Interpolating Points on a Non-Uniform Grid using a Mixture of Gaussians

TL;DR

This paper introduces a Gaussian Mixture Model-based method for non-uniform image interpolation, enabling image reconstruction from arbitrarily positioned pixels and differentiability for downstream tasks.

Contribution

It presents a novel interpolation approach that handles non-uniform pixel positions using Gaussian mixtures, with an optimized CUDA implementation.

Findings

Effective reconstruction from arbitrary pixel arrangements

Differentiable interpolation enabling integration into neural networks

Open-source CUDA implementation available

Abstract

In this work, we propose an approach to perform non-uniform image interpolation based on a Gaussian Mixture Model. Traditional image interpolation methods, like nearest neighbor, bilinear, Hamming, Lanczos, etc. assume that the coordinates you want to interpolate from, are positioned on a uniform grid. However, it is not always the case in practice and we develop an interpolation method that is able to generate an image from arbitrarily positioned pixel values. We do this by representing each known pixel as a 2D normal distribution and considering each output image pixel as a sample from the mixture of all the known ones. Apart from the ability to reconstruct an image from arbitrarily positioned set of pixels, this also allows us to differentiate through the interpolation procedure, which might be helpful for downstream applications. Our optimized CUDA kernel and the source code to reproduce the benchmarks is located at https://github.com/universome/non-uniform-interpolation.