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: Two classes of closed piecewiee bicubic surfaces are considered that are geometrically smooth about each extraordinary point and, for a large mesh and a large control polyhedron, they are parametrically smooth away from the extraordinary points.
Abstract: Two classes of closed piecewiee bicubic surfaces are considered. These surfaces are geometrically smooth about each extraordinary point and, for a large mesh and a large control polyhedron, they are parametrically smooth away from the extraordinary points. Furthermore, free parameters are available for manipulating the shape of the surface without changing the control polyhedron. The control is local for a large control polyhedron.
22 citations
TL;DR: A new type of C^1-rational cubic spline Fractal Interpolation Function (FIF) for convexity preserving univariate interpolation, well suited for the approximation of a convex function @F whose derivative is continuous but has varying irregularity.
21 citations
TL;DR: A tight bound on the complexity of smoothing quad meshes with bicubic tensor-product B-spline patches is proven to be sharp by suitably interpreting an existing surface construction.
21 citations
Patent•
27 Aug 2014
TL;DR: In this paper, a super-resolution method based on a single image is proposed, which includes the steps that S1, bicubic interpolation is carried out on the input low-resolution image to obtain an initial high-resolution images; S2, the initial high resolution image is divided into a plurality of image blocks overlapped mutually, then a similar image block grouping is obtained, and image noise of the similar image blocks grouping is removed; S3, the multiple denoised image blocks are fused into a whole highresolution image, a non-local similar
Abstract: The invention relates to a super-resolution method based on a single image. The super-resolution method includes the steps that S1, bicubic interpolation is carried out on the input low-resolution image to obtain an initial high-resolution image; S2, the initial high-resolution image is divided into a plurality of image blocks overlapped mutually, then a similar image block grouping is obtained, and image noise of the similar image block grouping is removed; S3, the multiple denoised image blocks are fused into a whole high-resolution image, a non-local similar image block and a weighting coefficient of each image block are solved, and the redundancy weight of a non-local similar image block grouping is calculated; S4, an on-line dictionary is updated according to the similar image block grouping and fused with an off-line dictionary; S5, the sparse representation coefficient, about a fused dictionary, of each image block is solved; S6, all the image blocks and the whole high-resolution image are reconstructed, if iterations do not converge and the number of the iterations is smaller than a preset threshold value, the previous steps are executed again, and otherwise the high-resolution image is output. The reality sense and accuracy of super-resolution reconstruction are promoted, and the super-resolution method has the advantage of removing the image noise at the same time.
21 citations
TL;DR: This algorithm is based on the observation that a tensor product spline surface fitting problem can be split into two spline curve fitting problems, and each of these problems can be carried out in parallel by cyclic reduction.
Abstract: A parallel fitting algorithm using uniform bicubic B-spline surfaces is presented. This algorithm is based on the observation that a tensor product spline surface fitting problem can be split into two spline curve fitting problems, and each of these problems can be carried out in parallel by cyclic reduction. Using this approach, the control points of a uniform bicubic B-spline surface that interpolates a grid of m x n points can be found in O(log m + log n) time on mn processors. Furthermore, since smaller systems of equations are solved in the algorithm, the accumulated error resulting from this approach is smaller than that of the traditional algorithms.
21 citations