Deep learning has achieved remarkable performance in medical image segmentation, yet it suffers from critical limitations: mathematical intractability, substantial parameter requirements, and lack of clinical interpretability. We propose RadiomicNet, a novel two-stream hybrid architecture that enhances standard deep learning by integrating handcrafted radiomics features directly into the segmentation learning process. The key contribution is the Radiomics Attention Gate (RAG), which leverages Gray-Level Co-occurrence Matrix (GLCM) and Local Binary Pattern (LBP) features to modulate skip-connection attention in a lightweight MobileNetV2-based encoder-decoder, providing ante-hoc interpretability without post-hoc approximations. A novel Radiomics Consistency Loss further enforces alignment between texture complexity and prediction uncertainty, reducing Expected Calibration Error (ECE) from 0.142 to 0.118. RadiomicNet achieves a Dice Similarity Coefficient (DSC) of 0.763 +/- 0.231 on the Breast Ultrasound Images (BUSI) dataset and 0.854 +/- 0.112 on Kvasir-SEG, outperforming U-KAN by 1.2% and 1.8%, respectively (p < 0.05, Wilcoxon signed-rank test), with only 3.27M parameters, 9.5x fewer than standard U-Net and 4.3x fewer than U-KAN. Gradient-based feature importance analysis reveals that GLCM dissimilarity (15.24%), GLCM energy (14.56%), and LBP entropy (11.49%) are the dominant radiomics cues, providing clinically meaningful explanations for segmentation decisions. The proposed approach demonstrates that compact, interpretable models grounded in domain knowledge can deliver state-of-the-art segmentation performance with substantially reduced computational overhead.

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