Bilinear interpolation is a mathematical method used to estimate values at points within a two-dimensional grid. It works by taking the average of the values at the four nearest grid points, weighted by their distance from the point of interest. This technique is commonly used in image processing and computer graphics to create smooth transitions between pixel values. This method is an extension of linear interpolation, which operates in one dimension. By applying linear interpolation twice—first in one direction and then in the other—bilinear interpolation provides a more accurate estimate for values in a two-dimensional space, making it useful in applications like geographic information systems and image scaling.