A signed distance function (SDF) as the 3D shape description is one of the most effective approaches to represent 3D geometry for rendering and reconstruction. Our work is inspired by the state-of-the-art method DeepSDF that learns and analyzes the 3D shape as the iso-surface of its shell and this method has shown promising results especially in the 3D shape reconstruction and compression domain. In this paper, we consider the degeneration problem of reconstruction coming from the capacity decrease of the DeepSDF model, which approximates the SDF with a neural network and a single latent code. We propose Local Geometry Code Learning (LGCL), a model that improves the original DeepSDF results by learning from a local shape geometry of the full 3D shape. We add an extra graph neural network to split the single transmittable latent code into a set of local latent codes distributed on the 3D shape. Mentioned latent codes are used to approximate the SDF in their local regions, which will alleviate the complexity of the approximation compared to the original DeepSDF. Furthermore, we introduce a new geometric loss function to facilitate the training of these local latent codes. Note that other local shape adjusting methods use the 3D voxel representation, which in turn is a problem highly difficult to solve or even is insolvable. In contrast, our architecture is based on graph processing implicitly and performs the learning regression process directly in the latent code space, thus make the proposed architecture more flexible and also simple for realization. Our experiments on 3D shape reconstruction demonstrate that our LGCL method can keep more details with a significantly smaller size of the SDF decoder and outperforms considerably the original DeepSDF method under the most important quantitative metrics.
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