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

TL;DR

A contour generation network is proposed based on Structural Low-Rank Descriptors for shape consistency, termed SLoRD, which is a plug-and-play framework to refine the segmentation inconsistency existing in coarse predictions from other approaches.

Abstract

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.

Figures (12)

• Figure 1: (a) CT case 1. (b-c) Coarse prediction by 3D UNet & refined outcome by 3D UNet + SLoRD on case 1. (d) CT case 2 with metal artifacts. (e-f) Coarse prediction by the multi-stage pipeline Spine-Transformer tao2022spine & our refined prediction on case 2.
• Figure 2: Spherical coordinate system for contour representations of 3D vertebrae. (a). red point: the spherical center, green point: the contour point, blue line: the radial vector. (b). x, y, and z axis adopt the orientations shown in the figure. $\rho$: the radial distance away from the spherical center, $\phi$: the azimuth angle between the radial vector and $z^{+}$, $\theta$: the polar angle between $x^{+}$ and the projected radial vector in the XOY plane.
• Figure 3: Upper: The flow of contour decomposition and restoration. Lower: The linear combination process between basic contour descriptors. The first row indicates basic descriptors of specific ranks. The second row refers to weighted visualizations.
• Figure 4: The two-stage framework. (a) The first stage adopts arbitrary segmentation networks to output inconsistent predictions, which will be refined with intra-vertebrae segmentation consistency by SLoRD in a sliding-window fashion. (b) Gaussian positional prompts are acquired based on the position of coarse spherical centers and the size of instance masks. Instance-wise positional priors are beneficial to promote the spherical centroid localization by SLoRD. (c) SLoRD consists of the spherical center decoder, the coefficient decoder, and the binary mask decoder. Specifically, the center decoder will regress spherical centroids with better precision. The coefficient decoder will generate linear coefficients, which are transformed into contour points under the interaction with low-rank contour descriptors. The mask decoder is aimed for precise shape representations of vertebrae, which boost the precision of generated contours. SLoRD aims to regress contour points close to vertebral boundaries via explicit contour and shape regularizations.
• Figure 5: Iterative refinement for coarse masks in the inference stage.