This paper introduces a novel method for generating high-quality Digital Image Correlation (DIC) dataset based on non-uniform B-spline surfaces. By randomly generating control point coordinates, we construct displacement fields that encompass a variety of realistic displacement scenarios, which are subsequently used to generate speckle pattern datasets. This approach enables the generation of a large-scale dataset that capture real-world displacement field situations, thereby enhancing the training and generalization capabilities of deep learning-based DIC algorithms. Additionally, we propose a novel network architecture, termed Bayes-DIC Net, which extracts information at multiple levels during the down-sampling phase and facilitates the aggregation of information across various levels through a single skip connection during the up-sampling phase. Bayes-DIC Net incorporates a series of lightweight convolutional blocks designed to expand the receptive field and capture rich contextual information while minimizing computational costs. Furthermore, by integrating appropriate dropout modules into Bayes-DIC Net and activating them during the network inference stage, Bayes-DIC Net is transformed into a Bayesian neural network. This transformation allows the network to provide not only predictive results but also confidence levels in these predictions when processing real unlabeled datasets. This feature significantly enhances the practicality and reliability of our network in real-world displacement field prediction tasks. Through these innovations, this paper offers new perspectives and methods for dataset generation and algorithm performance enhancement in the field of DIC.

This paper concerns the undetermined problem of estimating geometric transformation between image pairs.

Thanks to reviewers' pointer, we are excited to learn about the alignment with the latest trend of 3D surface

We first introduce two useful known lemmas, and prove the propositions in their order of appearance. We refer the reader to the original references for proofs. We will also need a uniform law of large numbers for functions. The following lemma is a consequence of Example 19.7 and Lemma 19.36 of V an der V aart (2000), and is copied in Lemma B.6 in We use Theorem 1 from Diaconis and Freedman (1999). We then turn to prove Proposition 2. A.3.1 Noise-free online Sinkhorn Proposition 5. Proof of Proposition 2. For discrete realizations ˆ α and ˆ β, we define the perturbation terms ε From Eq. (8), for all t > 0, we have 0 null e Following the derivations of Moulines and Bach (2011, Theorem 2), we have the following bias-variance decomposed upper-bound, provided that 0 null a < 1 and a + b > 1 .

Accurate and efficient modeling of soft-tissue interactions is fundamental for advancing surgical simulation, surgical robotics, and model-based surgical automation. To achieve real-time latency, classical Finite Element Method (FEM) solvers are often replaced with neural approximations; however, naively training such models in a fully data-driven manner without incorporating physical priors frequently leads to poor generalization and physically implausible predictions. We present a novel physics-informed neural simulation framework that enables real-time prediction of soft-tissue deformations under complex single- and multi-grasper interactions. Our approach integrates Kelvinlet-based analytical priors with large-scale FEM data, capturing both linear and nonlinear tissue responses. This hybrid design improves predictive accuracy and physical plausibility across diverse neural architectures while maintaining the low-latency performance required for interactive applications. We validate our method on challenging surgical manipulation tasks involving standard laparoscopic grasping tools, demonstrating substantial improvements in deformation fidelity and temporal stability over existing baselines. These results establish Kelvinlet-augmented learning as a principled and computationally efficient paradigm for real-time, physics-aware soft-tissue simulation in surgical AI.

The contractile motion of the heart is strongly determined by the distribution of the fibers that constitute cardiac tissue. Strain analysis informed with the orientation of fibers allows to describe several pathologies that are typically associated with impaired mechanics of the myocardium, such as cardiovascular disease. Several methods have been developed to estimate strain-derived metrics from traditional imaging techniques. However, the physical models underlying these methods do not include fiber mechanics, restricting their capacity to accurately explain cardiac function. In this work, we introduce WarpPINN-fibers, a physics-informed neural network framework to accurately obtain cardiac motion and strains enhanced by fiber information. We train our neural network to satisfy a hyper-elastic model and promote fiber contraction with the goal to predict the deformation field of the heart from cine magnetic resonance images. For this purpose, we build a loss function composed of three terms: a data-similarity loss between the reference and the warped template images, a regularizer enforcing near-incompressibility of cardiac tissue and a fiber-stretch penalization that controls strain in the direction of synthetically produced fibers. We show that our neural network improves the former WarpPINN model and effectively controls fiber stretch in a synthetic phantom experiment. Then, we demonstrate that WarpPINN-fibers outperforms alternative methodologies in landmark-tracking and strain curve prediction for a cine-MRI benchmark with a cohort of 15 healthy volunteers. We expect that our method will enable a more precise quantification of cardiac strains through accurate deformation fields that are consistent with fiber physiology, without requiring imaging techniques more sophisticated than MRI.

Abdominal aortic aneurysms (AAA) pose a significant clinical risk due to their potential for rupture, which is often asymptomatic but can be fatal. Although maximum diameter is commonly used for risk assessment, diameter alone is insufficient as it does not capture the properties of the underlying material of the vessel wall, which play a critical role in determining the risk of rupture. To overcome this limitation, we propose a deep learning-based framework for elasticity imaging of AAAs with 2D ultrasound. Leveraging finite element simulations, we generate a diverse dataset of displacement fields with their corresponding modulus distributions. We train a model with U-Net architecture and normalized mean squared error (NMSE) to infer the spatial modulus distribution from the axial and lateral components of the displacement fields. This model is evaluated across three experimental domains: digital phantom data from 3D COMSOL simulations, physical phantom experiments using biomechanically distinct vessel models, and clinical ultrasound exams from AAA patients. Our simulated results demonstrate that the proposed deep learning model is able to reconstruct modulus distributions, achieving an NMSE score of 0.73\%. Similarly, in phantom data, the predicted modular ratio closely matches the expected values, affirming the model's ability to generalize to phantom data. We compare our approach with an iterative method which shows comparable performance but higher computation time. In contrast, the deep learning method can provide quick and effective estimates of tissue stiffness from ultrasound images, which could help assess the risk of AAA rupture without invasive procedures.

The dataset is obtained from Li et al. (2022a), which consists of an interpolated dataset of Fourier layers with mode 12 and width 32 are used. F-FNO: Following the settings in Li et al. (2022a), we train the F-FNO model (Li et al., UNet: Analogous to the setup in Li et al. (2022a), we train a UNet model (Ronneberger A typical training curve can be found in Figure 8. Table 4: The per-epoch runtime (in seconds) of selected models for the hyperelasticity problem. We note that the numbers of trainable parameters for the "Geo-FNO" and "FNO" cases are different from The airfoil dataset is directly taken from Li et al. (2022a), which is an interpolated dataset of The physical parameters used in generating the data are: Y oung's modulus Symmetry is enforced only when the topology characteristic function χ is updated. Besides the resolution-independence property of DAFNO as shown in Figure 3, we further investigate the generalizability of DAFNO in both physical and temporal resolutions with this example. Specifically, the eDAFNO model is trained on a spatial resolution of 64 64 and a time step of 0.02 Our results show that eDAFNO prediction remains independent of the time step employed.