bicubicinterpolasjon

Bicubic interpolation is a mathematical method used to estimate the value of a function at unknown points based on its known values at surrounding points. It is an extension of the one-dimensional cubic interpolation to two dimensions. In essence, bicubic interpolation fits a smooth surface through a grid of known data points.

This technique is particularly useful in image processing and computer graphics for tasks such as resizing images, also known as scaling or resampling. When an image is enlarged, bicubic interpolation calculates the color values of the new pixels by considering the 16 nearest pixels in the original image and applying a cubic polynomial in two dimensions. This results in smoother transitions and less noticeable blockiness compared to simpler methods like bilinear interpolation.

The underlying principle involves calculating gradients and curvatures at the known points to create a continuous and smooth interpolating surface. This process ensures that not only the function values but also their first and second derivatives are continuous across the grid, leading to higher quality results. While computationally more intensive than bilinear interpolation, the improved visual fidelity often justifies its use in applications where image quality is paramount.