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Linear (or bilinear, in two dimensions) interpolation is typically good for changing the size of an image, but causes some undesirable softening of details and can still be somewhat jagged. Bicubic interpolation
Bicubic interpolation can be accomplished using either Lagrange polynomials, cubic splines, or cubic convolution algorithm. In image processing, bicubic interpolation is often chosen over bilinear or nearest-neighbor interpolation in image resampling, when speed is not an issue. In contrast to bilinear interpolation, which only takes 4 pixels ...
Example of bilinear interpolation on the unit square with the z values 0, 1, 1 and 0.5 as indicated. Interpolated values in between represented by color. In mathematics, bilinear interpolation is a method for interpolating functions of two variables (e.g., x and y) using repeated linear interpolation.
One weakness of bilinear, bicubic, and related algorithms is that they sample a specific number of pixels. When downscaling below a certain threshold, such as more than twice for all bi-sampling algorithms, the algorithms will sample non-adjacent pixels, which results in both losing data and rough results. [citation needed]
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.
Multivariate interpolation is the interpolation of functions of more than one variable. Methods include nearest-neighbor interpolation, bilinear interpolation and bicubic interpolation in two dimensions, and trilinear interpolation in three dimensions. They can be applied to gridded or scattered data.
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.
comparison of 1D and 2D interpolation: Image title: Comparison of nearest-neighbour, linear, cubic, bilinear and bicubic interpolation methods by CMG Lee. The black dots correspond to the point being interpolated, and the red, yellow, green and blue dots correspond to the neighbouring samples. Their heights above the ground correspond to their ...