ER2Net: an evidential reasoning rule–enabled neural network for reliable triple-negative breast cancer tumor segmentation in magnetic resonance imaging

Abstract. Purpose Triple-negative breast cancer (TNBC) is an aggressive subtype with limited treatment options and high recurrence rates. Magnetic resonance imaging (MRI) is widely used for tumor assessment, but manual segmentation is labor-intensive and variable. Existing deep learning methods often lack generalizability, calibrated confidence, and robust uncertainty quantification. Approach We propose ER2Net, an evidential reasoning–enabled neural network for reliable TNBC tumor segmentation on MRI. ER2Net trains multiple U-Net variants with dropouts to generate diverse predictions and introduces pixel-wise reliability to quantify model agreement. We then introduce two ensemble fusion techniques: weighted reliability (WR) segmentation, which leverages pixel-wise reliability to enhance sensitivity, and Bayesian fusion (BF), which integrates predictions probabilistically for robust consensus. Confidence calibration is achieved using evidential reasoning, and we further propose pixel-wise reliable confidence entropy (PWRE) as a uncertainty measure. Results ER2Net improved performance compared with individual models. WR achieved IoU = 0.886, sensitivity = 0.928, precision = 0.952, and Hausdorff distance = 5.429 mm, whereas BF achieved IoU = 0.885 and sensitivity = 0.929. Reliable fusion provided the best calibration [expected calibration error = 0.00003; maximum calibration error = 0.017]. PWRE produced lower variance than conventional entropy, yielding more stable uncertainty estimates. Conclusion ER2Net introduces WR segmentation and BF as enhanced fusion techniques and PWRE as a uncertainty metric. Together, these advances improve segmentation accuracy, sensitivity, confidence calibration, and uncertainty estimation, paving the way for reliable MRI-based tools to support personalized treatment planning and response assessment in TNBC.