Abstract: In this paper, we present a novel approach to learn texture mapping for an isometrically deformed 3D surface and apply it for texture unwrapping of documents or other objects. 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. 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. Using the learned parameterized implicit 3D surface we demonstrate state-of-the-art document-unwarping via texture extraction in both synthetic and real scenarios. We also show that our approach can reconstruct high-frequency textures for arbitrary objects. We further demonstrate the usefulness of our system by applying it to document and object texture editing.

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