Related papers: On multi-conditioned conic fitting in Geometric al…
Quadratic surfaces gain more and more attention among the Geometric Algebra community and some frameworks were proposed in order to represent, transform, and intersect these quadratic surfaces. As far as the authors know, none of these…
We consider several basic questions pertaining to the geometry of image of a general quadratic map. In general the image of a quadratic map is non-convex, although there are several known classes of quadratic maps when the image is convex.…
Introducing inequality constraints in Gaussian process (GP) models can lead to more realistic uncertainties in learning a great variety of real-world problems. We consider the finite-dimensional Gaussian approach from Maatouk and Bay (2017)…
We present a hybrid algorithm for optimizing a convex, smooth function over the cone of positive semidefinite matrices. Our algorithm converges to the global optimal solution and can be used to solve general large-scale semidefinite…
The geometric calibration of the Planck satellite is investigated, specifically those parameters which require the use of the science data for their extraction. Methods for the recovery of these geometric-calibration parameters from point…
We introduce and study conic geometric programs (CGPs), which are convex optimization problems that unify geometric programs (GPs) and conic optimization problems such as semidefinite programs (SDPs). A CGP consists of a linear objective…
Geometric matching is a key step in computer vision tasks. Previous learning-based methods for geometric matching concentrate more on improving alignment quality, while we argue the importance of naturalness issue simultaneously. To deal…
The paper studies coincidence points of parameterized set-valued mappings (multifunctions), which provide an extended framework to cover several important topics in variational analysis and optimization that include the existence of…
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…
In our implementation of geometric resolution, the most costly operation is subsumption testing (or matching): One has to decide for a three-valued, geometric formula, if this formula is false in a given interpretation. The formula contains…
This paper studies the parameter tuning problem of positive linear systems for optimizing their stability properties. We specifically show that, under certain regularity assumptions on the parametrization, the problem of finding the…
Despite encouraging recent progresses in ensemble approaches, classification methods seem to have reached a plateau in development. Further advances depend on a better understanding of geometrical and topological characteristics of point…
In this paper we build an Orlik-Solomon model for the canonical gradation of the cohomology algebra with integer coefficients of the complement of a toric arrangement. We give some results on the uniqueness of the representation of…
An efficient way to get implicit equations of conics on five points and quadrics on nine, using pencils of conics and quadrics, is revealed. Parallel axis right cones intersect on a conic. An example, to show how to place five coplanar…
We introduce a manifold-based framework for addressing optimization problems with equality and inequality constraints found in robotics. Our approach transforms the original problem into an unconstrained optimization problem directly on the…
Enumerative algebraic geometry counts the solutions to certain geometric constraints. Numerical algebraic geometry determines these solutions for any given instance. This article illustrates how these two fields complement each other. Our…
This paper explores in some detail a recent proposal (the Rieffel induction/refined algebraic quantization scheme) for the quantization of constrained gauge systems. Below, the focus is on systems with a single constraint and, in this…
We address the problem of determining correspondences between two images in agreement with a geometric model such as an affine or thin-plate spline transformation, and estimating its parameters. The contributions of this work are…
In high-stakes engineering applications, optimization algorithms must come with provable worst-case guarantees over a mathematically defined class of problems. Designing for the worst case, however, inevitably sacrifices performance on the…
This work presents a novel method for fitting superquadrics to point clouds under the contamination of noise and outliers, which has many applications for shape modeling across diverse fields. Unlike prior approaches that either exclusively…