Shape Reconstruction Using Differentiable Projections and Deep Priors

We investigate the problem of reconstructing shapes from noisy and incomplete projections in the presence of viewpoint uncertainities. The problem is cast as an optimization over the shape given measurements obtained by a projection operator and a prior. We present differentiable projection operators for a number of reconstruction problems which when combined with the deep image prior or shape prior allows efficient inference through gradient descent. We apply our method on a variety of reconstruction problems, such as tomographic reconstruction from a few samples, visual hull reconstruction incorporating view uncertainties, and 3D shape reconstruction from noisy depth maps. Experimental results show that our approach is effective for such shape reconstruction problems, without requiring any task-specific training.