VERIDAH: Solving Enumeration Anomaly Aware Vertebra Labeling across Imaging Sequences

Hendrik Möller; Hanna Schoen; Robert Graf; Matan Atad; Nathan Molinier; Anjany Sekuboyina; Bettina K. Budai; Fabian Bamberg

cs.CVJan 20, 2026

VERIDAH: Solving Enumeration Anomaly Aware Vertebra Labeling across Imaging Sequences

Authors: Hendrik Möller, Hanna Schoen, Robert Graf, Matan Atad, Nathan Molinier, Anjany Sekuboyina, Bettina K. Budai, Fabian Bamberg,

Organizations: Department for Interventional and Diagnostic Neuroradiology, TUM University Hospital · Chair for AI in Healthcare and Medicine, Technical University of Munich (TUM) · Department of Diagnostic and Interventional Radiology, Pediatric Radiology and Neuroradiology, Rostock University Medical Center · NeuroPoly Lab, Institute of Biomedical Engineering, Polytechnique Montreal, and Mila – Quebec AI Institute · Department of Quantitative Biomedicine, University of Zurich · Department of Diagnostic and Interventional Radiology, University Hospital Heidelberg · Department of Diagnostic and Interventional Radiology, Medical Center – University of Freiburg · Molecular Epidemiology Research Group, Max-Delbrueck-Center for Molecular Medicine in the Helmholtz Association (MDC) · Berlin Ultrahigh Field Facility (B.U.F.F.), Max Delbrueck Center for Molecular Medicine · Department of Diagnostic and Interventional Radiology, University Hospital Augsburg · Department of Computing, Imperial College London

Abstract

The human spine commonly consists of seven cervical, twelve thoracic, and five lumbar vertebrae. However, enumeration anomalies may result in individuals having eleven or thirteen thoracic vertebrae and four or six lumbar vertebrae. Although the identification of enumeration anomalies has potential clinical implications for chronic back pain and operation planning, the thoracolumbar junction is often poorly assessed and rarely described in clinical reports. Additionally, even though multiple deep-learning-based vertebra labeling algorithms exist, there is a lack of methods to automatically label enumeration anomalies. Our work closes that gap by introducing "Vertebra Identification with Anomaly Handling" (VERIDAH), a novel vertebra labeling algorithm based on multiple classification heads combined with a weighted vertebra sequence prediction algorithm. We show that our approach surpasses existing models on T2w TSE sagittal (98.30% vs. 94.24% of subjects with all vertebrae correctly labeled, p < 0.001) and CT imaging (99.18% vs. 77.26% of subjects with all vertebrae correctly labeled, p < 0.001) and works in arbitrary field-of-view images. VERIDAH correctly labeled the presence 2 Möller et al. of thoracic enumeration anomalies in 87.80% and 96.30% of T2w and CT images, respectively, and lumbar enumeration anomalies in 94.48% and 97.22% for T2w and CT, respectively. Our code and models are available at: https://github.com/Hendrik-code/spineps.

Figures & tables

NAKO T2w sagittal	Summary	Train	Test
Number of Scans	6291	5291	1000
Age Range (yrs)	20 – 72	20 – 72	22 – 72
M. Age (yrs) $\pm$ SD	$52\pm 11$	$52\pm 12$	$52\pm 11$
M. Weight (kg) $\pm$ SD	$80\pm 16$	$80\pm 16$	$80\pm 16$
M. Height (m) $\pm$ SD	$1.7\pm 0.1$	$1.7\pm 0.1$	$1.7\pm 0.1$
Sex ( $\%$ female)	52.4	52.4	52.1

Table 1: Demographics for the whole datasets and individual train and test splits. Abbreviations: yrs: years, kg: kilogram, m: meters, M.: Mean, SD: standard deviation, TEA: Thoracolumbar Enumeration Anomaly, LEA: Lumbar Enumeration Anomaly.

Figure 1: Example data samples from our CT (A, B) and MRI (C, D) dataset. For each sample, it shows a sagittal and coronal projection along the spine as well as the corpus centroids with vertebra labels associated with each. While the CT images contain various field-of-views, the NAKO T2w sagittal MRI images always cover the whole spine. A) spine with eleven thoracic vertebrae, B) normal spine with twelve thoracic and five lumbar vertebrae, C) has an additional thoracic vertebra, and D), a subject with only eleven thoracic vertebrae but six lumbar ones.

Figure 2: Overview of the VERIDAH approach. We take an input image and the vertebra localizations to crop around each vertebra. We then input these 3D cropped images separately into our classification model. The classification model has four output heads. We weigh their predictions based on our calibration and combine them into a cost matrix. Finally, an algorithm finds the optimal label sequence path that minimizes this cost, making our final sequence prediction.

Parameter	Value
Data
Number of 3D scans	5291 / 1171
Orientation	(Posterior, Inferior, Right)
Resolution (mm)	(0.85, 0.85, 3.3) / (1.0, 1.0, 1.0)
Crop Size (voxel count)	(200, 160, 32) / (128, 128, 128)
Training Setup

Table 2: Training Hyperparameters. Different setups for the sequences are written with slashes (T2w sag / CT)

Figure 3: Example of our sequence predictor on an artificially created sample containing

n=4

vertebrae (

V_{1}

–

V_{4}

) in the FOV. The classifier outputs specific vertebra class predictions

c_{ij}

and region prediction scores

r_{ij}

for each class (already combined into the label cost matrix

L

and reduced to T11 to L2 for simplicity), their visibility

s_{i}

, and the vertebra transitions output

t_{ik}

. Depending on the utilized classification head, either the path [T11, T12, L1, L2] (red arrows) or [T11, T12, T12, L1] (blue arrows) is returned by the sequence predictor. In the case of the latter one, the post-processing relabels the path [T11, T12, T12, L1] to [T11, T12, T13, L1], making this a TEA case. All unspecified classifier outputs have a value of zero.

Figure 4: Example of a CT test subject where all models failed. The reference data (left) shows an L6 LEA case with an ordinary number of twelve thoracic vertebrae. VERIDAH (right) mistakes the L1 for a thoracic vertebra, resulting in thirteen thoracic and five lumbar vertebrae (red arrows). The prediction of Meng et al. has a shift error by one, but correctly labels the L1. The center shows the reference T12 and L1 in multiple axial slices (top to bottom). While the T12 has clear ribs on both sides (yellow arrows), the L1 has thoracic-looking facets while having no ribs, making this a TLTV.

Metric	VERIDAH	Meng et al. [ 16 ]	Meng et al. [ 16 ] ZP
PL perc.	99.18	$77.81$	$77.26$
sub. corr.	99.63 $\pm$ 4.37	$89.04\pm 27.73$	$88.48\pm 28.28$
TEA rec.	96.30	$11.11$	$14.81$
LEA rec.	97.22	$61.11$	$61.11$

Table 3: Labeling Performance for CT data. Abbreviations: rec: recall, TEA: Thoracolumbar Enumeration Anomaly, LEA: Lumbar Enumeration Anomaly. Meng et al. ZP is the approach from Meng et al., but setting the TEA and LEA penalty costs to zero.

Figure 5: Example of a CT test subject with a T13 and only four lumbar vertebrae. The axial slices of the reference data (left) show that the T13 has a rib on either side (yellow arrows). While VERIDAH (right) correctly classifies the whole sequence of labels, the prediction of Meng et al. made two major errors, leading to six lumbar vertebrae instead of four (red arrows).

Metric	VERIDAH	SpineNetv2 [ 31 ]	TotalSpineSeg [ 29 ]
PL perc.	98.30	$91.49$	$94.24$
sub. corr.	99.58 $\pm$ 3.19	$97.89\pm 9.32$	$98.98\pm 4.13$
TEA rec.	87.80	$0.0$	$27.63$
LEA rec.	94.48	$83.72$	$83.04$

Table 4: Labeling Performance for T2w sagittal MRI data. Abbreviations: rec: recall, TEA: Thoracolumbar Enumeration Anomaly, LEA: Lumbar Enumeration Anomaly.

Metric	VH-V	VH-P	4H-AM	4H-P
T2w sagittal
PL perc.	$82.00$	$95.6$	$82.10$	98.30
sub. corr.	$97\pm 6.75$	$98.92\pm 5.05$	$97.45\pm 6.69$	99.58 $\pm$ 3.19
TEA rec.	$56.10$	$80.49$	$57.32$	87.80
LEA rec.	$65.52$	$80.69$	$67.59$	94.48
CT

Table 5: Ablation Labeling Performance. Abbreviations: rec: recall, TEA: Thoracolumbar Enumeration Anomaly, LEA: Lumbar Enumeration Anomaly, VH-V: Taking only the vertebra labeling without sequence predictor, VH-P: Inputting only the vertebra output to the sequence predictor, 4H-AM: Taking the Argmax of the four outputs instead of the sequence predictor. 4H-P: The proposed approach of utilizing the four classification outputs with the sequence predictor.

Panel of Figure 6 — Figure 6: The behavior of three metrics in relation to a specified artificial cost punishment of $\gamma$ on our test data. We sample these results in $0.25$ steps, as indicated by the plot markers. The baseline is represented by $\gamma=0$ .

Panel of Figure 7 — Figure 7: The behavior of three metrics, if we allow arbitrary label gaps in our sequence predictor on the test data. The x-axis shows different costs to punish these skips. We sample these results in $0.25$ steps, as indicated by the plot markers.

Panel of Figure 8 — Figure 8: The behavior of three metrics, if we allow arbitrary label gaps in our sequence predictor on the test data, and we remove exactly one random vertebra in each subject. The x-axis shows different costs to punish these skips. We sample these results in $0.25$ steps, as indicated by the plot markers.

T2w sagittal
Metric	VERIDAH	4H-P-NA	VH-P-NA
PL perc.	$98.30$	$93.40$	$93.10$
sub. corr.	99.58 $\pm$ 3.19	$98.32\pm 6.52$	$98.22\pm 6.96$
TEA rec.	$87.80$	$32.93$	$39.02$
LEA rec.	$94.48$	$82.76$	$77.24$
CT

Table 6: Labeling Performance T2w sagittal compared to training without labeled anomalies. Abbreviations: rec: recall, TEA: Thoracolumbar Enumeration Anomaly, LEA: Lumbar Enumeration Anomaly. 4H-P-NA: Taking all four classification heads with the sequence predictor using no TEA or LEA labels during training. VH-P-NA: Using only the vertebra output and the sequence predictor using no TEA or LEA labels during training.

Panel of Figure 9 — Figure 9: The behavior of three metrics over different FOVs of the test data. The x-axis shows the number of visible vertebrae fed into VERIDAH, while the y-axis showcases the different metric values.

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CTSpinoPelvic1K: spine, pelvis, ribs and femora in one coordinate frame, annotated for lumbosacral transitional anatomy

Gregory Schwing, Ashley Schehr, Annika Tekumulla, Margret Khoushi+10

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Medical Image Benchmarks 3D Medical Imaging

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Purpose: A vertebra at the lumbosacral junction is named by counting caudally from C2 on whole-spine imaging, but a lumbar case is planned on lumbar-only imaging (T12 to S1), without C2. Abdominopelvic CT holds that span plus the lowest ribs and pelvis. Where a lumbosacral transitional vertebra (LSTV) alters the count, the local anatomy is ambiguous: four rib-free vertebrae may be an L1 with a lumbar rib or an L5 assimilated to the sacrum, and six may be a sixth lumbar vertebra, a T12 with aplastic ribs, or a lumbarized S1. CTSpinoPelvic1K asks whether local morphology resolves it without the count. CTSpine1K's vertebrae and CTPelvic1K's pelvis covered these patients but were never joined; this release joins them on one series and adds the bones neither had. It provides 802 CT records with per-level ribs and femora, levels anchored on the lowest rib-bearing vertebra and S1, and classes for L6, T13, a separate S1 and lumbar ribs, so anomalies are recorded as such. Acquisition and Validation Methods: Records pair CTSpine1K and CTPelvic1K labels on each patient's bone-richest series under a VerSe-native scheme. Validation covered geometric invariants (802/802 pass), rib-vertebra incidence across 5,749 ribs (0.035% offset), and spinopelvic measures matching published values. Data Format and Usage Notes: NIfTI image/label pairs with patient-grouped LSTV-stratified five-fold splits and a loader; archived at https://doi.org/10.5281/zenodo.22139642. Potential Applications: Classifying a vertebra from local features; updating cadaveric morphometry; spinopelvic assessment; opportunistic screening; and, absent a public preoperative lumbar cohort, surgical planning research (377 records prone). Limitations: thoracic ground truth is field-of-view limited; postural angles supine; no held-out test set; ribs are triaged-review pseudolabels; Castellvi grades two-reader consensus on 33 records.

Abstract

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