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In mathematics, bicubic interpolation is an extension of cubic spline interpolation (a method of applying cubic interpolation to a data set) for interpolating data points on a two-dimensional regular grid.
Simple Fourier based interpolation based on padding of the frequency domain with zero components (a smooth-window-based approach would reduce the ringing). Beside the good conservation of details, notable is the ringing and the circular bleeding of content from the left border to right border (and way around).
Bicubic filter in Adobe Photoshop [5] 1/3 1/3 Mitchell–Netravali Mitchell filter in ImageMagick [4] 1 0 B-spline: Bicubic filter in Paint.net: Examples.
Each interpolation approach boils down to weighted averages of neighboring pixels. The goal is to find the optimal weights. Bilinear interpolation sets all the weights to be equal. Higher-order interpolation methods such as bicubic or sinc interpolation consider a larger number of neighbors than just the adjacent ones.
Image scaling can be interpreted as a form of image resampling or image reconstruction from the view of the Nyquist sampling theorem.According to the theorem, downsampling to a smaller image from a higher-resolution original can only be carried out after applying a suitable 2D anti-aliasing filter to prevent aliasing artifacts.
Another simple method is bilinear interpolation, whereby the red value of a non-red pixel is computed as the average of the two or four adjacent red pixels, and similarly for blue and green. More complex methods that interpolate independently within each color plane include bicubic interpolation, spline interpolation, and Lanczos resampling.
For more sophisticated shapes, the algorithm may be generalized as rendering the shape to a pixel grid with higher resolution than the target display surface (usually a multiple that is a power of 2 to reduce distortion), then using bicubic interpolation to determine the average intensity of each real pixel on the display surface.
Increase the proportions as well, for example font size 48 and a line thickness of 17 pixels. Then use software like Photoshop or GIMP to Gaussian blur it at 2 pixels. Finally reduce it down to about 1000 pixels on a side (e.g. 1300×975) using bicubic interpolation. This gives a plot with no jagged lines that is also big enough so that someone ...