Moebius-Invariant Natural Neighbor Interpolation

2000

In this paper we give a survey on natural neighbor based interpolation, a class of local scattered data interpolation schemes that define their support on natural neighbors in the Voronoi diagram of the input data sites. We discuss the existing work with respect to common aspects of scattered data interpolation and focus on smoothness of the interpolant.

1998

Standard methods for image interpolation are based on smoothly fitting the image intensity surface. Previous edge-directed interpolation methods add limited geometric information (edge maps) to build more accurate and visually appealing interpolations at key contours in the image. This paper presents a method for geometry-based interpolation that smoothly fits the isophote (intensity level curve) contours at all points in the image rather than just at selected contours. By using level set methods for curve evolution, no explicit extraction or representation of these contours is required (unlike earlier edge-directed methods). The method uses existing interpolation techniques as an initial approximation and then iteratively reconstructs the isophotes using constrained smoothing. Results show that the technique produces results that are more visually realistic than standard function-fitting methods

Numerical Algorithms, 1993

Based on the work of Robin Sibson concerning Natural Neighbor Interpolant, this paper is devoted to incorporate this concept in Spline theory. To do this, first a new concept, the "Covering Spheres", is presented, which is then linked with Sibson's interpolant. Finally, the interpolant is reformulated to present it as a Bernstein polynomial in local coordinates instead of the usual presentation as rational quartics. As a corollary, the whole idea is presented as modified Vertex Splines.

IEEE Transactions on Visualization and Computer Graphics, 2000

Natural-neighbor interpolation methods, such as Sibson's method, are well-known schemes for multivariate data fitting and reconstruction. Despite its many desirable properties, Sibson's method is computationally expensive and difficult to implement, especially when applied to higher-dimensional data. The main reason for both problems is the method's implementation based on a Voronoi diagram of all data points. We describe a discrete approach to evaluating Sibson's interpolant on a regular grid, based solely on finding nearest neighbors and rendering and blending d-dimensional spheres. Our approach does not require us to construct an explicit Voronoi diagram, is easily implemented using commodity three-dimensional graphics hardware, leads to a significant speed increase compared to traditional approaches, and generalizes easily to higher dimensions. For large scattered data sets, we achieve two-dimensional (2D) interpolation at interactive rates and three-dimensional (3D) interpolation with computation times of a few seconds.

IEEE Transactions on Image Processing, 2000

We propose an isophote-oriented, orientation-adaptive interpolation method. The proposed method employs an interpolation kernel that adapts to the local orientation of isophotes, and the pixel values are obtained through an oriented, bilinear interpolation. We show that, by doing so, the curvature of the interpolated isophotes is reduced, and, thus, zigzagging artifacts are largely suppressed. Analysis and experiments show that images interpolated using the proposed method are visually pleasing and almost artifact free.

Brazilian Symposium on Computer Graphics and Image Processing, 2002

Digital image interpolation techniques are frequently used to enlarge pictures, i.e. zooming in, and they are upon increasingly demand for developing product applications using digital still cameras. One common difficulty with conventional interpolation techniques is that of preserving details, i.e. edges, and at the same time smoothing the data for not introducing spurious artifacts. A definitive solution to this is

Computers & Geosciences, 1989

Synthese, 2008

We present a number of, somewhat unusual, ways of describing what Craig's interpolation theorem achieves, and use them to identify some open problems and further directions.

Citeseer

Subdivision schemes are used to interpolate data samples locally. By using temporary placeholders on a dense grid, we improve one of the best known subdivision scheme (Deslauriers-Dubuc). Interpolated values require 2 steps to stabilize as they are first interpolated on a coarse scale through a tetradic filter and then on a finer scale using a dyadic filter. The interpolants are C 1 and can be made to reproduce polynomials of degree 4 unlike regular subdivision schemes. These generalized interpolatory subdivision schemes have minimal support and no additional memory requirement.

IJARCCE, 2016

Image interpolation is the most basic requirement for many image processing task such as computer graphics, gaming, medical image processing, virtualization, camera surveillance and quality control. Image interpolation is a technique used in resizing images. To resize an image, every pixel in the new image must be mapped back to a location in the old image in order to calculate a value of new pixel. There are many algorithms available for determining new value of the pixel, most of which involve some form of interpolation among the nearest pixels in the old image. In this paper, we used Nearest-neighbor, Bilinear, Bicubic, Bicubic B-spline, Catmull-Rom, Mitchell-Netravali and Lanzcos of order three algorithms for image interpolation. Each algorithms generates varies artifact such as aliasing, blurring and moiré. This paper presents, quality and computational time consideration of images while using these interpolation algorithms.