Related papers: Distortion Varieties
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…
A class of parametric functions formed by alternating compositions of multivariate polynomials and rectification style monomial maps is studied (the layer-wise exponents are treated as fixed hyperparameters and are not optimized). For this…
Image representations (artificial or biological) are often compared in terms of their global geometric structure; however, representations with similar global structure can have strikingly different local geometries. Here, we propose a…
We construct polyhedral families of valuations on the branching algebra of a morphism of reductive groups. This establishes a connection between the combinatorial rules for studying a branching problem and the tropical geometry of the…
In recent years, deep learning-based methods have been successfully applied to the image distortion restoration tasks. However, scenarios that assume a single distortion only may not be suitable for many real-world applications. To deal…
We consider subtorus actions on divisorial toric varieties. Here divisoriality means that the variety has many Cartier divisors like quasiprojective and smooth ones. We characterize when a subtorus action on such a toric variety admits a…
In this paper we provide new methodology for inference of the geometric features of a multivariate density in deconvolution. Our approach is based on multiscale tests to detect significant directional derivatives of the unknown density at…
Blur is an image degradation that is difficult to remove. Invariants with respect to blur offer an alternative way of a~description and recognition of blurred images without any deblurring. In this paper, we present an original unified…
Ptychography is a popular technique to achieve diffraction limited resolution images of a two or three dimensional sample using high frame rate detectors. We introduce a relaxation of common projection algorithms to account for…
The Hurwitz form of a variety is the discriminant that characterizes linear spaces of complementary dimension which intersect the variety in fewer than degree many points. We study computational aspects of the Hurwitz form, relate this to…
We discuss methods to construct a polynomial parametrization of some interesting knotted surfaces (knotted spheres, knotted tori and knotted planes) and provide examples.
This paper deals with the problem of reconstructing a depth map from a sequence of differently focused images, also known as depth from focus or shape from focus. We propose to state the depth from focus problem as a variational problem…
Here we explore the geometry of the osculating spaces to projective varieties of arbitrary dimension. In particular, we classify varieties having very degenerate higher order osculating spaces and we determine mild conditions for the…
Cumulant mapping employs a statistical reconstruction of the whole by sampling its parts. The theory developed in this work formalises and extends ad hoc methods of `multi-fold' or `multi-dimensional' covariance mapping. Explicit formulae…
Three aspects of applying homotopy continuation, which is commonly used to solve parameterized systems of polynomial equations, are investigated. First, for parameterized systems which are homogeneous, we investigate options for performing…
Conformal and disformal transformations are now being very intensively studied in the context of various modified gravity theories. In particular, some special classes of them can be used for constructing Mimetic Dark Matter models.…
For the problem of 3D object recognition, researchers using deep learning methods have developed several very different input representations, including "multi-view" snapshots taken from discrete viewpoints around an object, as well as…
The paper introduces a methodology for visualizing on a dimension reduced subspace the classification structure and the geometric characteristics induced by an estimated Gaussian mixture model for discriminant analysis. In particular, we…
We present a simple geometric construction linking geometric to deformation quantization. Both theories depend on some apparently arbitrary parameters, most importantly a polarization and a symplectic connection, and for real polarizations…
The non-orthogonality of algebraic polynomials of field coordinates traditionally used to model field-dependent corrections to astrometric measurements, gives rise to subtle adverse effects. In particular, certain field dependent…