Title: Learning Surface Parameterization for Document Image Unwarping. Abstract: In this paper, we present a novel approach to learn texture mapping for a 3D surface and apply it to document image unwarping. We propose an efficient method to learn surface parameterization by learning a continuous bijective mapping between 3D surface positions and 2D texture-space coordinates. Our surface parameterization network can be conveniently plugged into a differentiable rendering pipeline and trained using multi-view images and rendering loss. Recent work on differentiable rendering techniques for implicit surfaces has shown high-quality 3D scene reconstruction and view synthesis results. However, these methods typically learn the appearance color as a function of the surface points and lack explicit surface parameterization. Thus they do not allow texture map extraction or texture editing. By introducing explicit surface parameterization and learning with a recent differentiable renderer for implicit surfaces, we demonstrate state-of-the-art document-unwarping via texture extraction. We show that our approach can reconstruct high-frequency textures for arbitrary document shapes in both synthetic and real scenarios. We also demonstrate the usefulness of our system by applying it to document texture editing.