相关论文: Anatomica: Localized Control over Geometric and To…
Topological lattices have recently generated a great deal of interest based on the unique mechanical properties rooted in their topological polarization, including the ability to support localized modes at certain floppy edges. The study of…
Recent advances in generative modeling, namely Diffusion models, have revolutionized generative modeling, enabling high-quality image generation tailored to user needs. This paper proposes a framework for the generative design of structural…
Trajectory analysis is not only about obtaining movement data, but it is also of paramount importance in understanding the pattern in which an object moves through space and time, as well as in predicting its next move. Due to the…
We introduce a new framework to analyze shape descriptors that capture the geometric features of an ensemble of point clouds. At the core of our approach is the point of view that the data arises as sampled recordings from a metric…
Despite the success of diffusion models (DMs), we still lack a thorough understanding of their latent space. To understand the latent space $\mathbf{x}_t \in \mathcal{X}$, we analyze them from a geometrical perspective. Our approach…
Segmentation masks of pathological areas are useful in many medical applications, such as brain tumour and stroke management. Moreover, healthy counterfactuals of diseased images can be used to enhance radiologists' training files and to…
In the present article the diffusion equation is used to model the spatio-temporal dynamics of a tumor, taking into account the heterogeneous of the medium. This approach makes it possible to take into account the complex geometric shape of…
We examine the topology of the subset of controls taking a given initial state to a given final state in quantum control, where "state" may mean a pure state |\psi>, an ensemble density matrix \rho, or a unitary propagator U(0,T). The…
Medical images are often acquired in different settings, requiring harmonization to adapt to the operating point of algorithms. Specifically, to standardize the physical spacing of imaging voxels in heterogeneous inference settings, images…
A major interest in longitudinal neuroimaging studies involves investigating voxel-level neuroplasticity due to treatment and other factors across visits. However, traditional voxel-wise methods are beset with several pitfalls, which can…
Although fully autonomous systems still face challenges due to patients' anatomical variability, teleoperated systems appear to be more practical in current healthcare settings. This paper presents an anatomy-aware control framework for…
We introduce Hodge Diffusion Maps, a novel manifold learning algorithm designed to analyze and extract topological information from high-dimensional data-sets. This method approximates the exterior derivative acting on differential forms,…
Smooth and curved microstructural topologies found in nature - from soap films to trabecular bone - have inspired several mimetic design spaces for architected metamaterials and bio-scaffolds. However, the design approaches so far have been…
When three-dimensional bodies contain thin features, non-trivial topology, or scan-derived surfaces, volumetric meshing can become the dominant bottleneck in simulation workflows. We replace this step with a learned geometric…
We study the spatiotemporal patterns that emerge when an active nematic film is topologically constraint. These topological constraints allow to control the non-equilibrium dynamics of the active system. We consider ellipsoidal shapes for…
We consider the problem of topological linearization of smooth (C infinity or real analytic) control systems, i.e. of their local equivalence to a linear controllable system via point-wise transformations on the state and the control…
Sampling from distributions of implicitly defined shapes enables analysis of various energy functionals used for image segmentation. Recent work describes a computationally efficient Metropolis-Hastings method for accomplishing this task.…
Image acquisition techniques such as micro-computed tomography are nowadays widely available. Quantitative analysis of the resulting 3D image data enables geometric characterization of the micro-structure of materials. Stochastic geometry…
Topological photonics sheds light on some of the surprising phenomena seen in condensed matter physics that arise with the appearance of topological invariants. Optical waveguides provide a well-controlled platform to investigate effects…
Existing angle-based contour descriptors suffer from lossy representation for non-starconvex shapes. By and large, this is the result of the shape being registered with a single global inner center and a set of radii corresponding to a…