6 citations · 21 across the 15 of their papers we have counts for
19 papers
Lagrangian Dual Sections: A Topological Perspective on Hidden Convexity
Venkat Chandrasekaran, Timothy Duff, Jose Israel Rodriguez +1
Hidden convexity is a powerful idea in optimization: under the right transformations, nonconvex problems that are seemingly intractable can be solved efficiently using convex optim…
Using monodromy to recover symmetries of polynomial systems
Timothy Duff, Viktor Korotynskiy, Tomas Pajdla +1
Galois/monodromy groups attached to parametric systems of polynomial equations provide a method for detecting the existence of symmetries in solution sets. Beyond the question of e…
Geometric Solution to the Angles-Only Initial Orbit Determination Problem
Michela Mancini, Timothy Duff, Anton Leykin +1
Initial orbit determination (IOD) from line-of-sight (i.e., bearing) measurements is a classical problem in astrodynamics. Indeed, there are many well-established methods for perfo…
Line Multiview Ideals
Paul Breiding, Timothy Duff, Lukas Gustafsson +2
We study the following problem in computer vision from the perspective of algebraic geometry: Using pinhole cameras we take pictures of a line in . This produc…
SubalgebraBases in Macaulay2
Michael Burr, Oliver Clarke, Timothy Duff +3
We describe a recently revived version of the software package SubalgberaBases, which is distributed in the Macaulay2 computer algebra system. The package allows the user to comput…
-generation: solving systems of polynomials equation-by-equation
Timothy Duff, Anton Leykin, Jose Israel Rodriguez
We develop a new method that improves the efficiency of equation-by-equation algorithms for solving polynomial systems. Our method is based on a novel geometric construction, and r…
An Atlas for the Pinhole Camera
Sameer Agarwal, Timothy Duff, Max Lieblich +1
We introduce an atlas of algebro-geometric objects associated with image formation in pinhole cameras. The nodes of the atlas are algebraic varieties or their vanishing ideals rela…
Learning to Solve Hard Minimal Problems
Petr Hruby, Timothy Duff, Anton Leykin +1
We present an approach to solving hard geometric optimization problems in the RANSAC framework. The hard minimal problems arise from relaxing the original geometric optimization pr…
Galois/monodromy groups for decomposing minimal problems in 3D reconstruction
Timothy Duff, Viktor Korotynskiy, Tomas Pajdla +1
We consider Galois/monodromy groups arising in computer vision applications, with a view towards building more efficient polynomial solvers. The Galois/monodromy group allows us to…
Nonlinear Algebra and Applications
Paul Breiding, Türkü Özlüm Çelik, Timothy Duff +5
We showcase applications of nonlinear algebra in the sciences and engineering. Our review is organized into eight themes: polynomial optimization, partial differential equations, a…
Polyhedral Homotopies in Cox Coordinates
Timothy Duff, Simon Telen, Elise Walker +1
We introduce the Cox homotopy algorithm for solving a sparse system of polynomial equations on a compact toric variety . The algorithm lends its name from a construction, desc…
Signatures of algebraic curves via numerical algebraic geometry
Timothy Duff, Michael Ruddy
We apply numerical algebraic geometry to the invariant-theoretic problem of detecting symmetries between two plane algebraic curves. We describe an efficient equality test which de…
PLP -- Point-line Minimal Problems under Partial Visibility in Three Views
Timothy Duff, Kathlén Kohn, Anton Leykin +1
We present a complete classification of minimal problems for generic arrangements of points and lines in space observed partially by three calibrated perspective cameras when each…
PLMP -- Point-Line Minimal Problems in Complete Multi-View Visibility
Timothy Duff, Kathlén Kohn, Anton Leykin +1
We present a complete classification of all minimal problems for generic arrangements of points and lines completely observed by calibrated perspective cameras. We show that there…
Trifocal Relative Pose from Lines at Points and its Efficient Solution
Ricardo Fabbri, Timothy Duff, Hongyi Fan +8
We present a method for solving two minimal problems for relative camera pose estimation from three views, which are based on three view correspondences of i) three points and one…
Certification for Polynomial Systems via Square Subsystems
Timothy Duff, Nickolas Hein, Frank Sottile
We consider numerical certification of approximate solutions to a system of polynomial equations with more equations than unknowns by first certifying solutions to a square subsyst…
Monodromy Solver: Sequential and Parallel
Nathan Bliss, Timothy Duff, Anton Leykin +1
We describe, study, and experiment with an algorithm for finding all solutions of systems of polynomial equations using homotopy continuation and monodromy. This algorithm follows…
Solving polynomial systems via homotopy continuation and monodromy
Timothy Duff, Cvetelina Hill, Anders Jensen +3
We study methods for finding the solution set of a generic system in a family of polynomial systems with parametric coefficients. We present a framework for describing monodromy ba…
Robust Graph Ideals
Adam Boocher, Bryan Christopher Brown, Timothy Duff +4
Let I be a toric ideal. We say I is robust if its universal Groebner basis is a minimal generating set. We show that any robust toric ideal arising from a graph G is also minimally…