Compact and accurate representations of 3D shapes are central to many perception and robotics tasks. State-of-the-art learning-based methods can reconstruct single objects but scale poorly to large datasets. We present a novel recursive implicit representation to efficiently and accurately encode large datasets of complex 3D shapes by recursively traversing an implicit octree in latent space.
Our implicit Recursive Octree Auto-Decoder (ROAD) learns a hierarchically structured latent space enabling state-of-the-art reconstruction results at a compression ratio above 99%. We also propose an efficient curriculum learning scheme that naturally exploits the coarse-to-fine properties of the underlying octree spatial representation. We explore the scaling law relating latent space dimension, dataset size, and reconstruction accuracy, showing that increasing the latent space dimension is enough to scale to large shape datasets. Finally, we show that our learned latent space encodes a coarse-to-fine hierarchical structure yielding reusable latents across different levels of details, and we provide qualitative evidence of generalization to novel shapes outside the training set.
Our method parameterizes each shape with a latent vector denoting the root note of an octree which is traversed recursively, up to a predefined Level-of-Detail (LoD). To recover the final shape, we perform the zero-isosurface projection 𝝃.
Our lightweight recursive representation is capable of encoding high-fidelity models at arbitrary resolution levels and we show compelling performance on datasets of over 1000 objects.
At higher LoDs, similar areas of the projected latent space are increasingly shared by the different classes, suggesting that our approach efficiently encodes object geometry by learning geometric primitives common in the dataset.