Related papers: Problems and related results in Algebraic Vision a…
Grassmann angles improve upon similar concepts of angle between subspaces that measure volume contraction in orthogonal projections, working for real or complex subspaces, and being more efficient when dimensions are different. Their…
The field of multiple view geometry has seen tremendous progress in reconstruction and calibration due to methods for extracting reliable point features and key developments in projective geometry. Point features, however, are not available…
The concept of viewing graph solvability has gained significant interest in the context of structure-from-motion. A viewing graph is a mathematical structure where nodes are associated to cameras and edges represent the epipolar geometry…
The field of numerical algebraic geometry consists of algorithms for numerically solving systems of polynomial equations. When the system is exact, such as having rational coefficients, the solution set is well-defined. However, for a…
This paper studies the problem of 3D volumetric reconstruction from two views of a scene with an unknown camera. While seemingly easy for humans, this problem poses many challenges for computers since it requires simultaneously…
Joint camera pose and dense geometry estimation from a set of images or a monocular video remains a challenging problem due to its computational complexity and inherent visual ambiguities. Most dense incremental reconstruction systems…
This contribution discusses the geometry of $k$D crystal cells given by $(k+1)$ points in a projective space $\R^{n+1}$. We show how the concepts of barycentric and fractional (crystallographic) coordinates, reciprocal vectors and dual…
One of the main problems in the study of system of equations of the gravitational lens, is the computation of coordinates from the known position of the source. In the process of computing finds the solution of equations with two unknowns.…
Training deep neural networks and Physics-Informed Neural Networks (PINNs) often leads to ill-conditioned and stiff optimization problems. A key structural feature of these models is that they are linear in the output-layer parameters and…
We introduce a new approach to high-fidelity 3D scene reconstruction from multi-view RGB images that tightly couples reconstruction with a strong generative 3D prior. We cast scene reconstruction as conditional 3D generation over a set of…
A survey on recent developments in (algebraic) integral geometry is given. The main focus lies on algebraic structures on the space of translation invariant valuations and applications in integral geometry.
We consider the problem of metric learning for multi-view data and present a novel method for learning within-view as well as between-view metrics in vector-valued kernel spaces, as a way to capture multi-modal structure of the data. We…
Recently, multiple formulations of vision problems as probabilistic inversions of generative models based on computer graphics have been proposed. However, applications to 3D perception from natural images have focused on low-dimensional…
The traditional study of plane and space algebraic curves by looking at their tangent vectors, curvatures and torsions provides geometric, but unfortunately not sufficient information about individual curves in order to be able to…
Electron tomography is becoming an increasingly important tool in materials science for studying the three-dimensional morphologies and chemical compositions of nanostructures. The image quality obtained by many current algorithms is…
A basic problem in computer vision is to understand the structure of a real-world scene given several images of it. Here we study several theoretical aspects of the intra multi-view geometry of calibrated cameras when all that they can…
Visual events in computer vision are studied from the perspective of algebraic geometry. Given a sufficiently general curve or surface in 3-space, we consider the image or contour curve that arises by projecting from a viewpoint.…
Generative reconstruction methods compute the 3D configuration (such as pose and/or geometry) of a shape by optimizing the overlap of the projected 3D shape model with images. Proper handling of occlusions is a big challenge, since the…
In the first part of the thesis, we study a classical invariant of projective varieties, the secant defectivity. The second part is devoted to modern algebraic geometry, we study the birational geometry of blow-ups of Grassmannians at…
The importance of wild video based image set recognition is becoming monotonically increasing. However, the contents of these collected videos are often complicated, and how to efficiently perform set modeling and feature extraction is a…