Related papers: Real-Time Visualization in Non-Isotropic Geometrie…
In considering the mathematical problem of describing the geodesics on a torus or any other surface of revolution, there is a tremendous advantage in conceptual understanding that derives from taking the point of view of a physicist by…
Neural networks have shown great success in extracting geometric information from color images. Especially, monocular depth estimation networks are increasingly reliable in real-world scenes. In this work we investigate the applicability of…
We propose a geometrical approach to the investigation of Hamiltonian systems on (Pseudo) Riemannian manifolds. A new geometrical criterion of instability and chaos is proposed. This approach is more generic than well known reduction to the…
Sketching is used as a ubiquitous tool of expression by novices and experts alike. In this thesis I explore two methods that help a system provide a geometric machine-understanding of sketches, and in-turn help a user accomplish a…
Many important problems in astrophysics, space physics, and geophysics involve flows of (possibly ionized) gases in the vicinity of a spherical object, such as a star or planet. The geometry of such a system naturally favors numerical…
In this work we look for a geometric description of non-gravitational forces. The basic ideas are proposed studying the interaction between a punctual particle and an electromagnetic external field. For this purpose, we introduce the…
Hyperbolic geometry has recently found applications in social networks, machine learning and computational biology. With the increasing popularity, questions about the best representations of hyperbolic spaces arise, as each representation…
We analyze a variational time discretization of geodesic calculus on finite- and certain classes of infinite-dimensional Riemannian manifolds. We investigate the fundamental properties of discrete geodesics, the associated discrete…
Single image pose estimation is a fundamental problem in many vision and robotics tasks, and existing deep learning approaches suffer by not completely modeling and handling: i) uncertainty about the predictions, and ii) symmetric objects…
Information visualization is essential in making sense out of large data sets. Often, high-dimensional data are visualized as a collection of points in 2-dimensional space through dimensionality reduction techniques. However, these…
The question of representation of 3D geometry is of vital importance when it comes to leveraging the recent advances in the field of machine learning for geometry processing tasks. For common unstructured surface meshes state-of-the-art…
Integrable systems in low dimensions, constructed through the symmetry reduction method, are studied using phase portrait and variable separation techniques. In particular, invariant quantities and explicit periodic solutions are…
Geometric algebra is an optimal frame work for calculating with vectors. The geometric algebra of a space includes elements that represent all the its subspaces (lines, planes, volumes, ...). Conformal geometric algebra expands this…
Visualization is a crucial step in exploratory data analysis. One possible approach is to train an autoencoder with low-dimensional latent space. Large network depth and width can help unfolding the data. However, such expressive networks…
One of the strategies to detect the pose and shape of unknown objects is their geometric modeling, consisting on fitting known geometric entities. Classical geometric modeling fits simple shapes such as spheres or cylinders, but often those…
Recent advances in implicit neural representations and differentiable rendering make it possible to simultaneously recover the geometry and materials of an object from multi-view RGB images captured under unknown static illumination.…
This paper presents the geometric aspect of the autoencoder framework, which, despite its importance, has been relatively less recognized. Given a set of high-dimensional data points that approximately lie on some lower-dimensional…
Discontinuous visibility changes remain a major bottleneck when optimizing surfaces within a physically-based inverse renderer. Many previous works have proposed sophisticated algorithms and data structures to sample visibility silhouettes…
Neural volumetric representations have become a widely adopted model for radiance fields in 3D scenes. These representations are fully implicit or hybrid function approximators of the instantaneous volumetric radiance in a scene, which are…
The use of geometric invariants has recently played an important role in the solution of classification problems in non-commutative ring theory. We construct geometric invariants of non-commutative projectivizations, a significant class of…