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We present an adaptive deep representation of volumetric fields of 3D shapesand an efficient approach to learn this deep representation for high-quality 3Dshape reconstruction and auto-encoding. Our method encodes the volumetric fieldof a 3D shape with an adaptive feature volume organized by an octree andapplies a compact multilayer perceptron network for mapping the features to thefield value at each 3D position. An encoder-decoder network is designed tolearn the adaptive feature volume based on the graph convolutions over the dualgraph of octree nodes. The core of our network is a new graph convolutionoperator defined over a regular grid of features fused from irregularneighboring octree nodes at different levels, which not only reduces thecomputational and memory cost of the convolutions over irregular neighboringoctree nodes, but also improves the performance of feature learning. Our methodeffectively encodes shape details, enables fast 3D shape reconstruction, andexhibits good generality for modeling 3D shapes out of training categories. Weevaluate our method on a set of reconstruction tasks of 3D shapes and scenesand validate its superiority over other existing approaches. Our code, data,and trained models are available at https://wang-ps.github.io/dualocnn.

Dual Octree Graph Networks for Learning Adaptive Volumetric Shape Representations