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In applied mathematics, an Akima spline is a type of non-smoothing spline that gives good fits to curves where the second derivative is rapidly varying. [1] The Akima spline was published by Hiroshi Akima in 1970 from Akima's pursuit of a cubic spline curve that would appear more natural and smooth, akin to an intuitively hand-drawn curve.
Examples of algorithms for this task include New Edge-Directed Interpolation (NEDI), [1] [2] Edge-Guided Image Interpolation (EGGI), [3] Iterative Curvature-Based Interpolation (ICBI), [citation needed] and Directional Cubic Convolution Interpolation (DCCI). [4] A study found that DCCI had the best scores in PSNR and SSIM on a series of test ...
Interpolation: Smooth out the discontinuities using a lowpass filter, which replaces the zeros. In this application, the filter is called an interpolation filter , and its design is discussed below. When the interpolation filter is an FIR type, its efficiency can be improved, because the zeros contribute nothing to its dot product calculations.
The key points, placed by the artist, are used by the computer algorithm to form a smooth curve either through, or near these points. For a typical example of 2-D interpolation through key points see cardinal spline. For examples which go near key points see nonuniform rational B-spline, or Bézier curve. This is extended to the forming of ...
Lanczos windows for a = 1, 2, 3. Lanczos kernels for the cases a = 1, 2, and 3, with their frequency spectra. A sinc filter would have a cutoff at frequency 0.5. The effect of each input sample on the interpolated values is defined by the filter's reconstruction kernel L(x), called the Lanczos kernel.
Gouraud's original paper described linear color interpolation. [1] In 1992, Blinn published an efficient algorithm for hyperbolic interpolation [4] that is used in GPUs as a perspective correct alternative to linear interpolation. Both the linear and hyperbolic variants of interpolation of colors from vertices to pixels are commonly called ...
Radial basis function (RBF) interpolation is an advanced method in approximation theory for constructing high-order accurate interpolants of unstructured data, possibly in high-dimensional spaces. The interpolant takes the form of a weighted sum of radial basis functions .
Linear interpolation on a data set (red points) consists of pieces of linear interpolants (blue lines). Linear interpolation on a set of data points (x 0, y 0), (x 1, y 1), ..., (x n, y n) is defined as piecewise linear, resulting from the concatenation of linear segment interpolants between each pair of data points.