ConvNeXt-FD: A Fractal-Based Deep Model for Robust Biomedical Image Segmentation

Image segmentation remains fundamentally limited by boundary ambiguity arising from sampling-induced information loss and inherent uncertainty in pixel-wise labeling. Although encoder-decoder architectures such as U-Net achieve strong performance, they often produce overconfident predictions that fail to capture transition-region ambiguity. To address this issue, we propose \textbf{NoiseUNet}, a simple yet effective framework that injects bounded perturbations into skip connections to regularize cross-scale feature fusion. This mechanism enforces robustness to local feature variations and promotes boundary-aware representations. Theoretically, the perturbation induces an implicit fuzzification effect, yielding soft, data-driven memberships without requiring explicit fuzzy modeling. We further introduce \textbf{ThyR}, a real-world thyroid ultrasound dataset with inherently ambiguous boundaries. Experiments demonstrate that NoiseUNet consistently improves both segmentation accuracy and boundary fidelity.

Accurate biomedical image segmentation requires not only high global overlap but also reliable delineation of clinically meaningful boundaries. In blood-smear microscopy, cytoplasm and nucleus contours provide the structural basis for downstream morphology analysis; however, deep segmentation models may remain uncertain or overconfident near ambiguous boundary regions even when achieving strong Dice scores. This work proposes a Reliability-Aware Boundary Refinement Network (RABR-Net), a two-stage framework for trustworthy image segmentation. A strong UNet++ EfficientNet-B4 base segmenter first produces initial class probabilities and logits. Predictive entropy, test-time augmentation variance, margin uncertainty, probability gradients, and soft boundary cues are then combined into a boundary-aware reliability representation. This representation guides a gated residual refiner that selectively corrects uncertain boundary pixels while preserving confident regions of the base prediction. The framework is evaluated using overlap accuracy, class-wise Dice, Boundary Dice, HD95/ASSD, calibration, risk--coverage analysis, robustness under image perturbations, qualitative correction maps, and paired statistical testing. On the held-out test set, the proposed method improves Dice from 0.9602 to 0.9614, Boundary Dice from 0.3448 to 0.3611, and HD95 from 3.0354 to 2.8274 compared with the cached base prediction. Statistical analysis confirms significant improvements in Dice, Boundary Dice, and HD95. Qualitative results show that the learned gate concentrates around uncertain cytoplasm and nucleus boundaries, and correction maps confirm localized boundary refinement. Although calibration does not automatically improve after refinement, the proposed framework provides an interpretable and reliability-focused strategy for boundary-sensitive biomedical image segmentation.

Accurate image segmentation remains challenging, particularly in generating sharp, confident boundaries. While modern architectures have advanced the field, many of them still rely on standard loss functions like Cross-Entropy and Dice, which often neglect the discriminative structure of learned features, leading to inaccurate boundaries. This work introduces Deep Discriminant Analysis (DDA), a differentiable, architecture-agnostic loss function that embeds classical discriminant principles for network training. DDA explicitly maximizes between-class variance while minimizing within-class one, promoting compact and separable feature distributions without increasing inference cost. Evaluations on the DIS5K benchmark demonstrate that DDA consistently improves segmentation accuracy, boundary sharpness, and model confidence across various architectures. Our results show that integrating discriminant analysis offers a simple, effective path for building more robust segmentation models.