Hyperspherical Embedding for Point Cloud Completion
CVPR 2023


Most real-world 3D measurements from depth sensors are incomplete, and to address this issue the point cloud completion task aims to predict the complete shapes of objects from partial observations. Previous works often adapt an encoder-decoder architecture, where the encoder is trained to extract embeddings that are used as inputs to generate predictions from the decoder. However, the learned embeddings have sparse distribution in the feature space, which leads to worse generalization results during testing. To address these problems, this paper proposes a hyperspherical module, which transforms and normalizes embeddings from the encoder to be on a unit hypersphere. With the proposed module, the magnitude and direction of the output hyperspherical embedding are decoupled and only the directional information is optimized. We theoretically analyze the hyperspherical embedding and show that it enables more stable training with a wider range of learning rates and more compact embedding distributions. Experiment results show consistent improvement of point cloud completion in both single-task and multi-task learning, which demonstrates the effectiveness of the proposed method.


Proposed Hyperspherical Module

The proposed module contains two layers, a multi-layer perceptron (MLP) layer and a normalization layer. The outputs from the encoder are first transformed by the MLP layer and then the normalization layer constrains sthe features onto the surface of hypersphere by l2 normalization.

Effects of Hyperspherical Embedding

☆ Larger embedding norm

Norm distribution of different embeddings on MVP dataset

☆ Wider range of learning rates

Multi-task learning (Classification & Completion) with different learning rates on MVP dataset

☆ Poorly conditioned weight matrix

Singular values distribution of different baselines on MVP dataset

☆ Compact embedding distribution

Cosine similarity distribution of different categories on MVP dataset

Quantitative Results

☆ Single-task learning

Point cloud completion result on MVP dataset

☆ Multi-task learning

Point cloud classification & completion result on MVP dataset

Qualitative Results

Point cloud completion on MVP dataset

3D detection, pose estimation, and point cloud completion results on GraspNet dataset

Samples of point cloud interpolation in the embedding space



This work is supported by the Ford Motor Company via award N022977 and the National Science Foundation under award 1751093.
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