Few-Shot Physics-Informed Neural Network for Shape Reconstruction of Concentric-Tube Robots

Modeling concentric tube robots (CTRs) involves complex nonlinear continuum mechanics, and despite recent progress, physics-based models often lack an accurate representation of the experimental setups. To overcome these limitations, deep neural network-based models have been explored as alternatives with superior accuracy; however, they often overlook known mechanics, require large training datasets, and typically discard shape estimation of the robot. We present a physics-informed neural network (PINN) for kinematic modeling of a 6-DoF CTR with three pre-curved tubes that embeds the Cosserat rod differential equations and learns from few-shot observational data, balancing physics priors with data-driven fitting. PINN enables full-state estimation of shape, twist angle, torsional strain, bending moment, and orientation. Benchmark tests show a mean shape error below 1% of the robot length and accurately recovered other kinematic states, outperforming a purely physics-based Cosserat rod model baseline while using a minimal training set. The resulting model is also computationally efficient and robust, making it well-suited for real-time control applications.

Transformer-Based Local Feature Matching for Multimodal Image Registration

Ultrasound imaging is a cost-effective and radiation-free modality for visualizing anatomical structures in real-time, making it ideal for guiding surgical interventions. However, its limited field-of-view, speckle noise, and imaging artifacts make it difficult to interpret the images for inexperienced users. In this paper, we propose a new 2D ultrasound to 3D CT registration method to improve surgical guidance during ultrasound-guided interventions. Our approach adopts a dense feature matching method called LoFTR to our multimodal registration problem. We learn to predict dense coarse-to-fine correspondences using a Transformer-based architecture to estimate a robust rigid transformation between a 2D ultrasound frame and a CT scan. Additionally, a fully differentiable pose estimation method is introduced, optimizing LoFTR on pose estimation error during training. Experiments conducted on a multimodal dataset of ex vivo porcine kidneys demonstrate the method's promising results for intraoperative, trackerless ultrasound pose estimation. By mapping 2D ultrasound frames into the 3D CT volume space, the method provides intraoperative guidance, potentially improving surgical workflows and image interpretation.