# SLoRD: Structural Low-Rank Descriptors for Shape Consistency in Vertebrae Segmentation

arXiv: https://arxiv.org/abs/2407.08555 · HTML: https://mlsanity.com/paper/2407.08555/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 21 of its 54 references that are in the map.
- First posted on arXiv 11 Jul 2024.

## Builds on (most cited first, 21 of 21)

- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [Segment Anything](https://mlsanity.com/paper/2304.02643/) (2023)
- [3D U-Net: Learning Dense Volumetric Segmentation from Sparse Annotation](https://mlsanity.com/paper/1606.06650/) (2016)
- [Self-Supervised Pre-Training of Swin Transformers for 3D Medical Image Analysis](https://mlsanity.com/paper/2111.14791/) (2021)
- [PolarMask: Single Shot Instance Segmentation with Polar Representation](https://mlsanity.com/paper/1909.13226/) (2019)
- [UNeXt: MLP-based Rapid Medical Image Segmentation Network](https://mlsanity.com/paper/2203.04967/) (2022)
- [MedNeXt: Transformer-driven Scaling of ConvNets for Medical Image Segmentation](https://mlsanity.com/paper/2303.09975/) (2023)
- [SAM-Med2D](https://mlsanity.com/paper/2308.16184/) (2023)
- [VerSe: A Vertebrae Labelling and Segmentation Benchmark for Multi-detector CT Images](https://mlsanity.com/paper/2001.09193/) (2020)
- [DeepSSM: A Deep Learning Framework for Statistical Shape Modeling from Raw Images](https://mlsanity.com/paper/1810.00111/) (2018)
- [Iterative fully convolutional neural networks for automatic vertebra segmentation and identification](https://mlsanity.com/paper/1804.04383/) (2018)
- [DeepSSM: A Blueprint for Image-to-Shape Deep Learning Models](https://mlsanity.com/paper/2110.07152/) (2021)
- [Fully Automatic Segmentation of Lumbar Vertebrae from CT Images using Cascaded 3D Fully Convolutional Networks](https://mlsanity.com/paper/1712.01509/) (2017)
- [Btrfly Net: Vertebrae Labelling with Energy-based Adversarial Learning of Local Spine Prior](https://mlsanity.com/paper/1804.01307/) (2018)
- [Eigencontours: Novel Contour Descriptors Based on Low-Rank Approximation](https://mlsanity.com/paper/2203.15259/) (2022)
- [Learning with Explicit Shape Priors for Medical Image Segmentation](https://mlsanity.com/paper/2303.17967/) (2023)
- [SPINEPS -- Automatic Whole Spine Segmentation of T2-weighted MR images using a Two-Phase Approach to Multi-class Semantic and Instance Segmentation](https://mlsanity.com/paper/2402.16368/) (2024)
- [Vertebrae localization, segmentation and identification using a graph optimization and an anatomic consistency cycle](https://mlsanity.com/paper/2110.12177/) (2021)
- [Automatic Segmentation, Localization, and Identification of Vertebrae in 3D CT Images Using Cascaded Convolutional Neural Networks](https://mlsanity.com/paper/2009.13798/) (2020)
- [Multi-View Vertebra Localization and Identification from CT Images](https://mlsanity.com/paper/2307.12845/) (2023)
- [A Localisation-Segmentation Approach for Multi-label Annotation of Lumbar Vertebrae using Deep Nets](https://mlsanity.com/paper/1703.04347/) (2017)

## Built on by (most cited first, 4 of 4)

- [FB-Diff: Fourier Basis-guided Diffusion for Temporal Interpolation of 4D Medical Imaging](https://mlsanity.com/paper/2507.04547/) (2025)
- [Temporal Differential Fields for 4D Motion Modeling via Image-to-Video Synthesis](https://mlsanity.com/paper/2505.17333/) (2025)
- [Towards Voxel Spacing Consistency for Medical Image Segmentation](https://mlsanity.com/paper/2606.31839/) (2026)
- [ARNAI: Artifact Removal Network based on Autoencoding and Inpainting for Robust Spinal Image Segmentation and Measurement](https://mlsanity.com/paper/2609.07013/) (2026)

## Abstract (arXiv)

Automatic and precise multi-class vertebrae segmentation from CT images is crucial for various clinical applications. However, due to similar appearances between adjacent vertebrae and the existence of various pathologies, existing single-stage and multi-stage methods suffer from imprecise vertebrae segmentation. Essentially, these methods fail to explicitly impose both contour precision and intra-vertebrae voxel consistency constraints synchronously, resulting in the intra-vertebrae segmentation inconsistency, which refers to multiple label predictions inside a singular vertebra. In this work, we intend to label complete binary masks with sequential indices to address that challenge. Specifically, a contour generation network is proposed based on Structural Low-Rank Descriptors for shape consistency, termed SLoRD. For a structural representation of vertebral contours, we adopt the spherical coordinate system and devise the spherical centroid to calculate contour descriptors. Due to vertebrae's similar appearances, basic contour descriptors can be acquired offline to restore original contours. Therefore, SLoRD leverages these contour priors and explicit shape constraints to facilitate regressed contour points close to vertebral surfaces. Quantitative and qualitative evaluations on VerSe 2019 and 2020 demonstrate the superior performance of our framework over other single-stage and multi-stage state-of-the-art (SOTA) methods. Further, SLoRD is a plug-and-play framework to refine the segmentation inconsistency existing in coarse predictions from other approaches. Source codes are available.