# SeqXY2SeqZ: Structure Learning for 3D Shapes by Sequentially Predicting 1D Occupancy Segments From 2D Coordinates

arXiv: https://arxiv.org/abs/2003.05559 · HTML: https://mlsanity.com/paper/2003.05559/

## Key facts

- Cited by 17 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 12 Mar 2020.

## Built on by (most cited first, 17 of 17)

- [SnowflakeNet: Point Cloud Completion by Snowflake Point Deconvolution with Skip-Transformer](https://mlsanity.com/paper/2108.04444/) (2021)
- [Reconstructing Surfaces for Sparse Point Clouds with On-Surface Priors](https://mlsanity.com/paper/2204.10603/) (2022)
- [PMP-Net++: Point Cloud Completion by Transformer-Enhanced Multi-step Point Moving Paths](https://mlsanity.com/paper/2202.09507/) (2022)
- [Surface Reconstruction from Point Clouds by Learning Predictive Context Priors](https://mlsanity.com/paper/2204.11015/) (2022)
- [Cycle4Completion: Unpaired Point Cloud Completion using Cycle Transformation with Missing Region Coding](https://mlsanity.com/paper/2103.07838/) (2021)
- [3D Shape Reconstruction from 2D Images with Disentangled Attribute Flow](https://mlsanity.com/paper/2203.15190/) (2022)
- [Snowflake Point Deconvolution for Point Cloud Completion and Generation with Skip-Transformer](https://mlsanity.com/paper/2202.09367/) (2022)
- [Unsupervised Inference of Signed Distance Functions from Single Sparse Point Clouds without Learning Priors](https://mlsanity.com/paper/2303.14505/) (2023)
- [Learning Signed Distance Functions from Noisy 3D Point Clouds via Noise to Noise Mapping](https://mlsanity.com/paper/2306.01405/) (2023)
- [Unsupervised Learning of Fine Structure Generation for 3D Point Clouds by 2D Projection Matching](https://mlsanity.com/paper/2108.03746/) (2021)
- [Latent Partition Implicit with Surface Codes for 3D Representation](https://mlsanity.com/paper/2207.08631/) (2022)
- [Fast Learning of Signed Distance Functions from Noisy Point Clouds via Noise to Noise Mapping](https://mlsanity.com/paper/2407.14225/) (2024)
- [Learning Neural Implicit through Volume Rendering with Attentive Depth Fusion Priors](https://mlsanity.com/paper/2310.11598/) (2023)
- [Hierarchical View Predictor: Unsupervised 3D Global Feature Learning through Hierarchical Prediction among Unordered Views](https://mlsanity.com/paper/2108.03743/) (2021)
- [Ray-ONet: Efficient 3D Reconstruction From A Single RGB Image](https://mlsanity.com/paper/2107.01899/) (2021)
- [Learning Local Pattern Modularization for Point Cloud Reconstruction from Unseen Classes](https://mlsanity.com/paper/2408.14279/) (2024)
- [Semantic Validation in Structure from Motion](https://mlsanity.com/paper/2304.02420/) (2023)

## Abstract (arXiv)

Structure learning for 3D shapes is vital for 3D computer vision. State-of-the-art methods show promising results by representing shapes using implicit functions in 3D that are learned using discriminative neural networks. However, learning implicit functions requires dense and irregular sampling in 3D space, which also makes the sampling methods affect the accuracy of shape reconstruction during test. To avoid dense and irregular sampling in 3D, we propose to represent shapes using 2D functions, where the output of the function at each 2D location is a sequence of line segments inside the shape. Our approach leverages the power of functional representations, but without the disadvantage of 3D sampling. Specifically, we use a voxel tubelization to represent a voxel grid as a set of tubes along any one of the X, Y, or Z axes. Each tube can be indexed by its 2D coordinates on the plane spanned by the other two axes. We further simplify each tube into a sequence of occupancy segments. Each occupancy segment consists of successive voxels occupied by the shape, which leads to a simple representation of its 1D start and end location. Given the 2D coordinates of the tube and a shape feature as condition, this representation enables us to learn 3D shape structures by sequentially predicting the start and end locations of each occupancy segment in the tube. We implement this approach using a Seq2Seq model with attention, called SeqXY2SeqZ, which learns the mapping from a sequence of 2D coordinates along two arbitrary axes to a sequence of 1D locations along the third axis. SeqXY2SeqZ not only benefits from the regularity of voxel grids in training and testing, but also achieves high memory efficiency. Our experiments show that SeqXY2SeqZ outperforms the state-ofthe-art methods under widely used benchmarks.