Operator-graph relaxation for enhanced automatic segmentation of cardiac anatomical structures in medical images

Operator-graph relaxation for enhanced automatic segmentation of cardiac anatomical structures in medical images

Pylov P.A. (KuzSTU, Kemerovo, Russia)
Maitak R.V. (KuzSTU, Kemerovo, Russia)
Pimonov A.G. (KuzSTU, Kemerovo, Russia)

Abstract

This article presents a graph-based relaxation method that improves the quality of automatic segmentation of heart ventricles in two-dimensional magnetic resonance imaging (MRI) slices from three orthogonal projections. Unlike pixel-oriented approaches, which perform independent classification of image elements, the proposed method treats the output of the base U-Net model as a continuous probability field that is structurally aligned with the image graph. An MRI slice is represented as an undirected graph whose vertices correspond to the slice's pixels. The edges are defined by local neighborhood relations and the edge weights are determined by spatial proximity, intensity difference, magnitude of the local gradient, and consistency of probability estimates of neighboring pixels. A key element of the method is the state transfer operator, which is defined as a linear transformation of a neighboring vertex's probability vector depending on the direction of information transfer, local intensity gradient, and anatomical class compatibility matrix. The operator parameters are analytically specified and not learned. This allows the method to be applied to the probability field of an arbitrary segmentation model without retraining or additional data labeling. For the iterative relaxation procedure, a compressibility condition has been proven to ensure the existence and uniqueness of a fixed point and a geometric convergence rate, as well as a quantitative stopping criterion. An experimental evaluation was performed on a clinical dataset using five-fold cross-validation at the patient level and stratification by projections. The proposed method was compared with the baseline U-Net model and the nnU-Net and U-Net+ViT models. It was also compared with post-processing procedures, such as connected component selection, morphological closing, and a fully connected conditional random field, in terms of segmentation quality and computational cost. An ablation study evaluated the contribution of individual components of the method. External testing was additionally performed on an independent cohort of 100 studies acquired at a different medical institution located in another region, on a scanner from a different vendor; the algorithm version and all of its parameters were frozen before the reference annotations were accessed, and no fine-tuning was carried out. Improvements in mean values were observed for all ten considered metrics–Dice coefficient, HD95, Contour F1, Overreach, and Underreach for both ventricles. After adjusting for multiple comparisons, nine of the differences were statistically significant, and the reduction in right ventricular Underreach was interpreted as a trend. On the external cohort, the advantage of the method over the baseline model was retained for nine of the ten metrics, with absolute quality decreasing by 3.0-3.9%. Ventricular volumes and functional cardiac indices were not computed in this study; the reported results therefore characterize segmentation quality and are not direct evidence of improved accuracy of clinical measurements.

Keywords

medical image segmentation; magnetic resonance imaging of the heart; operator-graph relaxation; probabilistic segmentation field; structural consistency of segmentation.

Edition

Proceedings of the Institute for System Programming, vol. 38, issue 6, part 1, 2026, pp. 323-352

ISSN 2220-6426 (Online), ISSN 2079-8156 (Print).

DOI: 10.15514/ISPRAS-2026-38(6)-21

For citation

Pylov P.A., Maitak R.V., Pimonov A.G. Operator-graph relaxation for enhanced automatic segmentation of cardiac anatomical structures in medical images. Proceedings of the Institute for System Programming, vol. 38, issue 6, part 1, 2026, pp. 323-352 DOI: 10.15514/ISPRAS-2026-38(6)-21.

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