Choosing the geometric transformation for interpolation.

[atlanswer]

Interpolation algorithms such as bilinear interpolation requires an inverse mapping from the output image to the original image. How exactly was it performed?

After some intense searching:

OpenCV: OpenCL resizeLN source code

float sx = ((dx + 0.5f) * ifx - 0.5f);

OpenCV's source code is available on GitHub. Locating the resize function yielded such a surprising result.

MATLAB: imresize discussion

u = x / scale + 0.5 * (1 - 1 / scale);

MATLAB's imresize uses internal functions to perform to interpolation, which are invisible to users. But a MATLAB stuff posed the inverse mapping formula in his answer.

Noted that C's index is 0-based and MATLAB's index is 1-based. These two implementations are the same. Why choosing this particular formula as the inverse mapping?