Nearest neighbor interpolation

The advent of artificial intelligence, specifically neural networks, has marked a significant turning point in the field of computation. During such transformative times, we are often faced with a dearth of appropriate vocabulary, which forces us to rely on existing terms, regardless of their inadequacy. This paper argues that the term "interpolation," typically used in deep learning (DL), is a prime example of this phenomenon. It is not uncommon for beginners to misunderstand its meaning, as DL pioneer Francois Chollet (2017) has noted. This misreading is especially true in the discipline of architecture, and this study aims to demonstrate how the meaning of "interpolation" has evolved in the second digital turn. We begin by illustrating, using 2D data, the difference between linear interpolation in the context of topological figures and its use in DL algorithms. We then demonstrate how 3DGANs can be employed to interpolate across different topologies in complex 3D space, highlighting the distinction between linear and manifold interpolation. In both 2D and 3D examples, our results indicate that the process does not involve continuous morphing but instead resembles the piecing together of a jigsaw puzzle to form many parts of a larger ambient space. Our study reveals how previous architectural research on DL has employed the term "interpolation" without clarifying the crucial differences from its use in the first digital turn. We demonstrate the new possibilities that manifold interpolation offers for architecture, which extend well beyond parametric variations of the same topology.

Super resolution is a method that reconstructs a higher resolution image from single captured image or set of captured low resolution images. Super resolution imaging is used for several image processing applications like medical imaging, earth observation systems and surveillance systems. Image interpolation is one of conventional methods used to enhance resolution of image. Basic linear interpolation methods like bilinear, bicubic give blurred image as a result. Nonlinear interpolation methods like New Edge Directed Interpolation (NEDI), Curvature based interpolation, neural network based interpolation enhance image but has limitations like several artifacts. In this paper, a novel innovative approach is proposed in which using dual tree complex wavelet transform (DT-CWT), low and high frequency sub bands are generated. High frequency sub band images are interpolated using improved NEDI which is NEDI with circular window and dynamic window. Improved NEDI (INEDI) algorithm proposed in the paper gives better results on high frequency components which lead to high resolution image without artifacts. Inverse DT-CWT is applied on interpolated sub bands to reconstruct high resolution image. Registration is applied on both images and shift adaptable bilinear interpolation is applied which reconstructs image into 4 interpolation factor. The proposed approach is verified for different interpolation factors and for different satellite images. The accuracy of proposed approach is verified by several contrast features. The algorithm proposed in this paper outperforms in comparison to state of the art algorithms.

Image interpolation has been used spaciously by customary interpolation techniques. Recently, Kriging technique has been widely implemented in simulation area and geostatistics for prediction. In this article, Kriging technique was used instead of the classical interpolation methods to predict the unknown points in the digital image array. The efficiency of the proposed technique was proven using the PSNR and compared with the traditional interpolation techniques. The results showed that Kriging technique is almost accurate as cubic interpolation and in some images Kriging has higher accuracy. A miscellaneous test images have been used to consolidate the proposed technique. 1

Image interpolation has been used spaciously by customary interpolation techniques. Recently, Kriging technique has been widely implemented in simulation area and geostatistics for prediction. In this article, Kriging technique was used instead of the classical interpolation methods to predict the unknown points in the digital image array. The efficiency of the proposed technique was proven using the PSNR and compared with the traditional interpolation techniques. The results showed that Kriging technique is almost accurate as cubic interpolation and in some images Kriging has higher accuracy. A miscellaneous test images have been used to consolidate the proposed technique. 1

This paper presents a fast single-image superresolution approach that involves learning multiple adaptive interpolation kernels. Based on the assumptions that each high-resolution image patch can be sparsely represented by several simple image structures and that each structure can be assigned a suitable interpolation kernel, our approach consists of the following steps. First, we cluster the training image patches into several classes and train each class-specific interpolation kernel. Then, for each input lowresolution image patch, we select few suitable kernels of it to make up the final interpolation kernel. Since the proposed approach is mainly based on simple linear algebra computations, its efficiency can be guaranteed. And experimental comparisons with state-of-the-art super-resolution reconstruction algorithms on simulated and real-life examples can validate the performance of our proposed approach.

The interpolation errors of the higher order bivariate Lagrange polynomial interpolation based on the rectangular, right and equilateral triangular interpolations are measured by using the maximum and root-mean-square (RMS) errors. The error distributions of above three kinds of interpolations are analyzed to find the regions having the smallest interpolation error. Both analytical and numerical results show that the right triangular interpolation is the most efficient interpolation method. Although both the maximum and RMS errors of the right triangular interpolation are larger than that of the rectangular interpolation, the number of data points used in the triangular interpolation is up to 50% less than that used in the rectangular one. On the other hand, the equilateral triangular interpolation using the regions inside a big triangle as interpolation area is proved to be the most accurate interpolation method. The interpolation errors of the equilateral triangular are almost half of that of the rectangular interpolation. In addition, the right triangular, equilateral triangular and rectangular interpolations for the third and fourth orders are applied to accelerate the calculation of doubly periodic Green's function (PGF). INDEX TERMS Doubly periodic Green's function (PGF), Lagrange polynomial interpolation, maximum error, plane waves, root-mean-square (RMS) error, triangular interpolations.

This paper compares Models-3/Community Multiscale Air Quality (CMAQ) outputs at multiple resolutions by interpolating from coarse resolution to fine resolution and analyzing the interpolation difference. Spatial variograms provide a convenient way to investigate the spatial character of interpolation differences and, importantly, to distinguish between naive (nearest neighbor) interpolation and bilinear interpolation, which takes a weighted average of four neighboring cells. For example, when the higher resolution is three times the lower, the variogram of the difference between naive interpolation of the lower resolution output and the higher resolution output shows a depression at every third lag. This phenomenon is related to the blocky nature of naive interpolation and demonstrates the inferiority of naive interpolation to bilinear interpolation in a way that pixelwise comparisons cannot. Theoretical investigations show when one can expect to observe this periodic depression in the variogram of interpolation differences. Naive interpolation is in fact used widely in a number of settings; our results suggest that it should be routinely replaced by bilinear interpolation.

The primary objective of this research was to explore the effectiveness of Neural Radiance Fields (NeRF) in acquiring architectural forms and compare them with traditional photogrammetry results. The study began with a comprehensive literature review on AI in architecture and NeRF. Afterwards, a single case study applicable to both NeRF and photogrammetry was selected for comparison. The NeRF model showed the ability to accurately represent details and light effects, adapting reflections and transparencies to real-world conditions, as well as handling occlusions, and inferring three-dimensional information. In similar situations, Photogrammetry generated less coherent volumetrics or failed to interpret objects. Additionally, tests with a reduced number of images showed that the NeRF model maintained its characteristics, while photogrammetry suffered a decrease in quality and completeness. However, NeRF's performance was influenced by data collection quality. Insufficient data led to lowerquality volumetrics with imperfections, highlighting the importance of careful data collection, even with technologies like NeRF.

The interpolation errors of bivariate Lagrange polynomial and triangular interpolations are studied for the plane waves. The maximum and root-mean-square (RMS) errors on the right triangular, equilateral triangular and rectangular (bivariate Lagrange polynomial) interpolations are analyzed. It is found that the maximum and RMS errors are directly proportional to the (p+1)'th power of kh for both one-dimensional (1D) and two-dimensional (2D, bivariate) interpolations, where k is the wavenumber and h is the mesh size. The interpolation regions for the right triangular, equilateral triangular and rectangular interpolations are selected based on the regions with smallest errors. The triangular and rectangular interpolations are applied to evaluate the 2D singly periodic Green's function (PGF). The numerical results show that the equilateral triangular interpolation is the most accurate interpolation method, while the right triangular interpolation is the most efficient interpolation method.

A multilevel kernel-based interpolation method, suitable for moderately high-dimensional function interpolation problems, is proposed. The method, termed multilevel sparse kernelbased interpolation (MLSKI, for short), uses both level-wise and direction-wise multilevel decomposition of structured (or mildly unstructured) interpolation data sites in conjunction with the application of kernel-based interpolants with different scaling in each direction. The multilevel interpolation algorithm is based on a hierarchical decomposition of the data sites, whereby at each level the detail is added to the interpolant by interpolating the resulting residual of the previous level. On each level, anisotropic radial basis functions are used for solving a number of small interpolation problems, which are subsequently linearly combined to produce the interpolant. MLSKI can be viewed as an extension of d-boolean interpolation (which is closely related to ideas in sparse grid and hyperbolic crosses literature) to kernel-based functions, within the hierarchical multilevel framework to achieve accelerated convergence. Numerical experiments suggest that the new algorithm is numerically stable and efficient for the reconstruction of large data in R d × R, for d = 2, 3, 4, with tens or even hundreds of thousands data points. Also, MLSKI appears to be generally superior over classical radial basis function methods in terms of complexity, run time and convergence at least for large data sets.

Risk and other market professionals often show a keen interest in the smooth interpolation of interest rates. Though smooth interpolation is intuitively appealing, there is little published research on its benefits. Adams and van Deventer's (1994) investigation into whether smooth ...

In this paper, we present a novel and robust spline interpolation algorithm given a noisy symmetric positive definite (SPD) tensor field. We construct a B-spline surface using the Riemannian metric of the manifold of SPD tensors. Each point of this surface corresponds to a diffusion tensor. We develop an algorithm for fitting such a Tensor Spline to a given tensor field and also an algorithm for evaluation of the spline at any intermediate points. The algorithm was tested on DTI data acquired from the isolated rabbit heart slice preparation. We also present validation results, which conclusively demonstrate superior interpolation performance of our algorithm over other existing methods. Motivation -The presence of outliers is common in DT-MRI data due to noise. Hence, robust smoothing and interpolation is necessary. Interpolation of DTIs has many other applications e.g., registration and atlas construction, both of which require an interpolation module. In order to interpolate in the space of DTs, which is negatively curved, an appropriate metric needs to be defined. We define a metric in this space and use it to perform smooth and robust interpolation between points (tensors) in this space. Existing Methods -Tensor interpolation can be done by evaluating the Riemannian geodesic between two neighbor tensors in a tensor field . An approximation to this method is the Log-Euclidean geodesic interpolation which is quite efficient [2]. However, both these methods are sensitive to outliers and are not sufficiently smooth. Tensor Splines -We develop a robust algorithm for constructing a tensor product of B-splines for interpolating DT-MRI data, using the Riemannian metric. Our method involves a two step procedure wherein the first step uses Riemannian distances in the well known DeBoor's spline evaluation algorithm [3] and the second step involves minimization of a robust distance measure between the evaluated spline curve and the given data. These two steps are alternated to achieve a smooth tensor spline approximation to the given tensor field. Experimental Results -In fig. we present comparison of our algorithm with two existing methods applied to synthetically generated noisy DTI data with outliers. Our results show significant improvement in the comparisons, specifically in the presence of noise and outliers. Figure and 3 demonstrate the performance of our algorithm applied on DTI data acquired from the isolated rabbit heart slice preparation. The first image in both figures is a T2-weighted MR image obtained using a zero gradient field. The bottom row of figure 3 depicts an ellipsoidal visualization (in color) of the presented tensor fields. Figures are explained with more details in their captions.

In this paper, we present a novel and robust spline interpolation algorithm given a noisy symmetric positive definite (SPD) tensor field. We construct a B-spline surface using the Riemannian metric of the manifold of SPD tensors. Each point of this surface corresponds to a diffusion tensor. We develop an algorithm for fitting such a Tensor Spline to a given tensor field and also an algorithm for evaluation of the spline at any intermediate points. The algorithm was tested on DTI data acquired from the isolated rabbit heart slice preparation. We also present validation results, which conclusively demonstrate superior interpolation performance of our algorithm over other existing methods. Motivation -The presence of outliers is common in DT-MRI data due to noise. Hence, robust smoothing and interpolation is necessary. Interpolation of DTIs has many other applications e.g., registration and atlas construction, both of which require an interpolation module. In order to interpolate in the space of DTs, which is negatively curved, an appropriate metric needs to be defined. We define a metric in this space and use it to perform smooth and robust interpolation between points (tensors) in this space. Existing Methods -Tensor interpolation can be done by evaluating the Riemannian geodesic between two neighbor tensors in a tensor field . An approximation to this method is the Log-Euclidean geodesic interpolation which is quite efficient [2]. However, both these methods are sensitive to outliers and are not sufficiently smooth. Tensor Splines -We develop a robust algorithm for constructing a tensor product of B-splines for interpolating DT-MRI data, using the Riemannian metric. Our method involves a two step procedure wherein the first step uses Riemannian distances in the well known DeBoor's spline evaluation algorithm [3] and the second step involves minimization of a robust distance measure between the evaluated spline curve and the given data. These two steps are alternated to achieve a smooth tensor spline approximation to the given tensor field. Experimental Results -In fig. we present comparison of our algorithm with two existing methods applied to synthetically generated noisy DTI data with outliers. Our results show significant improvement in the comparisons, specifically in the presence of noise and outliers. Figure and 3 demonstrate the performance of our algorithm applied on DTI data acquired from the isolated rabbit heart slice preparation. The first image in both figures is a T2-weighted MR image obtained using a zero gradient field. The bottom row of figure 3 depicts an ellipsoidal visualization (in color) of the presented tensor fields. Figures are explained with more details in their captions.

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 Scil...

The advent of artificial intelligence, specifically neural networks, has marked a significant turning point in the field of computation. During such transformative times, we are often faced with a dearth of appropriate vocabulary, which forces us to rely on existing terms, regardless of their inadequacy. This paper argues that the term "interpolation," typically used in deep learning (DL), is a prime example of this phenomenon. It is not uncommon for beginners to misunderstand its meaning, as DL pioneer Francois Chollet (2017) has noted. This misreading is especially true in the discipline of architecture, and this study aims to demonstrate how the meaning of "interpolation" has evolved in the second digital turn. We begin by illustrating, using 2D data, the difference between linear interpolation in the context of topological figures and its use in DL algorithms. We then demonstrate how 3DGANs can be employed to interpolate across different topologies in complex 3D space, highlighting the distinction between linear and manifold interpolation. In both 2D and 3D examples, our results indicate that the process does not involve continuous morphing but instead resembles the piecing together of a jigsaw puzzle to form many parts of a larger ambient space. Our study reveals how previous architectural research on DL has employed the term "interpolation" without clarifying the crucial differences from its use in the first digital turn. We demonstrate the new possibilities that manifold interpolation offers for architecture, which extend well beyond parametric variations of the same topology.

Image scaling methods allow us to obtain a given image at a different, higher (upscaling) or lower (downscaling), resolution to preserve as much as possible the original content and the quality of the image. In this paper, we focus on interpolation methods for scaling three-dimensional grayscale images. Within a unified framework, we introduce two different scaling methods, respectively based on the Lagrange and filtered de la Vallée Poussin type interpolation at the zeros of Chebyshev polynomials of the first kind. In both cases, using a non-standard sampling model, we take (via tensor product) the associated trivariate polynomial interpolating the input image. It represents a continuous approximate 3D image to resample at the desired resolution. Using discrete ∞ and 2 norms, we theoretically estimate the error achieved in output, showing how it depends on the error in the input and on the smoothness of the specific image we are processing. Finally, taking the special case of medical images as a case study, we experimentally compare the performances of the proposed methods and with the classical multivariate cubic and Lanczos interpolation methods.

Adaptive rational interpolation has been designed in the context of image processing as a new nonlinear technique that avoids the Gibbs phenomenon when we approximate a discontinuous function. In this work, we present a generalization to the method giving explicit expressions for all the weights for any order of the algorithm. It has a similar behavior to weighted essentially non oscillatory (WENO) technique, however because of the design of the weights in this case is more simple, we propose a new way to construct them obtaining the maximum order near the discontinuities. Some experiments are performed to demonstrate our results and to compare them with standard methods.

In this paper, we explore image reconstruction by natural neighbour interpolation from irregularly spaced samples. We sample the image irregularly with techniques based on the Laplacian or the derivative in the direction of the gradient. Local coordinates based on the Voronoi diagram are used in natural neighbour interpolation to quantify the "neighbourliness" of data sites. Then we use natural neighbour interpolation in order to reconstruct the image. The main result is that the image quality is always very good in the case of the sampling techniques based on the Laplacian.

Local coordinates based on the Voronoi diagram are used in natural neighbour interpolation to quantify the "neighbourliness" of data sites. In an earlier paper, we have extended the natural neighbour or stolen area interpolation technique from ordinary Voronoi diagrams to Voronoi diagrams for sets of points and line segments, by providing direct vectorial formulas for the first order and second

In this paper we present a novel method for interpolating images and we introduce the concept of non-local interpolation. Unlike other conventional interpolation methods, the estimation of the unknown pixel values is not only based on its local surrounding neighbourhood, but on the whole image (nonlocally). In particularly, we exploit the repetitive character of the image. A great advantage of our proposed approach is that we have more information at our disposal, which leads to better estimates of the unknown pixel values. Results show the effectiveness of non-local interpolation and its superiority at very large magnifications to other interpolation methods.

In this paper we present a novel method for interpolating images with repetitive structures. Unlike other conventional interpolation methods, the unknown pixel value is not estimated based on its local surrounding neighbourhood, but on the whole image. In particularly, we exploit the repetitive character of the image. A great advantage of our proposed approach is that we have more information at our disposal, which leads to a better reconstruction of the interpolated image. Results show the effectiveness of our proposed method and its superiority at very large magnifications to other traditional interpolation methods.

In this paper we present a novel method for interpolating images with repetitive structures. Unlike other conventional interpolation methods, the unknown pixel value is not estimated based on its local surrounding neighbourhood, but on the whole image. In particularly, we exploit the repetitive character of the image. A great advantage of our proposed approach is that we have more information at our disposal, which leads to a better reconstruction of the interpolated image. Results show the effectiveness of our proposed method and its superiority at very large magnifications to other traditional interpolation methods.

In this paper we present a novel method for interpolating images and we introduce the concept of non-local interpolation. Unlike other conventional interpolation methods, the estimation of the unknown pixel values is not only based on its local surrounding neighbourhood, but on the whole image (nonlocally). In particularly, we exploit the repetitive character of the image. A great advantage of our proposed approach is that we have more information at our disposal, which leads to better estimates of the unknown pixel values. Results show the effectiveness of non-local interpolation and its superiority at very large magnifications to other interpolation methods.

This paper presents an enhancement method to deal with the medical images which have low resolution as corneal images that have hexagonal nature and contain edges which must be preserved. So its resolution should be increased to help ophthalmologists to accurately diagnose and monitor diseases. Image interpolation is employed for resolution enhancement. In this paper, we consider interpolation techniques such as: polynomial interpolation, adaptive polynomial interpolation, inverse interpolation, and super-resolution (SR) reconstruction in order to enhance corneal image interpolation-based and learning-based techniques. The polynomial interpolation includes: bilinear, bicubic, cubic spline and cubic O-MOMS as well as their adaptive techniques. While the inverse interpolation techniques comprises linear minimum mean square error (LMMSE), maximum entropy, and a regularized image interpolation. Although polynomial based techniques are the most popular due to their simplicity, they don’t...

This unit continues the examination of spatial interpolation by looking at areal interpolation techniques and some applications. Non-volume preserving and volume preserving methods are described, and two special cases of interpolation—mapping populated areas and estimating trade areas—are outlined. The unit concludes with notes on the conceptual foundation of interpolation and its appropriate uses in GIS.

This paper presents an enhancement method to deal with the medical images which have low resolution as corneal images that have hexagonal nature and contain edges which must be preserved. So its resolution should be increased to help ophthalmologists to accurately diagnose and monitor diseases. Image interpolation is employed for resolution enhancement. In this paper, we consider interpolation techniques such as: polynomial interpolation, adaptive polynomial interpolation, inverse interpolation, and super-resolution (SR) reconstruction in order to enhance corneal image interpolation-based and learning-based techniques. The polynomial interpolation includes: bilinear, bicubic, cubic spline and cubic O-MOMS as well as their adaptive techniques. While the inverse interpolation techniques comprises linear minimum mean square error (LMMSE), maximum entropy, and a regularized image interpolation. Although polynomial based techniques are the most popular due to their simplicity, they don’t...

We propose an interpolation method that is invariant under Moebius transformations; that is, interpolation followed by transformation gives the same result as transformation followed by interpolation. The method uses natural (Delaunay) neighbors, but weights neighbors according to angles formed by Delaunay circles.

We propose an interpolation method that is invariant under Möbius transformations; that is, interpolation followed by transformation gives the same result as transformation followed by interpolation. The method uses natural (Delaunay) neighbors, but weights neighbors according to angles formed by Delaunay circles.

A critical limitation of current methods based on Neural Radiance Fields (NeRF) is that they are unable to quantify the uncertainty associated with the learned appearance and geometry of the scene. This information is paramount in real applications such as medical diagnosis or autonomous driving where, to reduce potentially catastrophic failures, the confidence on the model outputs must be included into the decision-making process. In this context, we introduce Conditional-Flow NeRF (CF-NeRF), a novel probabilistic framework to incorporate uncertainty quantification into NeRF-based approaches. For this purpose, our method learns a distribution over all possible radiance fields modelling which is used to quantify the uncertainty associated with the modelled scene. In contrast to previous approaches enforcing strong constraints over the radiance field distribution, CF-NeRF learns it in a flexible and fully data-driven manner by coupling Latent Variable Modelling and Conditional Normalizing Flows. This strategy allows to obtain reliable uncertainty estimation while preserving model expressivity. Compared to previous state-of-the-art methods proposed for uncertainty quantification in NeRF, our experiments show that the proposed method achieves significantly lower prediction errors and more reliable uncertainty values for synthetic novel view and depth-map estimation.

In this work, we study the Hermite interpolation on n-dimensional non-equally spaced, rectilinear grids over a field k of characteristic zero, given the values of the function at each point of the grid and the partial derivatives up to a maximum degree. First, we prove the uniqueness of the interpolating polynomial, and we further obtain a compact closed form that uses a single summation, irrespective of the dimensionality, which is algebraically simpler than the only alternative closed form for the n-dimensional classical Hermite interpolation [1]. We provide the remainder of the interpolation in integral form; we derive the ideal of the interpolation and express the interpolation remainder using only polynomial divisions, in the case of interpolating a polynomial function. Moreover, we prove the continuity of Hermite polynomials defined on adjacent n−dimensional grids, thus establishing spline behavior. Finally, we perform illustrative numerical examples to showcase the applicability and high accuracy of the proposed interpolant, in the simple case of few points, as well as hundreds of points on 3D-grids using a spline-like interpolation, which compares favorably to state-of-the-art spline interpolation methods.

We develop a reconstruction that combines interpolation and least squares fitting for point values in the context of multiresolution a la Harten. We study the smoothness properties of the reconstruction as well as its approximation order. We analyze how different adaptive techniques (ENO, SR and WENO) can be used within this reconstruction. We present some numerical examples where we compare the results obtained with the classical interpolation and the interpolation combined with least-squares approximation.

An interpolation function for triangular mid-edge finite elements is developed using an algebraic interpolation approach. A convenient method for deriving shape functions of serendipity type directly and explicitly arises also from the interpolation function proposed above.

The interpolation algorithm plays an essential role in the digital image correlation (DIC) technique for shape, deformation, and motion measurements with subpixel accuracies. At the present, little effort has been made to improve the interpolation methods used in DIC. In this Letter, a family of recursive interpolation schemes based on B-spline representation and its inverse gradient weighting version is employed to enhance the accuracy of DIC analysis. Theories are introduced, and simulation results are presented to illustrate the effectiveness of the method as compared with the common bicubic interpolation.

This article discusses adjusting inverse distance interpolation for use in unstructured mesh finite volume solutions. The adjustment was made on the weight function of the inverse distance interpolation using the Laplacian of the flow variable inside a Voronoi-dual of finite volume cells. We tested the accuracy of the adjusted inverse distance interpolation on two-dimensional potential flows. It was found that the adjusted and standard inverse distance interpolations have a similar degree of accuracy when used in unstructured, Delaunay based, finite volume mesh. However, the L1 norm error of the adjusted version of the inverse distance interpolation was much smaller than the L1 norm error of the standard version.

This article discusses adjusting inverse distance interpolation for use in unstructured mesh finite volume solutions. The adjustment was made on the weight function of the inverse distance interpolation using the Laplacian of the flow variable inside a Voronoi-dual of finite volume cells. We tested the accuracy of the adjusted inverse distance interpolation on two-dimensional potential flows. It was found that the adjusted and standard inverse distance interpolations have a similar degree of accuracy when used in unstructured, Delaunay based, finite volume mesh. However, the L1 norm error of the adjusted version of the inverse distance interpolation was much smaller than L1 norm error of the standard inverse distance interpolation.

Interpolation is a technique for obtaining new unknown data points within the range of discrete known data points and is often used to recover an image from its downsampled version, or to simply perform image expansion. Recently a lot of interpolation algorithms are proposed, but these interpolation algorithms are highly computationally expensive. Hence these algorithms cannot be implemented and used in real time applications. In view of real time applications we have proposed a computationally simple interpolation algorithm. In our proposed algorithm the unknown pixels are categorized into three types depending upon their spatial position. For each type of pixels, distinct methods are used for prediction. The experimental results show that our proposed algorithm excels the conventional interpolation methods in visual effect, and has a lower complexity. Therefore, the algorithm adapts to real-time image resizing.

It has been demonstrated that, for scalar images, edgedirected interpolation techniques are able to produce better results, both visually and quantitatively, than non-adaptive traditional interpolation methods. We have extended the edge-directed concept to the interpolation of multi-valued diffusion tensor images. The interpolation framework is based on the improved edge-directed scalar image interpolation, which does not require estimation of local edges, and which interpolates the tensors in their mathematically native Riemannian space in order to respect tensor geometry of positive semi-definiteness. The framework has been tested on phantom scalar images and real diffusion tensor images, and is shown to be able to achieve better results than the Euclidean non-adaptive methods.

A new 3-dimensional interpolation method is introduced in this paper. Corresponding to the method a novel interpolation operator has been constructed and used to obtain results. The main objective is to develop a mechanical way of interpolation that does not require very high degree of knowledge of mathematical analysis, but only elementary mathematics. The properties of the operator have been discussed in detail. Unlike other methods, the number of nodes required in the proposed interpolation method is much less. A numerical example is also furnished in support of the formula obtained.

to lOOmW even at 50°C. The high average T, value of 183.8 K was realised. Furthermore, a characteristic uniformity of less than 4.6% current deviation and less than 2.2% optical beam deviation has been presented. This laser array is suitable for a multibeam optical disk drive which allows parallel data processing to increase the data transfer rate.

A multidimensional interpolator based on convolution with the sine function is developed. The interpolator is global in nature, with all sampled data contributing to the computation. Preprocessing of the data by partial summation accelerates convergence of the actual interpolation, when repeatedly interpolating the same data. Modification of the interpolation procedure gives an efficient method for numerical differentiation. The method is intended for bandlimited functions with finite support. The interpolator was tested for a class of problems related to molecular dynamics, including interpolation of 1D. 2D and 3D Gaussian wave packets on a grid; integration of classical trajectories on an interpolated potential; and the transfer of a sampled wave function from a polar grid to a Cartesian grid and back. It was found that the interpolator is very accurate for Gaussian-like wave functions, and that even for functions which are not bandlimited, such as the Morse potential, a reasonable accuracy can be obtained.

This paper investigates a novel decision framework for efficient selection of interpolation curve based on distance minimization for 3D rendering applications. The point clouds obtained from low resolution 3D scanners like Microsoft's Kinect or from sparse reconstruction algorithms usually fail to provide accurate information about the surface, either due to occlusions during the scanning process or inability of the scanner to generate a dense model of the surface. The proposed decision framework selects the best interpolation technique on a local basis utilizing the voting parameters obtained from the original point cloud. This framework enables us to obtain the comparatively best fit interpolation curve for upsampling due to the decisive feature of the framework. Experimental results are carried out using two interpolation techniques viz., quadratic spline interpolation and cubic spline interpolation technique to demonstrate the usefulness of such a decision framework for 3D point cloud data. The proposed decision framework is generic and holds good for more than two interpolation techniques.

This paper is concerned with solving the image interpolation problem as an inverse problem using a regularized interpolation algorithm. The objective of the paper is how to solve the image interpolation problem as an inverse problem in an efficient manner. The paper suggests a new implementation for the regularized image interpolation algorithm. In this suggested implementation, a single matrix inversion process of small dimensions is required in the interpolation process avoiding the large computational complexity due to the matrices of large dimentions involved in the interpolation process. The performance of this suggested image interpolation algorithm is compared to the standard polynomial interpolation algorithm such as the bilinear, the bicubic and the cubic spline algorithms. Results iluustrate that the suggested implemetation of the regularized image interpolation algorithm is superior to the traditional implementation from the mean square error point of view and the computational complexity point of view as well.