Related papers: Galois/monodromy groups for decomposing minimal pr…
Recovering dense 3D geometry from unposed images remains a foundational challenge in computer vision. Current state-of-the-art models are predominantly trained on perspective datasets, which implicitly constrains them to a standard pinhole…
Over a non-closed field, it is a common strategy to use separable algebras as invariants to distinguish algebraic and geometric objects. The most famous example is the deep connection between Severi-Brauer varieties and central simple…
This paper proposes a new algorithm for simultaneous graph matching and clustering. For the first time in the literature, these two problems are solved jointly and synergetically without relying on any training data, which brings advantages…
Face alignment aims to estimate the locations of a set of landmarks for a given image. This problem has received much attention as evidenced by the recent advancement in both the methodology and performance. However, most of the existing…
We study the algebraic monodromy of families of cyclic Galois coverings of curves. Under a condition on the $G$-decomposition of the associated variation of Hodge structures, we prove a criterion for the maximality of the monodromy. The…
We introduce a new partial resolution of crystalline spaces of Galois representations when the gaps in Hodge--Tate weights are smaller than $p$, with no bound on ramification. Furthermore, when $n =3$ in the case of minimal regular weight,…
We develop a computational framework for classifying Galois groups of irreducible degree-7 polynomials over~$\mathbb{Q}$, combining explicit resolvent methods with machine learning techniques. A database of over one million normalized…
We introduce gamma structures on regular hypergeometric D--modules in dimension 1 as special one--parametric systems of solutions on the compact subtorus. We note that a balanced gamma product is in the Paley--Wiener class and show that the…
One of the difficulties in 3D reconstruction of molecules from images in single particle Cryo-Electron Microscopy (Cryo-EM), in addition to high levels of noise and unknown image orientations, is heterogeneity in samples: in many cases, the…
Absolute pose estimation is a fundamental problem in computer vision, and it is a typical parameter estimation problem, meaning that efforts to solve it will always suffer from outlier-contaminated data. Conventionally, for a fixed…
We compute new polynomials with Galois group $M_{11}$ over $\mathbb{Q}(t)$. These polynomials stem from various families of covers of $\mathbb{P}^1\mathbb{C}$ ramified over at least 4 points. Each of these families has features that make a…
Symmetry is an implicit objective in structural form-finding that often reconciles efficiency and aesthetics. This paper identifies the symmetry of polyhedral diagrams in three-dimensional graphic statics (3DGS) as point groups and…
Our aim is to find a general approach to the theory of classical solutions of the Garnier system in $n$-variables, ${\cal G}_n$, based on the Riemann-Hilbert problem and on the geometry of the space of isomonodromy deformations. Our…
The $\mathrm{SE}(3)$ invariants of a pose include its rotation angle and screw translation. In this paper, we present a complete comprehensive study of the relative pose estimation problem for a calibrated camera constrained by known…
We compute the Galois groups for a certain class of polynomials over the the field of rational numbers that was introduced by S. Mori and study the monodromy of corresponding hyperelliptic jacobians.
In this paper we study the problem of estimating the semi-generalized pose of a partially calibrated camera, i.e., the pose of a perspective camera with unknown focal length w.r.t. a generalized camera, from a hybrid set of 2D-2D and 2D-3D…
We establish a precise relation between Galois theory in its motivic form with the mathematical theory of perturbative renormalization (in the minimal subtraction scheme with dimensional regularization). We identify, through a…
Recent advances in monocular depth estimation methods (MDE) and their improved accuracy open new possibilities for their applications. In this paper, we investigate how monocular depth estimates can be used for relative pose estimation. In…
We study the interplay between the differential Galois group and the Lie algebra of infinitesimal symmetries of systems of linear differential equations. We show that some symmetries can be seen as solutions of a hierarchy of linear…
The main theorem of Galois theory states that there are no finite group-subgroup pairs with the same invariants. On the other hand, if we consider complex linear reductive groups instead of finite groups, the analogous statement is no…