Topic
Bicubic interpolation
About: Bicubic interpolation is a research topic. Over the lifetime, 3348 publications have been published within this topic receiving 73126 citations.
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TL;DR: Evaluating the performance of some of the widely used surface interpolation techniques to identify one or more good choices of such methods for envelope estimation in BEMD includes various radial basis function interpolators and Delaunay triangulation based interpolators.
Abstract: Scattered data interpolation is an essential part of bidimensional empirical mode decomposition (BEMD) of an image. In the decomposition process, local maxima and minima of the image are extracted at each iteration and then interpolated to form the upper and the lower envelopes, respectively. The number of two-dimensional intrinsic mode functions resulting from the decomposition and their properties are highly dependent on the method of interpolation. Though a few methods of interpolation have been tested and/or applied to the BEMD process, many others remain to be tested. This paper evaluates the performance of some of the widely used surface interpolation techniques to identify one or more good choices of such methods for envelope estimation in BEMD. The interpolation techniques studied in this paper include various radial basis function interpolators and Delaunay triangulation based interpolators. The analysis is done first using a synthetic texture image and then using two different real texture images. Simulations are made to focus mainly on the effect of interpolation methods by providing less or negligible control on the other parameters or factors of the BEMD process.
49 citations
TL;DR: The pycnophylactic interpolation method computes a continuous surface from polygon-based data and simultaneously enforces volume preservation in the polygons, which is extended to surface representations based on an irregular triangular network (TIN).
Abstract: The interpolation of continuous surfaces from discrete points is supported by most GIS software packages. Some packages provide additional options for the interpolation from 3D line objects, for example surface-specific lines, or contour lines digitized from topographic maps. Demographic, social and economic data can also be used to construct and display smooth surfaces. The variables are usually published as sums for polygonal units, such as the number of inhabitants in communities or counties. In the case of point and line objects the geometric properties have to be maintained in the interpolated surface. For polygon-based data the geometric properties of the polygon boundary and the volume should be preserved, avoiding redistribution of parts of the volume to neighboring units during interpolation. The pycnophylactic interpolation method computes a continuous surface from polygon-based data and simultaneously enforces volume preservation in the polygons. The original procedure using a regular grid is extended to surface representations based on an irregular triangular network (TIN).
49 citations
TL;DR: The morphological shape decomposition role to serve as an efficient image decomposition tool is extended to interpolation of images by means of generalized morphologicalshape decomposition.
Abstract: One of the main image representations in mathematical
morphology is the shape decomposition representation, useful for
image compression and pattern recognition. The morphological
shape decomposition representation can be generalized to extend
the scope of its algebraic characteristics as much as possible. With
these generalizations, the morphological shape decomposition
(MSD) role to serve as an efficient image decomposition tool is extended
to interpolation of images. We address the binary and grayscale
interframe interpolation by means of generalized morphological
shape decomposition. Computer simulations illustrate the
results.
49 citations
TL;DR: The use of a statistical estimation technique called kriging, which produces estimation error measurements and analyzes the volumetric grid to determine sample value variability, is described and the results indicate the potential of kriged for interpolation in 3D medical imaging and point out the need for further work.
Abstract: The use of a statistical estimation technique called kriging, which produces estimation error measurements and analyzes the volumetric grid to determine sample value variability, is described. The use of interpolation in 3D medical imaging are first reviewed. Several different interpolation techniques, including linear trilinear, and tricubic interpolation techniques, are described and assessed. The kriging statistical estimation process is presented, and the results of applying it to slice interpolation and surface visualization are reported. The results indicate the potential of kriging for interpolation in 3D medical imaging and point out the need for further work. >
49 citations
TL;DR: In this article, a weighted rational cubic spline interpolation has been constructed using the rational cubic interpolation with linear denominator and the rational spline based on function values, and the problems to constrain the weighted rational interpolation curves to lie strictly above or below a given piecewise linear curve and between two given piece-wise linear curves can be solved completely.
48 citations