Interpolating Points on a Non-Uniform Grid using a Mixture of Gaussians
This work provides a method for image interpolation from non-uniform grids, which is a practical problem for computer vision and graphics practitioners when dealing with irregularly sampled data.
This paper addresses the problem of interpolating images from arbitrarily positioned pixel values, moving beyond traditional methods that assume uniform grids. The authors propose a Gaussian Mixture Model approach, representing known pixels as 2D normal distributions and output pixels as samples from this mixture.
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.