Lanczosinterpolation

Lanczos interpolation, also called Lanczos resampling, is a resampling method used to estimate signal values at new points, with widespread application in image upsampling and downsampling. It is based on a windowed sinc function and belongs to the family of Lanczos resampling techniques. The kernel is obtained by truncating the ideal sinc low-pass filter to a finite window, controlled by a parameter a. In 1D, the Lanczos kernel is L(x) = sinc(x) · sinc(x / a) for |x| ≤ a and zero otherwise, where sinc(t) = sin(πt)/(πt). In two dimensions, the filter is applied separably along horizontal and vertical axes.

To interpolate a value at position u, one computes a weighted sum of nearby samples f(k) with weights L(u − k) for k in the interval [floor(u) − a + 1, floor(u) + a]. For 2D images, the same principle applies in both directions, effectively performing convolution with the separable Lanczos kernel. Common choices for a are 2 or 3, yielding Lanczos-2 and Lanczos-3 filters, which provide a balance between sharpness and ringing and are widely implemented in software.

Lanczos interpolation tends to preserve details better than simple methods such as nearest-neighbor or bilinear interpolation and often produces smoother results than pure sinc interpolation, due to the finite kernel. Compared with larger-window filters, it can reduce aliasing while avoiding excessive ringing, though mild ringing may appear near strong edges and very fine textures may be slightly blurred if the window is small. It is a standard option in many image processing libraries and resampling workflows.