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Background: Tissue characterisation with cardiovascular magnetic resonance (CMR) parametric mapping has the potential to detect and quantify both focal and diffuse alterations in myocardial structure not assessable by late gadolinium enhancement. Native T1 mapping in particular has shown promise as a useful biomarker to support diagnostic, therapeutic and prognostic decision-making in ischaemic and non-ischaemic cardiomyopathies. Methods: Convolutional neural networks (CNNs) with Bayesian inference are a category of artificial neural networks which model the uncertainty of the network output. This study presents an automated framework for tissue characterisation from native shortened modified Look-Locker inversion recovery ShMOLLI T1 mapping at 1.5 T using a Probabilistic Hierarchical Segmentation (PHiSeg) network (PHCUMIS 119–127, 2019). In addition, we use the uncertainty information provided by the PHiSeg network in a novel automated quality control (QC) step to identify uncertain T1 values. The PHiSeg network and QC were validated against manual analysis on a cohort of the UK Biobank containing healthy subjects and chronic cardiomyopathy patients (N=100 for the PHiSeg network and N=700 for the QC). We used the proposed method to obtain reference T1 ranges for the left ventricular (LV) myocardium in healthy subjects as well as common clinical cardiac conditions. Results: T1 values computed from automatic and manual segmentations were highly correlated (r=0.97). Bland-Altman analysis showed good agreement between the automated and manual measurements. The average Dice metric was 0.84 for the LV myocardium. The sensitivity of detection of erroneous outputs was 91%. Finally, T1 values were automatically derived from 11,882 CMR exams from the UK Biobank. For the healthy cohort, the mean (SD) corrected T1 values were 926.61 (45.26), 934.39 (43.25) and 927.56 (50.36) for global, interventricular septum and free-wall respectively. Conclusions: The proposed pipeline allows for automatic analysis of myocardial native T1 mapping and includes a QC process to detect potentially erroneous results. T1 reference values were presented for healthy subjects and common clinical cardiac conditions from the largest cohort to date using T1-mapping images. [ABSTRACT FROM AUTHOR]