# Learning to Rearrange Voxels in Binary Segmentation Masks for Smooth Manifold Triangulation

arXiv: https://arxiv.org/abs/2108.05269 · HTML: https://mlsanity.com/paper/2108.05269/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 6 of its 15 references that are in the map.
- First posted on arXiv 11 Aug 2021.

## Builds on (most cited first, 6 of 6)

- [3D Semantic Segmentation with Submanifold Sparse Convolutional Networks](https://mlsanity.com/paper/1711.10275/) (2017)
- [OctNet: Learning Deep 3D Representations at High Resolutions](https://mlsanity.com/paper/1611.05009/) (2016)
- [Submanifold Sparse Convolutional Networks](https://mlsanity.com/paper/1706.01307/) (2017)
- [Shape Completion using 3D-Encoder-Predictor CNNs and Shape Synthesis](https://mlsanity.com/paper/1612.00101/) (2016)
- [High-Resolution Shape Completion Using Deep Neural Networks for Global Structure and Local Geometry Inference](https://mlsanity.com/paper/1709.07599/) (2017)
- [A Baseline Approach for AutoImplant: the MICCAI 2020 Cranial Implant Design Challenge](https://mlsanity.com/paper/2006.12449/) (2020)

## Built on by (most cited first, 5 of 5)

- [Deep Learning-based Framework for Automatic Cranial Defect Reconstruction and Implant Modeling](https://mlsanity.com/paper/2204.06310/) (2022)
- [High-Resolution Cranial Defect Reconstruction by Iterative, Low-Resolution, Point Cloud Completion Transformers](https://mlsanity.com/paper/2308.03813/) (2023)
- [Back to the Roots: Reconstructing Large and Complex Cranial Defects using an Image-based Statistical Shape Model](https://mlsanity.com/paper/2204.05703/) (2022)
- [Improving Deep Learning-based Automatic Cranial Defect Reconstruction by Heavy Data Augmentation: From Image Registration to Latent Diffusion Models](https://mlsanity.com/paper/2406.06372/) (2024)
- [Automatic Skull Reconstruction by Deep Learnable Symmetry Enforcement](https://mlsanity.com/paper/2411.17342/) (2024)

## Abstract (arXiv)

Medical images, especially volumetric images, are of high resolution and often exceed the capacity of standard desktop GPUs. As a result, most deep learning-based medical image analysis tasks require the input images to be downsampled, often substantially, before these can be fed to a neural network. However, downsampling can lead to a loss of image quality, which is undesirable especially in reconstruction tasks, where the fine geometric details need to be preserved. In this paper, we propose that high-resolution images can be reconstructed in a coarse-to-fine fashion, where a deep learning algorithm is only responsible for generating a coarse representation of the image, which consumes moderate GPU memory. For producing the high-resolution outcome, we propose two novel methods: learned voxel rearrangement of the coarse output and hierarchical image synthesis. Compared to the coarse output, the high-resolution counterpart allows for smooth surface triangulation, which can be 3D-printed in the highest possible quality. Experiments of this paper are carried out on the dataset of AutoImplant 2021 (https://autoimplant2021.grand-challenge.org/), a MICCAI challenge on cranial implant design. The dataset contains high-resolution skulls that can be viewed as 2D manifolds embedded in a 3D space. Codes associated with this study can be accessed at https://github.com/Jianningli/voxel_rearrangement.