The following repo contains the code of take home assessment task. The task is to create an image using 2D Gaussian with mean vector (Nx2) and a covariance matrix (Nx2x2) where N is the number of Gaussian to fit the image.
The only requirement is pytorch and opencv, which was used to load and save the reconstructed image. Further I have tested the code on Pytorch 1.3.1 on ubuntu 20.04.
python 2d_gaussian_stable.py --num_gaussians $NUM_OF_GAUSSIAN_TO_FIT --image_path $PATH_TO_INPUT_IMAGE
I have tried to write multiple implementations due to the fact the covariance matrix that we need to optimize here is a (2x2), and we need to make sure that it's positive semi-definite, so for that, I have used multiple hacks to solve that like add small nudge in the diagonal based on the smallest eigenvalue. Also as authors did in the original paper, I divided the covariance matrix into a rotation matrix and scale vector for each Gaussian but that also doesn't solve the (2x2) scenario as mentioned by the author as well in the paper. Finally, I have tried to add comments to make it understandable as much as I could.
Input Image: 
Output Generation: 