Detection Instead of Inversion: T1-T2 Microstructure Quantification With Detection Transformers

Sebastian Endt; Fatih Özkan; Marion I. Menzel

cs.CVNov 1, 2026

Detection Instead of Inversion: T1-T2 Microstructure Quantification With Detection Transformers

Authors: Sebastian Endt, Fatih Özkan, Marion I. Menzel

Organizations: AImotion Bavaria, Technische Hochschule Ingolstadt, Ingolstadt, Germany · TUM School of Computation, Information and Technology, Technical University of Munich, Germany · TUM School of Natural Sciences, Technical University of Munich, Germany

Abstract

T1-T2 correlation MRI has strong potential to quantify microstructural compartments without imposing a biological model. Traditionally, full T1-T2 spectra per voxel are reconstructed with an ill-conditioned and time-consuming Inverse Laplace Transform. We propose to view this challenge as an object detection task: A Detection Transformer (DETR) takes 64 TI/TE signals and directly predicts a set of compartments specified by T1, T2, and signal fraction. We achieve a mean average precision mAP@10 of 76.8% on simulated data, outperforming both our previous model design (53.8%) and regularized NNLS (66.1%). We show that our DETR approach outperforms NNLS in almost every setting across compartment count, compartmental signal fraction, and SNR. Reconstruction is orders of magnitude faster than NNLS. The results are fully reproducible from our public code: github.com/SebastianEndtTHI/t1t2-detr

Figures & tables

Figure 1: T1-T2 spectra of random test voxels with $n_{c}\in\{2,3,4\}$ at SNR = 40. Grayscale: NNLS spectrum; orange crosses: NNLS compartments; filled blue circles: DETR (ours); empty black circles: ground truth. Marker size represents signal fraction.

Method	mAP@5	mAP@10	Strict	$n_{c}$				$f$
Method	[%]	[%]	acc. [%]	1	2	3	4	$<0.35$	$0.35$ – $0.65$	$\geq 0.65$
NNLS	43.3	66.1	40.5	99.0	78.2	62.1	51.4	42.8	82.6	93.3
DETR (diff)	25.6	53.8	39.4	98.5	74.0	50.1	39.2	33.2	73.2	93.8
DETR (ours)	49.2	76.8	49.0	98.9	89.8	77.4	64.6	60.8	91.9	98.0

Table 1: Quantitative results on 25,000 voxel test data. mAP@10 is additionally broken down for different numbers of compartments

n_{c}

and compartmental signal fractions

f

Figure 2: True vs. predicted $T_{1}$ (left), $T_{2}$ (middle), and signal fraction (right) for all matched DETR (ours) test compartments, colored by true signal fraction.

Figure 3: mAP@10 (top) and strict accuracy (bottom) vs. SNR on 5000 voxels with identical noise pattern. Shaded: bootstrap

95\%

CIs; gray: training SNR range.

Magnetic Resonance Imaging

Magnetic resonance imaging uses magnetic fields and radio waves to create images of anatomy and tissue function for research and clinical care.

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Fiber-Resolved Microstructure Quantification from Multi-Shell Diffusion MRI using Detection Transformers

Sebastian Endt, Marcus Wirth, Johannes Reinhold Schlund, Marion Irene Menzel

AImotion Bavaria, Technische Hochschule Ingolstadt, Ingolstadt, Germany · TUM School of Computation, Information and Technology, Technical University of Munich, Garching, Germany · TUM School of Natural Sciences, Technical University of Munich, Garching, Germany

Diffusion MRI

Open paper AskPDF arXiv

Fiber orientation and compartmental microstructure are central to the characterization of white matter tissue in diffusion MRI, yet existing methods either resolve fiber orientations without quantifying microstructure, or quantify microstructure while assuming a fixed number of compartments and a single fiber direction. Nonparametric approaches that recover both require tensor-valued diffusion encoding and computationally expensive Monte-Carlo inversion of an ill-posed inverse Laplace transform. We propose to reframe this problem as an object detection-like task, adopting the Detection Transformer (DETR) architecture to jointly predict mean diffusivity (MD), fractional anisotropy (FA), main fiber direction, and signal fraction for a variable number of compartments per voxel from standard multi-shell diffusion MRI with linear encoding. Hungarian matching during training resolves permutation invariance across compartments. We introduce mean Average Precision as a reproducible benchmark metric. Evaluated on synthetic test data with up to five compartments per voxel, our model achieves

R^2=0.95

for MD,

R^2=0.88

for FA, and a median angular error of 4.2°, with performance scaling naturally with compartmental signal fraction.

Abstract

Magnetic Resonance Imaging

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