Dense estimation of depth from stereo pinhole image pair is a well known problem and seems to be easily solvable by both classical as well as machine learning algorithms. However, dense depth estimation from stereo fisheye image pair is apparently a more challenging problem. There are two main factors adding to the complexity of the problem: (I) owing to the wider field of view, the fisheye lenses are inherently nonlinear thus making the estimation problem harder. (II) because we want to estimate depth for every pixel coordinate from just two images, i.e. a calibrated stereo pair, the data is statistically insufficient thus greatly complexifying the problem. To alleviate (II) many depth estimation algorithms enlarge their parameter space by incorporating pose parameters and work on image sequence (esp. videos). Here we stick to the stereo camera setting and provide a novel estimation technique and quantify its uncertainty. We use the technique of variational calculus to derive a (noisy) pde for which wellposedness is proved and then solved in the
least square
sense using proximal algorithms. This setting enables us to invoke the standard machinery of nonlinear least squares for generating the covariance estimates. Most state of the art algorithms that are based on deep learning (nonlinear regression) technique fail to say anything about the uncertainty of the outputs which is of paramount importance in safety critical applications for e.g. arising in automotive domain. Lastly, our methodology has the advantage of being massively parallelizable for hardware implementation thereby offering lesser runtime.