Bicubica

Bicubica, often referred to as bicubic interpolation, is a resampling method used in digital imaging and computer graphics to estimate new pixel values when scaling or transforming images. It uses cubic polynomials to interpolate values within a neighborhood.

The algorithm typically uses a 4x4 neighborhood of known pixels around the target sample and performs interpolation in two steps: first along one axis using a cubic kernel to obtain intermediate values, then along the other axis. The result is a smoother image than bilinear interpolation and avoids some jagged edges.

Common implementations use cubic convolution kernels parameterized by a, with a around -0.5 (Catmull-Rom) or -0.75 (a compromise between smoothness and sharpness). The most widely known formulation is Keys' cubic convolution. Boundary handling methods include clamping or extending edge values.

Applications include image resizing, transformation, anti-aliasing, font rendering, and texture mapping in 3D graphics. Advantages of bicubica include smooth results, good detail preservation, and relatively efficient computation compared with higher-order methods. Disadvantages include higher computational cost than simpler methods like bilinear or nearest-neighbor, and the potential for blur or ringing in high-frequency regions, as well as possible overshoot near sharp edges depending on the kernel used.

History notes indicate the method was described in the early 1980s, with Keys' cubic convolution contributing to its popularization. It remains widely used in image editors and graphics libraries for resizing and resampling tasks.