Related papers: Recovering an Algebraic Curve Using its Projection…
Many problems in computational geometry are not stated in graph-theoretic terms, but can be solved efficiently by constructing an auxiliary graph and performing a graph-theoretic algorithm on it. Often, the efficiency of the algorithm…
In this paper, we propose a novel lower dimensional representation of a shape sequence. The proposed dimension reduction is invertible and computationally more efficient in comparison to other related works. Theoretically, the differential…
We consider the problem of answering connectivity queries on a real algebraic curve. The curve is given as the real trace of an algebraic curve, assumed to be in generic position, and being defined by some rational parametrizations. The…
Shape recognition and classification is a problem with a wide variety of applications. Several recent works have demonstrated that topological descriptors can be used as summaries of shapes and utilized to compute distances. In this…
A criterion for the existence of a birational embedding of an algebraic curve into a projective plane with two Galois points is presented. Several novel examples of plane curves with two inner Galois points as an application are described.
Projection methods aim to reduce the dimensionality of the optimization instance, thereby improving the scalability of high-dimensional problems. Recently, Sakaue and Oki proposed a data-driven approach for linear programs (LPs), where the…
Many crucial tasks of image processing and computer vision are formulated as inverse problems. Thus, it is of great importance to design fast and robust algorithms to solve these problems. In this paper, we focus on generalized projected…
Computer-Aided Design is ubiquitous in todays world, as almost every manufactured object begins as a digital model across industries. At the same time, advances in 3D sensing have made point clouds a dominant form of raw 3D data. Recovering…
The arithmetic of elliptic curves, namely polynomial addition and scalar multiplication, can be described in terms of global sections of line bundles on $E\times E$ and $E$, respectively, with respect to a given projective embedding of $E$…
We consider an inverse problem for a finite graph $(X,E)$ where we are given a subset of vertices $B\subset X$ and the distances $d_{(X,E)}(b_1,b_2)$ of all vertices $b_1,b_2\in B$. The distance of points $x_1,x_2\in X$ is defined as the…
A two-dimensional tomographic problem is studied. The target is assumed to be a homogeneous object bounded by a smooth curve. A Non Uniform Rational Basis Splines (NURBS) curve is used as computational representation of the boundary. This…
We consider the problem of projecting a convex set onto a subspace, or equivalently formulated, the problem of computing a set obtained by applying a linear mapping to a convex feasible set. This includes the problem of approximating convex…
Learned iterative reconstruction algorithms for inverse problems offer the flexibility to combine analytical knowledge about the problem with modules learned from data. This way, they achieve high reconstruction performance while ensuring…
We propose to recover 3D shape structures from single RGB images, where structure refers to shape parts represented by cuboids and part relations encompassing connectivity and symmetry. Given a single 2D image with an object depicted, our…
Given two general rational curves of the same degree in two projective spaces, one can ask whether there exists a third rational curve of the same degree that projects to both of them. We show that, under suitable assumptions on the degree…
Iterative methods for tomographic image reconstruction have great potential for enabling high quality imaging from low-dose projection data. The computational burden of iterative reconstruction algorithms, however, has been an impediment in…
Deep learning-based models have demonstrated remarkable success in solving illposed inverse problems; however, many fail to strictly adhere to the physical constraints imposed by the measurement process. In this work, we introduce a…
The Strong Platonic Representation Hypothesis suggests that representational convergence in artificial neural networks can be harnessed constructively: embeddings can be translated across models through a universal latent space without…
In this paper, we study the computation of curvatures at the singular points of algebraic curves and surfaces. The idea is to convert the problem to compute the curvatures of the corresponding regular parametric curves and surfaces, which…
We give a new practical method for computing subvarieties of projective hypersurfaces. By computing the periods of a given hypersurface X, we find algebraic cohomology cycles on X. On well picked algebraic cycles, we can then recover the…