Shape from semantic segmentation via the geometric Rényi divergence

In this paper, we show how to estimate shape (restricted to a single object class via a 3D morphable model) using solely a semantic segmentation of a single 2D image. We propose a novel loss function based on a probabilistic, vertex-wise projection of the 3D model to the image plane. We represent both these projections and pixel labels as mixtures of Gaussians and compute the discrepancy between the two based on the geometric Rényi divergence. The resulting loss is differentiable and has a wide basin of convergence. We propose both classical, direct optimisation of this loss ("analysis-by-synthesis") and its use for training a parameter regression CNN. We show significant ad-vantages over existing segmentation losses used in state-of-the-art differentiable renderers Soft Rasterizer and Neural Mesh Renderer.