Related papers: Stochastic Metamorphosis in Imaging Science
Recent approaches for modelling dynamics of physical systems with neural networks enforce Lagrangian or Hamiltonian structure to improve prediction and generalization. However, when coordinates are embedded in high-dimensional data such as…
The aim of this article is to introduce a new methodology for constructing morphings between shapes that have identical topology. The morphings are obtained by deforming a reference shape, through the resolution of a sequence of linear…
A new approach is suggested for the study of geometric symmetries in general relativity, leading to an invariant characterization of the evolutionary behaviour for a class of Spatially Homogeneous (SH) vacuum and orthogonal $\gamma -$law…
Simulating the long-time evolution of Hamiltonian systems is limited by the small timesteps required for stable numerical integration. To overcome this constraint, we introduce a framework to learn Hamiltonian Flow Maps by predicting the…
We introduce a comprehensive benchmark for local features and robust estimation algorithms, focusing on the downstream task -- the accuracy of the reconstructed camera pose -- as our primary metric. Our pipeline's modular structure allows…
Modeling transformations between arbitrary data distributions is a fundamental scientific challenge, arising in applications like drug discovery and evolutionary simulation. While flow matching offers a natural framework for this task, its…
The one-dimensional shallow water equations in Eulerian coordinates are considered. Relations between symmetries and conservation laws for the potential form of the equations, and symmetries and conservation laws in Eulerian coordinates are…
We construct covariant theories incorporating fluctuating boundaries and soft cutoffs by introducing dynamical reference frames (DRFs). This framework generalizes the covariant action from a hard-cutoff to a soft-cutoff formulation,…
Common modal decomposition techniques for flowfield analysis, data-driven modeling and flow control, such as proper orthogonal decomposition (POD) and dynamic mode decomposition (DMD) are usually performed in an Eulerian (fixed) frame of…
In the field of fluid numerical analysis, there has been a long-standing problem: lacking of a rigorous mathematical tool to map from a continuous flow field to discrete vortex particles, hurdling the Lagrangian particles from inheriting…
Time-resolved single-cell omics data offers high-throughput, genome-wide measurements of cellular states, which are instrumental to reverse-engineer the processes underpinning cell fate. Such technologies are inherently destructive,…
Diffusion Purification, purifying noised images with diffusion models, has been widely used for enhancing certified robustness via randomized smoothing. However, existing frameworks often grapple with the balance between efficiency and…
Maximization of the path information entropy is a clear prescription for constructing models in non-equilibrium statistical mechanics. Here it is shown that, following this prescription under the assumption of arbitrary instantaneous…
In Positron Emission Tomography, movement leads to blurry reconstructions when not accounted for. Whether known a priori or estimated jointly to reconstruction, motion models are increasingly defined in continuum rather that in discrete,…
Computational imaging is crucial in many disciplines from autonomous driving to life sciences. However, traditional model-driven and iterative methods consume large computational power and lack scalability for imaging. Deep learning (DL) is…
On the basis of gauge principle in the field theory, a new variational formulation is presented for flows of an ideal fluid. The fluid is defined thermodynamically by mass density and entropy density, and its flow fields are characterized…
Using the wave equation as an example, it is shown how to extend the hydrodynamic Lagrangian-picture method of constructing field evolution using a continuum of trajectories to second-order theories. The wave equation is represented through…
Numerical resolution of high-dimensional nonlinear PDEs remains a huge challenge due to the curse of dimensionality. Starting from the weak formulation of the Lawson-Euler scheme, this paper proposes a stochastic particle method (SPM) by…
In computational anatomy, the statistical analysis of temporal deformations and inter-subject variability relies on shape registration. However, the numerical integration and optimization required in diffeomorphic registration often lead to…
Understanding disease progression is a central clinical challenge with direct implications for early diagnosis and personalized treatment. While recent generative approaches have attempted to model progression, key mismatches remain:…