Related papers: Crossing-Preserving Geodesic Tracking on Spherical…
Particle-based representations of radiance fields such as 3D Gaussian Splatting have found great success for reconstructing and re-rendering of complex scenes. Most existing methods render particles via rasterization, projecting them to…
Lensing in a spherically symmetric and static spacetime is considered, based on the lightlike geodesic equation without approximations. After fixing two radius values r_O and r_S, lensing for an observation event somewhere at r_O and static…
In this paper, we propose a method for tracking structures (e.g., ventricles and myocardium) in cardiac images (e.g., magnetic resonance) by propagating forward in time a previous estimate of the structures via a new deformation estimation…
Segmentation networks are not explicitly imposed to learn global invariants of an image, such as the shape of an object and the geometry between multiple objects, when they are trained with a standard loss function. On the other hand,…
Curved-spacetime geometric-optics maps derived from a deep photometric survey should contain information about the three-dimensional matter distribution and thus about cosmic voids in the survey, despite projection effects. We explore to…
Robust segmentation for non-elongated tissues in medical images is hard to realize due to the large variation of the shape, size, and appearance of these tissues in different patients. In this paper, we present an end-to-end trainable deep…
Manifolds discovered by machine learning models provide a compact representation of the underlying data. Geodesics on these manifolds define locally length-minimising curves and provide a notion of distance, which are key for reduced-order…
Retinal imaging serves as a valuable tool for diagnosis of various diseases. However, reading retinal images is a difficult and time-consuming task even for experienced specialists. The fundamental step towards automated retinal image…
We present a detailed physiological model of the retina that includes the biochemistry and electrophysiology of phototransduction, neuronal electrical coupling, and the spherical geometry of the eye. The model is a parabolic-elliptic system…
Looming, traditionally defined as the relative expansion of objects in the observer's retina, is a fundamental visual cue for perception of threat and can be used to accomplish collision free navigation. In this paper we derive novel…
Routine clinical imaging of the retina using optical coherence tomography (OCT) is performed with large slice spacing, resulting in highly anisotropic images and a sparsely scanned retina. Most learning-based methods circumvent the problems…
Optical imaging through scattering media is a fundamental challenge in many applications. Recently, substantial breakthroughs such as imaging through biological tissues and looking around corners have been obtained by the use of…
We study the base distribution in chart-based generative models on Riemannian manifolds. Standard methods sample in Euclidean tangent space and then map the sample to the manifold with a chart. This is convenient, but it changes the meaning…
Many applications of geometry modeling and computer graphics necessite accurate curvature estimations of curves on the plane or on manifolds. In this paper, we define the notion of the discrete geodesic curvature of a geodesic polygon on a…
Do contemporary diffusion models preserve the class geometry of hyperspherical data? Standard diffusion models rely on isotropic Gaussian noise in the forward process, inherently favoring Euclidean spaces. However, many real-world problems…
We study geodesics on the parameter manifold, for systems exhibiting second order classical and quantum phase transitions. The coupled non-linear geodesic equations are solved numerically for a variety of models which show such phase…
Tracking the spatiotemporal evolution of large-scale landslide scars is critical for understanding the evolution mechanisms and failure precursors, enabling effective early-warning. However, most existing studies have focused on…
Retinal vascular morphology is crucial for diagnosing diseases such as diabetes, glaucoma, and hypertension, making accurate segmentation of retinal vessels essential for early intervention. Traditional segmentation methods assume that…
The X-ray transform on the plane or on the three-dimensional Euclidean space can be considered as the measurements of CT scanners for normal human tissue. If the human body contains metal regions such as dental implants, stents in blood…
Surface comparison and matching is a challenging problem in computer vision. While reparametrization-invariant Sobolev metrics provide meaningful elastic distances and point correspondences via the geodesic boundary value problem, solving…