# Explainable vertebral fracture analysis with uncertainty estimation using differentiable rule-based classification

arXiv: https://arxiv.org/abs/2407.02926 · HTML: https://mlsanity.com/paper/2407.02926/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 25 references that are in the map.
- First posted on arXiv 3 Jul 2024.

## Builds on (most cited first, 11 of 11)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [End-to-End Object Detection with Transformers](https://mlsanity.com/paper/2005.12872/) (2020)
- [Grad-CAM: Visual Explanations from Deep Networks via Gradient-based Localization](https://mlsanity.com/paper/1610.02391/) (2016)
- [Variational Inference with Normalizing Flows](https://mlsanity.com/paper/1505.05770/) (2015)
- [Density estimation using Real NVP](https://mlsanity.com/paper/1605.08803/) (2016)
- [Generalized Intersection over Union: A Metric and A Loss for Bounding Box Regression](https://mlsanity.com/paper/1902.09630/) (2019)
- [DINO: DETR with Improved DeNoising Anchor Boxes for End-to-End Object Detection](https://mlsanity.com/paper/2203.03605/) (2022)
- [Why Normalizing Flows Fail to Detect Out-of-Distribution Data](https://mlsanity.com/paper/2006.08545/) (2020)
- [Human Pose Regression with Residual Log-likelihood Estimation](https://mlsanity.com/paper/2107.11291/) (2021)
- [Multi-View Vertebra Localization and Identification from CT Images](https://mlsanity.com/paper/2307.12845/) (2023)
- [Robust vertebra identification using simultaneous node and edge predicting Graph Neural Networks](https://mlsanity.com/paper/2308.02509/) (2023)

## Built on by (most cited first, 2 of 2)

- [Uncertainty Quantification for Machine Learning in Healthcare: A Survey](https://mlsanity.com/paper/2505.02874/) (2025)
- [Exemplar Diffusion: Improving Medical Object Detection with Opportunistic Labels](https://mlsanity.com/paper/2603.15267/) (2026)

## Abstract (arXiv)

We present a novel method for explainable vertebral fracture assessment (XVFA) in low-dose radiographs using deep neural networks, incorporating vertebra detection and keypoint localization with uncertainty estimates. We incorporate Genant's semi-quantitative criteria as a differentiable rule-based means of classifying both vertebra fracture grade and morphology. Unlike previous work, XVFA provides explainable classifications relatable to current clinical methodology, as well as uncertainty estimations, while at the same time surpassing state-of-the art methods with a vertebra-level sensitivity of 93% and end-to-end AUC of 97% in a challenging setting. Moreover, we compare intra-reader agreement with model uncertainty estimates, with model reliability on par with human annotators.