Ensuring fairness in medical image segmentation is critical due to biases in imbalanced clinical data acquisition caused by demographic attributes (e.g., age, sex, race) and clinical factors (e.g., disease severity). To address these challenges, we introduce Distribution-aware Mixture of Experts (dMoE), inspired by optimal control theory. We provide a comprehensive analysis of its underlying mechanisms and clarify dMoE's role in adapting to heterogeneous distributions in medical image segmentation. Furthermore, we integrate dMoE into multiple network architectures, demonstrating its broad applicability across diverse medical image analysis tasks. By incorporating demographic and clinical factors, dMoE achieves state-of-the-art performance on two 2D benchmark datasets and a 3D in-house dataset. Our results highlight the effectiveness of dMoE in mitigating biases from imbalanced distributions, offering a promising approach to bridging control theory and medical image segmentation within fairness learning paradigms. The source code is available at https://github.com/tvseg/dMoE.

Scoring systems are widely adopted in medical applications for their inherent simplicity and transparency, particularly for classification tasks involving tabular data. In this work, we introduce RegScore, a novel, sparse, and interpretable scoring system specifically designed for regression tasks. Unlike conventional scoring systems constrained to integer-valued coefficients, RegScore leverages beam search and k-sparse ridge regression to relax these restrictions, thus enhancing predictive performance. We extend RegScore to bimodal deep learning by integrating tabular data with medical images. We utilize the classification token from the TIP (Tabular Image Pretraining) transformer to generate Personalized Linear Regression parameters and a Personalized RegScore, enabling individualized scoring. We demonstrate the effectiveness of RegScore by estimating mean Pulmonary Artery Pressure using tabular data and further refine these estimates by incorporating cardiac MRI images. Experimental results show that RegScore and its personalized bimodal extensions achieve performance comparable to, or better than, state-of-the-art black-box models. Our method provides a transparent and interpretable approach for regression tasks in clinical settings, promoting more informed and trustworthy decision-making. We provide our code at https://github.com/SanoScience/RegScore .

Solving inverse problems—recovering signals from incomplete or noisy measurements—is fundamental in science and engineering. Score-based generative models (SGMs) have recently emerged as a powerful framework for this task. Two main paradigms have formed: unsupervised approaches that adapt pretrained generative models to inverse problems, and supervised bridge methods that train stochastic processes conditioned on paired clean and corrupted data. While the former typically assume knowledge of the measurement model, the latter have largely overlooked this structural information. We introduce System-embedded Diffusion Bridge Models (SDBs), a new class of supervised bridge methods that explicitly embed the known linear measurement system into the coefficients of a matrix-valued SDE. This principled integration yields consistent improvements across diverse linear inverse problems and demonstrates robust generalization under system misspecification between training and deployment, offering a promising solution to real-world applications.

Design optimization and fabrication of concentric tube robots are time consuming because of the complexity of their workspaces and the characteristics of the superelastic materials used to make them. This paper presents a procedure for the expeditious design and fabrication of a concentric tube robot for applications that require rapid tube preparation but have less complex design constraints. This procedure reduces a 3D workspace optimization problem to a 2D problem. The continuum robot includes a heat-shrink tube to reduce fabrication time and to give it a small radius of curvature. Experimental results illustrate the feasibility of the proposed procedure.