Organizations: Department of Mathematics, Bareilly College, Bareilly (MJP Rohilkhand University), Uttar Pradesh, 243005, India · CSIR-Central Electronics Engineering Research Institute, Pilani, Rajasthan, 333031, India · CICMR, Regional Medical Research Center, Dibrugarh, India · Department of Statistics, Bareilly College, Bareilly, Uttar Pradesh, 243005, India
Accurate brain image segmentation, particularly for distinguishing various tissues from magnetic resonance imaging (MRI) images, plays a pivotal role in finding the neurological dis ease and medical image computing. In deep learning approaches, loss functions are very crucial for optimizing the model. In this study, we introduce a novel loss function integrating fuzzy logic to deals uncertainty issues in brain image segmentation into various tissues. It integrates the well-known categorical cross-entropy (CCE) loss function and fuzzy entropy based on fuzzy logic. By employing fuzzy logic, this loss function accounts for the inherent uncertainties in pixel classifications. The proposed loss function has been evaluated on two publicly available benchmark datasets, IBSR and OASIS, using two widely recognised architectures, U-Net and U-Net++. Experimental results demonstrate that the trained model with proposed loss function provided better results in comparison to the CCE optimisation function in terms of various performance metrics. Additionally, it effectively enhances segmentation performance while handling meaningful uncer tainty during training. The findings suggest that this approach not only improves segmentation outcomes but also contributes to the reliability of model predictions.
Figures & tables
Fig. 1 : Deep learning architecture with proposed fuzzy categorial cross entropy for brain image segmentation.
Fig. 2 : U-Net architecture featuring various neurons and 2D convolution with a kernel size of 3×3 , followed by max pooling with a kernel size of 2×2 . The ReLU activation function is used, followed by Batch normalization.
Fig. 3 : U-Net++ architecture with the skip connectionsn.
Algorithm
Metrics
LCCE
LFCCE
U-Net
AC
0.9986
0.9991
ACval
0.9907
0.9910
DC
0.9980
0.9986
DCval
0.9903
0.9906
IoU
0.9960
0.9972
IoUval
0.9808
0.9815
TABLE I : U-Net and U-Net++ architecture segmentation performance with LCCE and LFCCE loss function for IBSR data. We take the number of epochs 100 and Batch size 2. And use the segmentation metrices as accuracy (AC) , Dice coefficient (DC) and Intersection over Union (IoU) and their corresponding validations.
Fig. 4 : Plot for training versus validation performance for U-Net and U-Net++ architecture for IBSR data with categorical cross-entropy (LCCE) and fuzzy categorical cross entropy (LFCCE) loss optimization function along with epoch in term of performance metrices: accuracy, Dice coefficient and Intersection over Union. The performance of U-Net and U-Net++ with LFCCE in term of AC , DC , IoU performance slightly better with the epoch. During training the model, the U-Net validation with LFCCE in term of ACval , DCval , IoUval providing better results with optimizing with fuzzy logic. The U-Net++ validation with LFCCE in term of ACval , DCval , IoUval providing more better results in comparison to LCCE . The fuzzy categorical cross entropy (LFCCE) optimizing the objective with the quantifying the uncertainty during training the model.
Fig. 5 : Qualitative segmentation results using U-Net with LCCE , and U-Net with LFCCE (proposed loss function) on the IBSR brain data for the various image (a), (b) and (c). The most left row, comprised the raw image and corresponding predicted image comprises with various tissues such as background (BG), CSF, GM, and WM in this study. U-Net architecture with loss function is trained and designed and then predicted and depicted for same images (a), (b) and (c) respectively. The U-Net with LFCCE shows the better segmentation in CSF, GM and WM tissues as it handles the uncertainty at the boundary region, as shown in case of CSF tissues. The boundary pixels in CSF tissues are changing which can be promising with uncertainty.
Fig. 6 : Qualitative segmentation results using U-Net++ with LCCE , and U-Net++ with LFCCE (proposed loss function) on the IBSR brain data for the various image (a), (b) and (c). The most left row, comprised the raw image and corresponding predicted image comprises with various tissues such as background (BG), CSF, GM, and WM. The U-Net++ with LFCCE shows the better segmentation in CSF, GM and WM tissues as it handles the uncertainty at the boundary region, as shown in case of CSF tissues.
Algorithm
Metrics
LCCE
LFCCE
U-Net
AC
0.9873
0.9889
ACval
0.9518
0.9306
DC
0.9801
0.9842
DCval
0.9488
0.9296
IoU
0.9612
0.9691
IoUval
0.9034
0.8701
TABLE II : U-Net and U-Net++ architecture segmentation performance with LCCE and LFCCE loss function for OASIS data in term of AC , DC , IoU and respective validations ACval , DCval , IoUval . We use EarlyStopping and Batch size 2 for the OASIS data.
Fig. 7 : Plot for training versus validation performance for U-Net and U-Net++ architecture for OASIS brain data with (LCCE) and (LFCCE) loss optimization function along with epoch in term of performance metrices: accuracy, Dice coefficient and Intersection over Union. For OASIS data we used the early stoppage to avoid the overfitting problem. The epoch varies as the model achieve the optimization. The performance of U-Net and U-Net++ with (LFCCE) in term of AC , DC , IoU performance slightly better with the epoch for OASIS data. During training the model, the U-Net validation with (LFCCE) in term of ACval , DCval , IoUval providing less or equal results. The U-Net++ validation with (LFCCE) in term of ACval , DCval , IoUval providing more better results in comparison to (LCCE) .
Medical image segmentation delineates organs, lesions, and other structures in scans to support measurement, diagnosis, treatment planning, and research.
Accurate segmentation of brain images from magnetic resonance imaging (MRI) scans plays a pivotal role in brain image analysis and the diagnosis of neurological disorders. Deep learning algorithms, particularly U-Net and U-Net++, are widely used for image segmentation. However, it finds difficult to deal with uncertainty in images. To address this challenge, this work integrates intuitionistic fuzzy logic into U-Net and U-Net++, propose a novel framework, named as IFS U-Net and IFS U-Net++. These models accept input data in an intuitionistic fuzzy representation to manage uncertainty arising from vague ness and imprecise data. This approach effectively handles tissue ambiguity caused by the partial volume effect and boundary uncertainties. To evaluate the effectiveness of IFS U-Net and IFS U-Net++, experiments are conducted on two publicly available MRI brain datasets: the Internet Brain Segmentation Repository (IBSR) and the Open Access Series of Imaging Studies (OASIS). Segmentation performance is quantitatively assessed using Accuracy, Dice Coefficient, and Intersection over Union (IoU). The results demonstrate that the proposed architectures consistently improve segmentation performance by effectively addressing uncertainty
Hanuman Verma, Kiho Im, Akshansh Gupta +1
Department of Mathematics, Bareilly College, Bareilly (MJP Rohilkhand University), Uttar Pradesh, 243005, India · Fetal Neonatal Neuroimaging and Developmental Science Center, Boston Children’s Hospital, Harvard Medical School, Boston, MA 02115, USA · Division of Newborn Medicine, Boston Children’s Hospital, Harvard Medical School, Boston, MA 02115, USA +3
Accurate brain tumor segmentation from MRI scans is critical for diagnosis and treatment planning. Despite the strong performance of recent deep learning approaches, two fundamental limitations remain: (1) the lack of reliable uncertainty quantification in single-model predictions, which is essential for clinical deployment because the level of uncertainty may impact treatment decision-making, and (2) the under-utilization of rich information in radiology reports that can guide segmentation in ambiguous regions. In this paper, we propose the Disagreement-Guided Refinement Network (DGRNet), a novel framework that addresses both limitations through multi-view disagreement-based uncertainty estimation and text-conditioned refinement. DGRNet generates diverse predictions via four lightweight view-specific adapters attached to a shared encoder-decoder, enabling efficient uncertainty quantification within a single forward pass. Afterward, we build disagreement maps to identify regions of high segmentation uncertainty, which are then selectively refined according to clinical reports. Moreover, we introduce a diversity-preserving training strategy that combines pairwise similarity penalties and gradient isolation to prevent view collapse. The experimental results on the TextBraTS dataset show that DGRNet favorably improves state-of-the-art segmentation accuracy by 2.4% and 11% in main metrics Dice and HD95, respectively, while providing meaningful uncertainty estimates.
Bahram Mohammadi, Yanqiu Wu, Vu Minh Hieu Phan +6
Macquarie University, Sydney, NSW, Australia · Adelaide University, Adelaide, SA, Australia · Flinders University, Adelaide, SA, Australia +1
Medical image segmentation models often report high benchmark accuracy under ideal imaging conditions, yet their failures under clinical degradation can be quiet: sensor noise, patient motion, low- resolution acquisition, and contrast variability may all alter model behavior without producing an obvious warning. We present a reproducible framework for evaluating uncertainty-aware segmentation under con- trolled clinical degradation. Our experiments use a synthetic multimodal brain tumor MRI cohort generated with a biophysical phantom simulator that follows the BraTS protocol. We train U-Net and Attention U-Net baselines for multi-class tumor sub-region segmentation and augment both models with Monte Carlo dropout to estimate per-voxel uncertainty. Across eight clinically motivated corruption types at five severity levels, we measure segmentation accuracy, calibration, failure detection, and selective prediction coverage. On clean data, Attention U-Net achieves a whole-tumor Dice of 0.990; under severe Gaussian noise, its performance falls to 0.089. Predictive uncertainty rises with degradation and tracks segmentation error (Pearson r = 0.53 under severity-3 Gaussian noise), allowing us to flag failures with an AUROC of 0.843. These results argue for uncertainty-aware inference as a practical safety layer in physician-in-the-loop radiology workflows. We release the code, trained models, and evaluation protocol to support direct reproduction.
Pranav Kaliaperumal, Manisha Kaliaperumal
Department of Computer Science University of Colorado Denver Aurora, CO, USA · Department of Biology (Pre-Medical) Creighton University Omaha, NE, USA