction maps were made.
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12

Myers, Donald E. "Spatial interpolation: an overview." Geoderma 62, no. 1-3 (March 1994): 17–28. http://dx.doi.org/10.1016/0016-7061(94)90025-6.

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13

Yang, Jie, Weiqi Jin, Su Qiu, Fuduo Xue, and Meishu Wang. "Residual Interpolation Integrated Pixel-by-Pixel Adaptive Iterative Process for Division of Focal Plane Polarimeters." Sensors 22, no. 4 (February 16, 2022): 1529. http://dx.doi.org/10.3390/s22041529.

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Residual interpolations are effective methods to reduce the instantaneous field-of-view error of division of focal plane (DoFP) polarimeters. However, their guide-image selection strategies are improper, and do not consider the DoFP polarimeters’ spatial sampling modes. Thus, we propose a residual interpolation method with a new guide-image selection strategy based on the spatial layout of the pixeled polarizer array to improve the sampling rate of the guide image. The interpolation performance is also improved by the proposed pixel-by-pixel, adaptive iterative process and the weighted average fusion of the results of the minimized residual and minimized Laplacian energy guide filters. Visual and objective evaluations demonstrate the proposed method’s superiority to the existing state-of-the-art methods. The proposed method proves that considering the spatial layout of the pixeled polarizer array on the physical level is vital to improving the performance of interpolation methods for DoFP polarimeters.
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14

Imanian, Hanifeh, Hamidreza Shirkhani, Abdolmajid Mohammadian, Juan Hiedra Hiedra Cobo, and Pierre Payeur. "Spatial Interpolation of Soil Temperature and Water Content in the Land-Water Interface Using Artificial Intelligence." Water 15, no. 3 (January 25, 2023): 473. http://dx.doi.org/10.3390/w15030473.

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The distributed measured data in large regions and remote locations, along with a need to estimate climatic data for point sites where no data have been recorded, has encouraged the implementation of spatial interpolation techniques. Recently, the increasing use of artificial intelligence has become a promising alternative to conventional deterministic algorithms for spatial interpolation. The present study aims to evaluate some machine learning-based algorithms against conventional strategies for interpolating soil temperature data from a region in southeast Canada with an area of 1000 km by 550 km. The radial basis function neural networks (RBFN) and the deep learning approach were used to estimate soil temperature along a railroad after the spline deterministic spatial interpolation method failed to interpolate gridded soil temperature data on the desired locations. The spline method showed weaknesses in interpolating soil temperature data in areas with sudden changes. This limitation did not improve even by increasing the spline nonlinearity. Although both radial basis function neural networks and the deep learning approach had successful performances in interpolating soil temperature data even in sharp transition areas, deep learning outperformed the former method with a normalized RMSE of 9.0% against 16.2% and an R-squared of 89.2% against 53.8%. This finding was confirmed in the same investigation on soil water content.
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15

TANJUNG, MAULINA, SAUMI SYAHREZA, and MUHAMMAD RUSDI. "Comparison of interpolation methods based on Geographic Information System (GIS) in the spatial distribution of seawater intrusion." Jurnal Natural 20, no. 2 (June 16, 2020): 24–30. http://dx.doi.org/10.24815/jn.v20i2.16440.

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The study of monitoring seawater intrusion and groundwater quality in a coastal area needs to be done regularly to prevent the clean water crisis problems in the future. Accurate and reliable interpolation of seawater intrusion over a region is the requirement of an efficient monitoring. In this study, different interpolation methods were investigated and compared to determine the best interpolation method for predicting the spatial distribution of seawater intrusion in the coastal area of Banda Aceh. Groundwater electrical conductivity (EC) was analyzed to identify the contamination of seawater intrusion into the coastal aquifers. Four interpolation methods such as Empirical Bayesian Kriging (EBK), Global Polynomial Interpolation (GPI), Inverse Distance Weighting (IDW), and Local Polynomial Interpolation (LPI), were used to create the spatial distribution of the groundwater electrical conductivity. The accuracy of interpolation methods was evaluated by using a cross-validation technique through the coefficient of determination (R2) and the Root Mean Square Error (RMSE). The results showed that IDW performed the most accurate prediction values and the best surface which were indicated by the least RMSE and the highest R2 value. It can be concluded that IDW interpolation method is the best method for interpolating the groundwater electrical conductivity associated with seawater intrusion in the coastal area of Banda Aceh.
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Jain, P., and M. D. Flannigan. "Comparison of methods for spatial interpolation of fire weather in Alberta, Canada." Canadian Journal of Forest Research 47, no. 12 (December 2017): 1646–58. http://dx.doi.org/10.1139/cjfr-2017-0101.

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Spatial interpolation of fire weather variables from station data allow fire danger indices to be mapped continuously across the landscape. This information is crucial to fire management agencies, particularly in areas where weather data are sparse. We compare the performance of several standard interpolation methods (inverse distance weighting, spline, and geostatistical interpolation methods) for estimating output from the Canadian Fire Weather Index (FWI) system at unmonitored locations. We find that geostatistical methods (kriging) generally outperform the other methods, particularly when elevation is used as a covariate. We also find that interpolation of the input meteorological variables and the previous day’s moisture codes to unmonitored locations followed by calculation of the FWI output variables is preferable to first calculating the FWI output variables and then interpolating, in contrast to previous studies. Alternatively, when the previous day’s moisture codes are estimated from interpolated weather, rather than directly interpolated, errors can accumulate and become large. This effect is particularly evident for the duff moisture code and drought moisture code due to their significant autocorrelation.
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17

Pithani, Manikanta B., Shubhashis Sanyal, and Anuj K. Shukla. "Bilinear and Bicubic Interpolations for Image Presentation of Mechanical Stress and Temperature Distribution." Power Engineering and Engineering Thermophysics 1, no. 1 (October 31, 2022): 8–18. http://dx.doi.org/10.56578/peet010103.

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Bilinear and bicubic interpolations were often used in digital elevation models (DEMs), image scaling, and image restoration, with the aid of spatial transform techniques. This paper resorts to bilinear and bicubic interpolations, along with the spatial transform of images, to present the temperature distribution on a plate with a circular hole. The Dirichlet boundary conditions were applied, a rectangular grid was created, and the nodal values were calculated using the finite difference method (FDM). These methods were also employed to represent the mechanical stress distribution on a plate with a circular hole, under the presence of uniaxial stress. In this case, the nodal values were calculated using the analytical method. Experimental results show that bicubic interpolation generated continuous contours, while bilinear interpolation had a discontinuity in some cases. The results were comparative to images for similar cases when solved through ANSYS.
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18

张, 婕. "Research on Spatial Data Interpolation." Advances in Applied Mathematics 08, no. 11 (2019): 1859–69. http://dx.doi.org/10.12677/aam.2019.811216.

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19

J. B. Harcum and Jim C. Loftis. "spatial Interpolation of Penman Evapotranspiration." Transactions of the ASAE 30, no. 1 (1987): 0129–36. http://dx.doi.org/10.13031/2013.30414.

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20

Gedeon, T. D., K. W. Wong, P. M. Wong, and Y. Huang. "Spatial Interpolation Using Fuzzy Reasoning." Transactions in GIS 7, no. 1 (January 2003): 55–66. http://dx.doi.org/10.1111/1467-9671.00129.

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21

Rhee, Jinyoung, Gregory J. Carbone, and James Hussey. "Drought Index Mapping at Different Spatial Units." Journal of Hydrometeorology 9, no. 6 (December 1, 2008): 1523–34. http://dx.doi.org/10.1175/2008jhm983.1.

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Abstract This paper investigates the influence of spatial interpolation and aggregation of data to depict drought at different spatial units relevant to and often required for drought management. Four different methods for drought index mapping were explored, and comparisons were made between two spatial operation methods (simple unweighted average versus spatial interpolation plus aggregation) and two calculation procedures (whether spatial operations are performed before or after the calculations of drought index values). Deterministic interpolation methods including Thiessen polygons, inverse distance weighted, and thin-plate splines as well as a stochastic and geostatistical interpolation method of ordinary kriging were compared for the two methods that use interpolation. The inverse distance weighted method was chosen based on the cross-validation error. After obtaining drought index values for different spatial units using each method in turn, differences in the empirical binned frequency distributions were tested between the methods and spatial units. The two methods using interpolation and aggregation introduced fewer errors in cross validation than the two simple unweighted average methods. Whereas the method performing spatial interpolation and aggregation before calculating drought index values generally provided consistent drought information between various spatial units, the method performing spatial interpolation and aggregation after calculating drought index values reduced errors related to the calculations of precipitation data.
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Jaffar, Azhar, Norashikin M. Thamrin, Megat Syahirul Amin Megat Ali, Mohamad Farid Misnan, Ahmad Ihsan Mohd Yassin, and Noorolpadzilah Mohamed Zan. "Spatial interpolation method comparison for physico-chemical parameters of river water in Klang River using MATLAB." Bulletin of Electrical Engineering and Informatics 11, no. 4 (August 1, 2022): 2368–77. http://dx.doi.org/10.11591/eei.v11i4.3615.

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Water quality is one of the most highly debated issues worldwide at the moment. Inadequate water supplies affect human health, hinder food production, and degrade the environment. Using contemporary technology to analyze pollution statistics can help solve pollution issues. One option is to take advantage of advancements in intelligent data processing to conduct hydrological parameter analysis. To perform conclusive water quality studies, a lot of data is necessary. Unfilled data (information gaps) in the long-term hydrological data set may be due to equipment faults, collection schedule delays, or the data collection officer’s absence. The lack of hydrological data skews its interpretation. Therefore, interpolation is used to recreate and fill missing hydrological data. From 2012 to 2017, the Klang River’s biochemical oxygen demand (BOD) in Selangor, Malaysia, was sampled. This study examined three methods of interpolation for their effectiveness using the MATLAB software: piecewise cubic hermite interpolating polynomial (PCHIP), cubic Spline data interpolation (Spline), and modified Akima partitioned cubic hermite interpolation (Makima). The accuracy is assessed using root mean square error (RMSE). All interpolation algorithms offer excellent results with low RMSE. However, PCHIP delivers the best match between interpolated and original data.
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Zhan, Junda, Sensen Wu, Jin Qi, Jindi Zeng, Mengjiao Qin, Yuanyuan Wang, and Zhenhong Du. "A generalized spatial autoregressive neural network method for three-dimensional spatial interpolation." Geoscientific Model Development 16, no. 10 (May 24, 2023): 2777–94. http://dx.doi.org/10.5194/gmd-16-2777-2023.

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Abstract. Spatial interpolation, a fundamental spatial analysis method, predicts unsampled spatial data from the values of sampled points. Generally, the core of spatial interpolation is fitting spatial weights via spatial correlation. Traditional methods express spatial distances in a conventional Euclidean way and conduct relatively simple spatial weight calculation processes, limiting their ability to fit complex spatial nonlinear characteristics in multidimensional space. To tackle these problems, we developed a generalized spatial distance neural network (GSDNN) unit to generally and adaptively express spatial distances in complex feature space. By combining the spatial autoregressive neural network (SARNN) with the GSDNN unit, we constructed a generalized spatial autoregressive neural network (GSARNN) to perform spatial interpolation in three-dimensional space. The GSARNN model was examined and compared with traditional methods using two three-dimensional cases: a simulated case and a real Argo case. The experiment results demonstrated that exploiting the feature extraction ability of neural networks, the GSARNN achieved superior interpolation performance and was more adaptable than inverse distance weighted, ordinary Kriging, and SARNN methods.
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Wu, Wenjun, Ruijie Gan, Junli Li, Xiu Cao, Xinxin Ye, Jie Zhang, and Hongjiao Qu. "A Spatial Interpolation of Meteorological Parameters considering Geographic Semantics." Advances in Meteorology 2020 (September 2, 2020): 1–14. http://dx.doi.org/10.1155/2020/9185283.

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Spatial interpolation of meteorological parameters, closely related to the earth surface, plays important roles in climatological study. However, most of traditional spatial interpolation methods ignore the geographic semantics of interpolation sample points in practical application. This paper attempts to propose an improved inverse-distance weighting interpolation algorithm considering geographic semantics (S-IDW), which adds geographic semantic similarity to the traditional IDW formula and adjusts weight coefficient. In the interpolation process, the geographic semantic differences between sample points and estimation points are considered comprehensively. In this study, 3 groups of land surface temperature data from 2 different areas were selected for experiments, and several commonly used spatial interpolation methods were compared. Experimental results indicated that S-IDW outperformed IDW and several existing spatial interpolation methods, but there were also some abnormal value and interpolation outliers. This method provides a new insight toward the estimation accuracy, data missing, and error correction of spatial attributes related to meteorological parameters.
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Ahrens, B. "Distance in spatial interpolation of daily rain gauge data." Hydrology and Earth System Sciences 10, no. 2 (April 4, 2006): 197–208. http://dx.doi.org/10.5194/hess-10-197-2006.

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Abstract. Spatial interpolation of rain gauge data is important in forcing of hydrological simulations or evaluation of weather predictions, for example. This paper investigates the application of statistical distance, like one minus common variance of observation time series, between data sites instead of geographical distance in interpolation. Here, as a typical representative of interpolation methods the inverse distance weighting interpolation is applied and the test data is daily precipitation observed in Austria. Choosing statistical distance instead of geographical distance in interpolation of available coarse network observations to sites of a denser network, which is not reporting for the interpolation date, yields more robust interpolation results. The most distinct performance enhancement is in or close to mountainous terrain. Therefore, application of statistical distance in the inverse distance weighting interpolation or in similar methods can parsimoniously densify the currently available observation network. Additionally, the success further motivates search for conceptual rain-orography interaction models as components of spatial rain interpolation algorithms in mountainous terrain.
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De Jesus, Kevin Lawrence M., Delia B. Senoro, Jennifer C. Dela Cruz, and Eduardo B. Chan. "A Hybrid Neural Network–Particle Swarm Optimization Informed Spatial Interpolation Technique for Groundwater Quality Mapping in a Small Island Province of the Philippines." Toxics 9, no. 11 (October 21, 2021): 273. http://dx.doi.org/10.3390/toxics9110273.

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Water quality monitoring demands the use of spatial interpolation techniques due to on-ground challenges. The implementation of various spatial interpolation methods results in significant variations from the true spatial distribution of water quality in a specific location. The aim of this research is to improve mapping prediction capabilities of spatial interpolation algorithms by using a neural network with the particle swarm optimization (NN-PSO) technique. Hybrid interpolation approaches were evaluated and compared by cross-validation using mean absolute error (MAE) and Pearson’s correlation coefficient (R). The governing interpolation techniques for the physicochemical parameters of groundwater (GW) and heavy metal concentrations were the geostatistical approaches combined with NN-PSO. The best methods for physicochemical characteristics and heavy metal concentrations were observed to have the least MAE and R values, ranging from 1.7 to 4.3 times and 1.2 to 5.6 times higher than the interpolation technique without the NN-PSO for the dry and wet season, respectively. The hybrid interpolation methods exhibit an improved performance as compared to the non-hybrid methods. The application of NN-PSO technique to spatial interpolation methods was found to be a promising approach for improving the accuracy of spatial maps for GW quality.
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Hewitson, B. C., and R. G. Crane. "Gridded Area-Averaged Daily Precipitation via Conditional Interpolation." Journal of Climate 18, no. 1 (January 1, 2005): 41–57. http://dx.doi.org/10.1175/jcli3246.1.

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Abstract A growing need for gridded observational datasets of area-average values to support research, specifically in relation to climate models, raises questions about the adequacy of traditional interpolation techniques. Conventional interpolation techniques (particularly for precipitation) suffer from not recognizing the changing spatial representivity of stations as a function of the driving synoptic state, nor the bounded nature of the precipitation field—that the precipitation field is spatially discontinuous. Further, many interpolation techniques explicitly estimate new point location values, and do not directly address the need arising from climate modeling for area-average values. A new procedure, termed conditional interpolation, is presented to estimate daily gridded area-average precipitation from station observations. The approach explicitly recognizes that the point observations represent a mixture of synoptic forcing shared in common with surrounding stations, and a response that is unique to the station. Consequently the spatial representivity of a station is conditional on the synoptic forcing and is a function of the radial direction from the station. The conditional interpolation accommodates this in a two-stage process through conditioning the interpolation parameters as a function of the synoptic state. First, the spatial pattern of wet/dry conditions is estimated, following which the magnitude of the precipitation is derived for those locations determined as “wet.” In a test based on a high-resolution dataset for South Africa the conditional interpolation is very effective in defining the spatial extent of the precipitation field. It then derives gridded values that are representative of the area average. In comparison, both these characteristics appear to be significantly overestimated by one of the commonly used interpolation schemes (Cressman interpolation). Overall the interpolation conditioned by the synoptic state appears to better estimate realistic gridded area-average values.
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Respati, Sara, and Totok Sulistyo. "THE EFFECT OF THE NUMBER OF INPUTS ON THE SPATIAL INTERPOLATION OF ELEVATION DATA USING IDW AND ANNS." Geodesy and cartography 49, no. 1 (March 21, 2023): 60–65. http://dx.doi.org/10.3846/gac.2023.16591.

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Spatial interpolation is a required method to generate a continuous surface such as Digital Elevation Model (DEM) because field investigation for most of the surface’s part is time-consuming with a high demand in both human resources and monetory cost. One of the most used deterministic interpolation models is Inverse Distance Weighting (IDW) model. The model takes several neighbors’ information, and the weights are constructed based on the distance between the interpolated point and the neighbors’ points. From the machine learning model, Artificial Neural Networks (ANNs) model has also been used for spatial interpolation. The input of ANNs model is also one of the parameters that need to be defined when building the model. This paper evaluated the effect of the number of inputs (neighbors) on the elevation interpolation accuracy. We applied IDW and ANNs to interpolate the elevation of Balikpapan City, Indonesia. The results show that the accuracy increases significantly when the number of inputs is between one and three. However, after three inputs, additional input would not change the accuracy significantly. ANNs performed better than IDW. For three or more inputs, the MAE of ANNs and IDW interpolations are below 1.1 and around 2 meters, respectively.
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29

Rogelis, M. C., and M. G. F. Werner. "Spatial Interpolation for Real-Time Rainfall Field Estimation in Areas with Complex Topography." Journal of Hydrometeorology 14, no. 1 (February 1, 2013): 85–104. http://dx.doi.org/10.1175/jhm-d-11-0150.1.

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Abstract For many hydrological applications interpolation of point rainfall measurements is needed. One such application is flood early warning, particularly where spatially distributed hydrological models are used. Operation in real time poses challenges to the interpolation procedure, as this should then both be automatic and efficiently provide robust interpolation of gauged data. The differences in performance of ordinary kriging, universal kriging, and kriging with external drift with individual and pooled variograms were assessed for 139 daily datasets with significant precipitation in a study area in Bogotá, Colombia. Interpolators were compared using the percentage of variability explained and the root-mean-square error found in cross validation, aiming at identifying a procedure for real-time interpolation. The results showed that interpolators using pooled variograms provide a performance comparable to when the interpolators were applied to the storms individually, showing that they can be used successfully for interpolation in real-time operation in the study area. The analysis identified limitations in the use of kriging with external drift. Only when the adjusted R2 between the secondary variables and precipitation is higher than the percentage of variability explained found in ordinary kriging, then kriging with external drift provided a consistent improvement. This interpolator was found to give a lower performance in all other cases. The distribution of precipitation over basins of interest for each of the storms, derived through sampling rainfall fields generated through conditional Gaussian simulation, shows that, while differences between the interpolators may appear to be significant, the variability of the precipitation volume is less significant.
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30

Ahrens, B. "Distance in spatial interpolation of daily rain gauge data." Hydrology and Earth System Sciences Discussions 2, no. 5 (September 8, 2005): 1893–922. http://dx.doi.org/10.5194/hessd-2-1893-2005.

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Abstract. Spatial interpolation of rain gauge data is important in forcing of hydrological simulations or evaluation of weather predictions, for example. The spatial density of available data sites is often changing with time. This paper investigates the application of statistical distance, like one minus common variance of time series, between data sites instead of geographical distance in interpolation. Here, as a typical representative of interpolation methods the inverse distance weighting interpolation is applied and the test data is daily precipitation observed in Austria. Choosing statistical distance instead of geographical distance in interpolation of an actually available coarse observation network yields more robust interpolation results at sites of a denser network with actually lacking observations. The performance enhancement is in or close to mountainous terrain. This has the potential to parsimoniously densify the currently available observation network. Additionally, the success further motivates search for conceptual rain-orography interaction models as components of spatial rain interpolation algorithms in mountainous terrain.
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Szczepańska, Agnieszka, Dariusz Gościewski, and Małgorzata Gerus-Gościewska. "A GRID-Based Spatial Interpolation Method as a Tool Supporting Real Estate Market Analyses." ISPRS International Journal of Geo-Information 9, no. 1 (January 14, 2020): 39. http://dx.doi.org/10.3390/ijgi9010039.

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The spatial distribution of prices is closely linked with the urban real estate market. Property prices are one of the key indicators of economic activity because they influence economic decisions. Decision-makers and consumers often need information about the spatial distribution of prices, but spatial-temporal analyses of the real estate market are based on the prices quoted in different locations across years (epochs). Due to this idiosyncrasy, the resulting datasets are dispersed (different across years) and difficult to compare. For this reason, the existing interpolation methods are not always effective in analyses of the real estate market. A different approach to interpolating real estate prices that supports the generation of continuous interpolated surfaces while maintaining the values of measurement points is thus needed. This paper proposes a method for replacing dispersed spatial data with a regular GRID structure. The GRID structure covers the measured object with a regular network of nodes, which supports uniform interpolation at every point of the analyzed space and a comparison of interpolation models in successive epochs (years). The proposed method was tested on a selected object. The results indicate that the GRID structure can be used in analyses of highly complex real estate markets where input data are incomplete, irregular and dispersed.
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DAS, MADHURIMA, ARNAB HAZRA, ADITI SARKAR, SABYASACHI BHATTACHARYA, and PABITRA BANIK. "Comparison of spatial interpolation methods for estimation of weekly rainfall in West Bengal, India." MAUSAM 68, no. 1 (November 30, 2021): 41–50. http://dx.doi.org/10.54302/mausam.v68i1.407.

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Rainfall is one of the most eloquently researched contemporary meteorological phenomena affecting the agricultural practices dramatically, particularly along the humid, sub-tropics, where agriculture is predominantly rainfed. It is a key parameter of agricultural production in West Bengal due to lack irrigation facilities in most of the areas. Thus, it is very important to have detailed information of rainfall distribution pattern of West Bengal. In practice rainfall data is collected only at few discrete stations scattered all over the whole state. However, rainfall is a spatially continuous phenomenon rather than discrete. Thus it becomes essential to apply a robust spatial interpolation technique to transform the discrete values into a continuous spatial pattern. In the present study, three spatial interpolation techniques namely Kriging, Inverse Distance Weighted (IDW) and SPLINE, are used for a comparative analysis to identify the most efficient interpolation technique. Weekly average rainfall data available between 1901 and 1985 for 19 standard meteorological weeks (SMW), Week 22 to Week 40 are used for the analysis. The errors of the three interpolation techniques are analyzed and the best method is chosen based on the minimum mean absolute deviation (MAD) and the minimum mean squared deviation (MSD) criteria. The IDW method is found to be the best spatial interpolation technique.
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33

Asadov, H. H., and R. Sh Mammadli. "Conditional spatial interpolation method for detecting minimally polluted areas with selective aerosol emissions to the city atmosphere." Radio industry (Russia) 30, no. 3 (September 8, 2020): 57–66. http://dx.doi.org/10.21778/2413-9599-2020-30-3-57-66.

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Continuous surface interpolation is an important aspect of spatial analysis. A number of methods are used to interpolate a continuous surface, one of which is the spatial interpolation method with the Inverse Distance Weight (IDW) ratio. The purpose of this article is to develop a method of conditional spatial interpolation for finding such spatial points in the urban zone where the impact of selective accidental aerosol emissions into the city atmosphere is minimal. Conditional spatial interpolation refers to the case when the distances to the interpolated points are set by a certain condition, and it is necessary to determine the interpolated point where the above influence is minimal. In this case, spatial samples or base points used for interpolation are formed when a single powerful aerosol source is exposed to individual channels (distances). It is shown that there is an optimal relationship between the distances from the sampling point to the interpolation point and from the sampling point to the powerful aerosol source, at which the total effect of the powerful source on the interpolated point is minimal.
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Teegavarapu, Ramesh S. V. "Estimation of missing precipitation records integrating surface interpolation techniques and spatio-temporal association rules." Journal of Hydroinformatics 11, no. 2 (March 1, 2009): 133–46. http://dx.doi.org/10.2166/hydro.2009.009.

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Deterministic and stochastic weighting methods are the most frequently used methods for estimating missing rainfall values. These methods may not always provide accurate estimates due to their inability to completely characterize the spatial and temporal variability of rainfall. A new association rule mining (ARM) based spatial interpolation approach is proposed, developed and investigated in the current study to estimate missing precipitation values at a gauging station. As an integrated approach this methodology combines the power of data mining techniques and spatial interpolation approaches. Data mining concepts are used to extract and formulate rules based on spatial and temporal associations among observed precipitation data series. The rules are then used to improve the precipitation estimates obtained from spatial interpolation methods. A stochastic spatial interpolation technique and three deterministic weighting methods are used as interpolation methods in the current study. Historical daily precipitation data obtained from 15 rain gauging stations from a temperate climatic region (Kentucky, USA) are used to test this approach and derive conclusions about its efficacy for estimating missing precipitation data. Results suggest that the use of association rule mining in conjunction with a spatial interpolation technique can improve the precipitation estimates.
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35

MacKie, Emma J., Michael Field, Lijing Wang, Zhen Yin, Nathan Schoedl, Matthew Hibbs, and Allan Zhang. "GStatSim V1.0: a Python package for geostatistical interpolation and conditional simulation." Geoscientific Model Development 16, no. 13 (July 6, 2023): 3765–83. http://dx.doi.org/10.5194/gmd-16-3765-2023.

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Abstract. The interpolation of geospatial phenomena is a common problem in Earth science applications that can be addressed with geostatistics, where spatial correlations are used to constrain interpolations. In certain applications, it can be particularly useful to a perform geostatistical simulation, which is used to generate multiple non-unique realizations that reproduce the variability in measurements and are constrained by observations. Despite the broad utility of this approach, there are few open-access geostatistical simulation software applications. To address this accessibility issue, we present GStatSim, a Python package for performing geostatistical interpolation and simulation. GStatSim is distinct from previous geostatistical tools in that it emphasizes accessibility for non-experts, geostatistical simulation, and applicability to remote sensing data sets. It includes tools for performing non-stationary simulations and interpolations with secondary constraints. This package is accompanied by a Jupyter Book with user tutorials and background information on different interpolation methods. These resources are intended to significantly lower the technological barrier to using geostatistics and encourage the use of geostatistics in a wider range of applications. We demonstrate the different functionalities of this tool for the interpolation of subglacial topography measurements in Greenland.
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36

Hasníková, Eliška, Jiří Pavlásek, and Marek Vach. "Spatial interpolation of point velocities in stream cross-section." Journal of Hydrology and Hydromechanics 63, no. 1 (March 1, 2015): 21–28. http://dx.doi.org/10.1515/johh-2015-0006.

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Abstract The most frequently used instrument for measuring velocity distribution in the cross-section of small rivers is the propeller-type current meter. Output of measuring using this instrument is point data of a tiny bulk. Spatial interpolation of measured data should produce a dense velocity profile, which is not available from the measuring itself. This paper describes the preparation of interpolation models. Measuring campaign was realized to obtain operational data. It took place on real streams with different velocity distributions. Seven data sets were obtained from four cross-sections varying in the number of measuring points, 24-82. Following methods of interpolation of the data were used in the same context: methods of geometric interpolation arithmetic mean and inverse distance weighted, the method of fitting the trend to the data thin-plate spline and the geostatistical method of ordinary kriging. Calibration of interpolation models carried out in the computational program Scilab is presented. The models were tested with error criteria by cross-validation. Ordinary kriging was proposed to be the most suitable interpolation method, giving the lowest values of used error criteria among the rest of the interpolation methods.
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37

Host, Gudmund, Henning Omre, and Paul Switzer. "Spatial Interpolation Errors for Monitoring Data." Journal of the American Statistical Association 90, no. 431 (September 1995): 853. http://dx.doi.org/10.2307/2291319.

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38

Xue, Kefu. "An edge-restricted spatial interpolation algorithm." Journal of Electronic Imaging 1, no. 2 (April 1, 1992): 152. http://dx.doi.org/10.1117/12.55185.

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39

MURAKAMI, Daisuke, and Morito TSUTSUMI. "EIGENVECTOR SPATIAL FILTERING BASED AREAL INTERPOLATION." Journal of Japan Society of Civil Engineers, Ser. D3 (Infrastructure Planning and Management) 68, no. 1 (2012): 59–69. http://dx.doi.org/10.2208/jscejipm.68.59.

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40

Wilcox, L. M., and P. A. Duke. "Spatial scaling of 3D surface interpolation." Journal of Vision 1, no. 3 (March 14, 2010): 177. http://dx.doi.org/10.1167/1.3.177.

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41

Upton, Graham J. G. "Rectangular cartograms, spatial autocorrelation, and interpolation." Papers in Regional Science 70, no. 3 (July 1991): 287–302. http://dx.doi.org/10.1007/bf01434423.

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42

Nykaza, Edward T. "Spatial interpolation of noise monitor levels." Journal of the Acoustical Society of America 142, no. 4 (October 2017): 2514. http://dx.doi.org/10.1121/1.5014184.

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43

Kang, Dong Wook. "Two-channel spatial interpolation of images." Signal Processing: Image Communication 16, no. 4 (November 2000): 395–99. http://dx.doi.org/10.1016/s0923-5965(00)00004-7.

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44

Oosterhaven, Jan. "Spatial Interpolation and Disaggregation of Multipliers." Geographical Analysis 37, no. 1 (January 2005): 69–84. http://dx.doi.org/10.1111/j.1538-4632.2005.00522.x.

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45

Høst, Gudmund, Henning Omre, and Paul Switzer. "Spatial Interpolation Errors for Monitoring Data." Journal of the American Statistical Association 90, no. 431 (September 1995): 853–61. http://dx.doi.org/10.1080/01621459.1995.10476584.

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46

Murakami, Daisuke, and Morito Tsutsumi. "Practical Spatial Statisics for Areal Interpolation." Environment and Planning B: Planning and Design 39, no. 6 (December 2012): 1016–33. http://dx.doi.org/10.1068/b38034t.

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47

Upton, Graham J. G. "RECTANGULAR CARTOGRAMS, SPATIAL AUTOCORRELATION, AND INTERPOLATION." Papers in Regional Science 70, no. 3 (January 14, 2005): 287–302. http://dx.doi.org/10.1111/j.1435-5597.1991.tb01733.x.

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48

Thanh, Vo Quoc, Dano Roelvink, Mick van der Wegen, Le Xuan Tu, Johan Reyns, and Vo Thi Phuong Linh. "Spatial Topographic Interpolation for Meandering Channels." Journal of Waterway, Port, Coastal, and Ocean Engineering 146, no. 5 (September 2020): 04020024. http://dx.doi.org/10.1061/(asce)ww.1943-5460.0000582.

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49

Lan, Nanying, Fanchang Zhang, and Chuanhui Li. "Robust high-dimensional seismic data interpolation based on elastic half norm regularization and tensor dictionary learning." GEOPHYSICS 86, no. 5 (August 31, 2021): V431—V444. http://dx.doi.org/10.1190/geo2020-0784.1.

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Due to the limitations imposed by acquisition cost, obstacles, and inaccessible regions, the originally acquired seismic data are often sparsely or irregularly sampled in space, which seriously affects the ability of seismic data to image underground structures. Fortunately, compressed sensing provides theoretical support for interpolating and recovering irregularly or undersampled data. Under the framework of compressed sensing, we have adopted a robust interpolation method for high-dimensional seismic data, based on elastic half norm regularization and tensor dictionary learning. Inspired by the elastic net, we first develop the elastic half norm regularization as a sparsity constraint, and we establish a robust high-dimensional interpolation model with this technique. Then, considering the multidimensional structure and spatial correlation of seismic data, we introduce a tensor dictionary learning algorithm to train a high-dimensional adaptive tensor dictionary from the original data. This tensor dictionary is used as the sparse transform for seismic data interpolation because it can capture more detailed seismic features to achieve the optimal and fast sparse representation of high-dimensional seismic data. Finally, we solve the robust interpolation model by an efficient iterative thresholding algorithm in the transform space and perform the space conversion by a modified imputation algorithm to recover the wavefields at the unobserved spatial positions. We conduct high-dimensional interpolation experiments on model and field seismic data on a regular data grid. Experimental results demonstrate that this method has superior performance and higher computational efficiency in noise-free and noisy seismic data interpolation, compared to extensively used dictionary learning-based interpolation methods.
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Säring, D., H. Handels, and J. Ehrhardt. "Structure-preserving Interpolation of Temporal and Spatial Image Sequences Using an Optical Flow-based Method." Methods of Information in Medicine 46, no. 03 (2007): 300–307. http://dx.doi.org/10.1160/me9047.

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Summary Objectives: Modern tomographic imaging devices enable the acquisition of spatial and temporal image sequences. But, the spatial and temporal resolution of such devices is limited and therefore image interpolation techniques are needed to represent images at a desired level of discretization. This paper presents a method for structure-preserving interpolation between neighboring slices in temporal or spatial image sequences. Methods: In a first step, the spatiotemporal velocity field between image slices is determined using an optical flow-based registration method in order to establish spatial correspondence between adjacent slices. An iterative algorithm is applied using the spatial and temporal image derivatives and a spatiotemporal smoothing step. Afterwards, the calculated velocity field is used to generate an interpolated image at the desired time by averaging intensities between corresponding points. Three quantitative measures are defined to evaluate the performance of the interpolation method. Results: The behaviorand capability of the algorithm is demonstrated by synthetic images. A population of 17 temporal and spatial image sequences are utilized to compare the optical flow-based interpolation method to linear and shape-based interpolation. The quantitative results show that the optical flow-based method outperforms the linear and shape-based interpolation statistically significantly. Conclusions: The interpolation method presented is able to generate image sequences with appropriate spatial or temporal resolution needed for image comparison, analysis or visualization tasks. Quantitative and qualitative measures extracted from synthetic phantoms and medical image data show that the new method definitely has advantages over linear and shape-based interpolation.
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