Description
🚀 Feature
transform (and perhaps inverse_transform) should allow for interpolation (partial) transformation, given lambda (default=1).
Motivation
Interpolation allows one to seamlessly "morph" between two distributions.
Pitch
This is useful for all kinds of image processing tasks, where one does not want to fully transform a distribution, but gradually or partially transform the distribution.
For example, consider this blog post where your toolkit is used to transform the color map from a day image onto a night image. Interpolated transport would allow this tranformation to happen gradually and generate a video.
Alternatives
Kludging the matrix and then running transform. Any guidance on how to do this would be greatly appreciated.
Additional context
Roma et al. (2020) describe this process for audio morphing: "Displacement interpolation is then accomplished by sliding
through the non-zero entries of the transport matrix: given an interpolation parameter λ, each pair of masses in the matrix are interpolated to (1 − λ)xi + λyi and added to the output spectrum."
Attached is an image from their work:
