Scattered data interpolation with multilevel B-splines

The paper describes a fast algorithm for scattered data interpolation and approximation. Multilevel B-splines are introduced to compute a C² continuous surface through a set of irregularly spaced points. The algorithm makes use of a coarse to fine hierarchy of control lattices to generate a sequence of bicubic B-spline functions whose sum approaches the desired interpolation function. Large performance gains are realized by using B-spline refinement to reduce the sum of these functions into one equivalent B-spline function. Experimental results demonstrate that high fidelity reconstruction is possible from a selected set of sparse and irregular samples     

Scattered data interpolation and approximation with error bounds

Methods for interpolating and approximating three-dimensional scattered data are presented. These methods consist of several local least squares approximations, followed by a piecewise bicubic Hermite interpolant to gridded data, and then optionally followed by a modified Shepard's method. Error bounds are derived for the interpolation and approximation methods that depend on the maximum distance from the nearest data point. The visual smoothness and the discrete errors for these methods applied to known functional data compare favorably with other methods in the literature. The storage and computational complexities of these methods are linear in the number of data points.     

Scattered data modeling

A variety of methods for modeling scattered data are discussed, with an emphasis on two types of data: volumetric and spherical. To demonstrate the performance of the various methods, results from an empirical study using trivariate scattered data are presented. The author's objective is to provide information to aid in selecting a type of method or to form the basis for customizing a method for a particular application     

Hilbert transforms from interpolation data

This paper studies the construction of stable transfer functions for which the real or imaginary part takes prescribed values at discrete uniformly spaced points on the unit circle. Formulas bounding the error between a particular interpolating function and any function consistent with the data are presented; these have the desirable property that the error goes to zero exponentially fast with the number of interpolating points. The paper also examines construction of stable minimum phase transfer functions for which the magnitude takes prescribed values at uniformly spaced points on the unit circle, and presents error bounds for this problem. Connection with the discrete Hilbert transform is made. The effect of uncertainty in the original data is also examined, and we show that oversampling is possible.     

Parametric interpolation using sampled data

Trajectory in high-speed precision machining requires very small feed-rate fluctuation and contour error, which can be achieved with parametric interpolation. Since it is impossible to exactly compute the arc-length of a general parametric curve, the conventional parametric interpolation obtains a parameter through a real-time update. Thus it cannot be used with a preplanned feed-rate profile, which restricts its applications. To overcome such a problem, the proposed algorithm estimate parameters using tabulated parameter and length data. The simulations show the proposed method useful with smaller contour error and acceptable feed-rate fluctuation comparable to the second order real-time parametric interpolation.     

Spline interpolation and smoothing of data

A surface plotting program is used to produce projections of three-dimensional data from two slightly different view-points forming a stereo-pair. The data can then be observed in three dimensions with the aid of a stereo-viewer. The technique has been applied to sets of data arising in a number of different areas.     

On linear interpolation under interval data

Some results related to the problem of interpolation of n vertical segments (x_k, Y_k), k = 1,…,n, in the plane with generalized polynomial functions that are linear combinations of m basic functions are presented. It is proved that the set of interpolating functions (if not empty) is bounded in every subinterval (x_k, x_k+1) by two unique such functions η_k⁻ and η_k⁺. An algorithm with result verification for the determination of the boundary functions η_k⁻, η_k⁺ and for their effective tabulation is reported and some examples are discussed.     

Image warping with scattered data interpolation

Discusses a new approach to image warping based on scattered data interpolation methods which provides smooth deformations with easily controllable behavior. A new, efficient deformation algorithm underlies the method     

Raised cosine function for image data interpolation

Spline functions because of their smoothing and interpolating properties are gaining popularity in engineering applications and image processing. In the present paper a new set of functions is proposed which has all the useful properties of spline function but are more smooth and are practically a band-limited type. These functions are the convolved raised cosine functions. The performance of image data reconstruction through the raised cosine functions is found to be better than that of spline functions for the two representative images.     

Visualization of AMR data with multi-level dual-mesh interpolation

We present a new technique for providing interpolation within cell-centered Adaptive Mesh Refinement (AMR) data that achieves C(0) continuity throughout the 3D domain. Our technique improves on earlier work in that it does not require that adjacent patches differ by at most one refinement level. Our approach takes the dual of each mesh patch and generates "stitching cells" on the fly to fill the gaps between dual meshes. We demonstrate applications of our technique with data from Enzo, an AMR cosmological structure formation simulation code. We show ray-cast visualizations that include contributions from particle data (dark matter and stars, also output by Enzo) and gridded hydrodynamic data. We also show results from isosurface studies, including surfaces in regions where adjacent patches differ by more than one refinement level.     

基于空间数据插值算法的空间散乱数据体绘制实现

体绘制技术是一种能够真实地反映空间数据场内部信息的可视化技术。在体绘制研究领域中,非规则的空间散乱数据体绘制目前仍然是一个研究热点。文中采用空间数据插值算法对散乱的原始数据进行网格化插值,然后使用光投影体绘制算法对规则网格数据进行体绘制。最后,通过新方法实现了某油藏区地下流体压力和孔隙度分布结构的体绘制。     

四元数样条插值的人体运动数据重构

为了得到平滑的人体动画,提出一种基于四元数的样条插值算法,利用提取的关键帧实现人体运动序列的有效重构。为减少重构误差、加快收敛速度,将已知关键帧集合作为初始条件,通过迭代算法求出样条曲线的控制点集合。利用样条曲线控制点计算贝塞尔曲线控制点,构造贝塞尔样条曲线段,将各段贝塞尔样条曲线段组合,构造一条基于四元数的样条曲线。根据德卡斯特里奥（de Casteljau）算法插值重构人体运动。实验结果表明,该算法在保证执行效率的同时,可得到光滑的插值结果,实现满足视觉要求的人体运动重构。     

Tri-cubic polynomial natural spline interpolation for scattered data

In this paper an interpolation problem for 3D scattered data defined on a rectangular parallelepiped with natural boundary conditions is considered. By using spline function theory in Hilbert space, we discuss the existence, uniqueness and characterization of the solution of the interpolation problem as well as its convergence. We show that the solution can be constructed in a simple way without using reproducing kernel semi-Hilbert space theory. Moreover, the solution can be written as the sum of tri-linear polynomials and piecewise tri-cubic polynomials and its coefficients can be determined by solving a positive semi-definite linear system. Numerical examples are presented to illustrate the proposed approach.     

Random linear interpolation data augmentation for person re-identification

Person Re-Identification (person re-ID) is an image retrieval task which identifies the same person in different camera views. Generally, a good person re-ID model requires a large dataset containing over 100000 images to reduce the risk of over-fitting. Most current handcrafted person re-ID datasets, however, are insufficient for training a learning model with high generalization ability. In addition, the lacking of images with various levels of occlusion is still remaining in most existing datasets. Motivated by these two problems, this paper proposes a new data augmentation method called Random Linear Interpolation that can enlarge the sizes of person re-ID datasets and improve the generalization ability of the learning model. The key enabler of our approach is generating fused images by interpolating pairs of original images. In other words, the innovation of the proposed approach is considering data augmentation between two random samples. Plenty of experimental results demonstrates that the proposed method is effective to improve baseline models. On Market1501 and DukeMTMC-reID datasets, our approach can achieve 92.71% and 82.19% rank-1 accuracy, respectively.

     

Powell-Sabin splines in range restricted interpolation of scattered data

Computing - The construction of range restricted bivariateC 1 interpolants to scattered data is considered. In particular, we deal with quadratic spline interpolation on a Powell-Sabin refinement...     

薄板样条函数在空间数据插值中的应用

薄板样条函数是空间数据插值中一种重要的方法,介绍了该方法的基本原理,并以珠江河道地形数据为例,借助地理信息系统的二次开发功能,将薄板样条函数应用于空间插值,通过与测试样本点以及克里金插值在最大值、标准误等方面的比较分析,证明薄板样条函数是一种有效的空间数据插值方法。     

A new family of convex splines for data interpolation

This paper develops a new family of convexity-preserving splines of order n, hereby entitled the CPn-spline, that preserves convexity when derivatives at the data points satisfy some reasonable conditions. The spline comprises four components: a constant term, a first order term, and two nth order binomials. A slope-averaging-method is proposed for the general implementation of the new spline. Numerical results that allow for an assessment of the new spline are provided. In particular, a comparative analysis of the CPn-spline, the cubic spline, and of the Carnicer '92 spline is performed. By varying two parameters, the spline shape can be controlled at the local level, while other conventional means can be used to control the shape at the global level. The CPn-spline has no singularities in the case where inflection points are present. Additionally, a less general form of the CPn-spline that applies to most practical cases can be implemented with extreme ease.