Fully Differentiable RANSAC

We propose the fully differentiable $\nabla$-RANSAC.It predicts the inlier probabilities of the input data points, exploits the predictions in a guided sampler, and estimates the model parameters (e.g., fundamental matrix) and its quality while propagating the gradients through the entire procedure. The random sampler in $\nabla$-RANSAC is based on a clever re-parametrization strategy, i.e.\ the Gumbel Softmax sampler, that allows propagating the gradients directly into the subsequent differentiable minimal solver. The model quality function marginalizes over the scores from all models estimated within $\nabla$-RANSAC to guide the network learning accurate and useful probabilities.$\nabla$-RANSAC is the first to unlock the end-to-end training of geometric estimation pipelines, containing feature detection, matching and RANSAC-like randomized robust estimation. As a proof of its potential, we train $\nabla$-RANSAC together with LoFTR, i.e. a recent detector-free feature matcher, to find reliable correspondences in an end-to-end manner. We test $\nabla$-RANSAC on a number of real-world datasets on fundamental and essential matrix estimation. It is superior to the state-of-the-art in terms of accuracy while being among the fastest methods. The code and trained models will be made public.