Related papers: Involutions of polynomially parametrized surfaces
Polytopic matrix factorization (PMF) is a recently introduced matrix decomposition method in which the data vectors are modeled as linear transformations of samples from a polytope. The successful recovery of the original factors in the…
This paper presents a complete Pascal interpolation scheme for use in the plane geometry mapping applied in association with numerical methods. The geometry of a domain element is approximated by a complete Pascal polynomial. The…
We present an algorithmic equivalent statement to the Jacobian conjecture. Given a polynomial map F on an affine space of dimension n, our algorithm constructs n sequences of polynomials such that F is invertible if and only if the zero…
Matrix inversion problems are often encountered in experimental physics, and in particular in high-energy particle physics, under the name of unfolding. The true spectrum of a physical quantity is deformed by the presence of a detector,…
In this paper, we consider topological featurizations of data defined over simplicial complexes, like images and labeled graphs, obtained by convolving this data with various filters before computing persistence. Viewing a convolution…
In this paper we present an algorithm to compute the (real and complex) straight lines contained in a rational surface, defined by a rational parameterization. The algorithm relies on the well-known theorem of Differential Geometry that…
We prove some new degeneracy results for integral points and entire curves on surfaces; in particular, we provide the first example, to our knowledge, of a simply connected smooth variety whose sets of integral points are never…
Shape from shading is a classical inverse problem in computer vision. This shape reconstruction problem is inherently ill-defined; it depends on the assumed light source direction. We introduce a novel mathematical formulation for…
Volumetric parameterization problem refers to parameterization of both the interior and boundary of a 3D model. It is a much harder problem compared to surface parameterization where a parametric representation is worked out only for the…
Reconstructing geometry and topology structures from raw unstructured data has always been an important research topic in indoor mapping research. In this paper, we aim to reconstruct the floorplan with a vectorized representation from…
A one parameter set of noncommutative complex algebras is given. These may be considered deformation quantisation algebras. The commutative limit of these algebras correspond to the algebra of polynomial functions over a manifold or…
This paper presents a new axis-based shape representation scheme along with a matching framework to address the problem of generic shape recognition. The main idea is to define the relative spatial arrangement of local symmetry axes and…
We present a novel surface convolution operator acting on vector fields that is based on a simple observation: instead of combining neighboring features with respect to a single coordinate parameterization defined at a given point, we have…
Loop invariants are properties of a program loop that hold before and after each iteration of the loop. They are often employed to verify programs and ensure that algorithms consistently produce correct results during execution.…
We introduce novel mathematical and computational tools to develop a complete algorithm for computing the set of non-properness of polynomials maps in the plane. In particular, this set, which we call \emph{the Jelonek set}, is a subset of…
Probabilistic programming has emerged as a powerful paradigm in statistics, applied science, and machine learning: by decoupling modelling from inference, it promises to allow modellers to directly reason about the processes generating…
Convolution is a fundamental operation in image processing and machine learning. Aimed primarily at maintaining image size, padding is a key ingredient of convolution, which, however, can introduce undesirable boundary effects. We present a…
Seamless global parametrization of surfaces is a key operation in geometry processing, e.g. for high-quality quad mesh generation. A common approach is to prescribe the parametric domain structure, in particular the locations of…
In their precedent work, the authors constructed closed oriented hyperbolic surfaces with pseudo-Anosov homeomorphisms from certain class of integral matrices. In this paper, we present a very simple algorithm to compute the Teichmueller…
Given the implicit equation $F(x,y,t,s)$ of a family of algebraic plane curves depending on the parameters $t,s$, we provide an algorithm for studying the topology types arising in the family. For this purpose, the algorithm computes a…