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Timothy Duff

Assistant Professor of Mathematics (courtesy appointment in EECS)
University of Missouri - Columbia
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Email: tduff@missouri.edu      Office: Math Sciences 218

I co-organize the Missouri Math & Data Seminar.

My current research is primarily focused on the application of algebraic and geometric methods to solving 3D reconstruction problems in computer vision. These methods are of increasing importance in applications ranging from visual localization to space exploration. For an overview of "algebraic vision", I highly recommend this recent survey.

Some of my specific interests include characterizing complete sets of constraints for various reconstruction tasks ("multiview ideals", etc.), efficiently solving algebraic equations arising in such tasks ("minimal problems"), reconstruction from geometric features (eg. points, lines, incidences, conics...), and different types of geometric imaging models.

More broadly, I am interested in a wide variety of problems at the interface of pure and applied mathematics, as best represented by the SIAM Activity Group on Algebraic Geometry.

Teaching

University of Missouri Spring 2025:

Preprints / Under Review

  1. A computer vision problem in flatland (With Sameer Agarwal, Erin Connelly, Annalisa Crannell, Rekha Thomas.)
  2. SAGBI and Gröbner Bases Detection (With Viktoriia Borovik, Elima Shehu.)
    To be presented at MEGA 2024.
  3. Metric Multiview Geometry---A Catalogue in Low Dimensions (With Felix Rydell.)
  4. Algebra and Geometry of Camera Resectioning (With Erin Connelly, Jessie Loucks-Tavitas.)
  5. Geometric Solution to the Angles-Only Initial Orbit Determination Problem.
    (With Michela Mancini, John Christian, Anton Leykin.)
    Conference version: 2022 AAS/AIAA Astrodynamics Specialist Conference.

Research Publications

    Where applicable, conference and journal versions are listed together.
    Please be advised that final versions may only be available through publishers.

  1. Efficient Solution of Point-Line Absolute Pose (With Petr Hruby, Marc Pollefeys.)
    Accepted to CVPR 2024.
    2. Highlight paper!
  2. Minimal Perspective Autocalibration (With Andrea Porfiri Dal Cin, Luca Magri, Tomas Pajdla.)
    Accepted to CVPR 2024.
  3. Subalgebra and Khovanskii Bases Equivalence (With Colin Alstad, Michael Burr, Oliver Clarke.)
    Accepted to ISSAC 2024.
  4. Certified homotopy tracking using the Krawcyzk method (With Kisun Lee.)
    Accepted to ISSAC 2024.
  5. Line Multiview Ideals. (With Paul Breiding, Lukas Gustafsson, Felix Rydell, Elima Shehu.)
    To appear in Communications in Algebra.
  6. SubalgebraBases in Macaulay2. (With Michael Burr, Oliver Clarke, Jackson Leaman, Nathan Nichols, Elise Walker.)
    The Journal of Software for Algebra and Geometry, Volume 14, 2024.
  7. Using monodromy to recover symmetries of polynomial systems
    (With Viktor Korotynskiy, Tomas Pajdla, Margaret Regan.)
    Extended version under review
    Conference version in proceedings of ISSAC 2023.
  8. Four-view geometry with unknown radial distortion
    (With Petr Hruby, Viktor Korotynskiy, Luke Oeding, Marc Pollefeys, Tomas Pajdla, Viktor Larsson.) Proceedings of CVPR 2023.
  9. u-generation: solving systems of polynomials equation-by-equation
    (With Jose Israel Rodriguez , Anton Leykin.) Numerical Algorithms, 2023.
  10. Learning to Solve Hard Minimal Problems (With Petr Hrubý, Anton Leykin, Tomas Pajdla.)
    To appear in a special issue of TPAMI, 2024.
    Conference version: Proceedings of CVPR 2022. Won best paper!
  11. Galois/monodromy groups for decomposing minimal problems in 3D reconstruction
    (With Viktor Korotynskiy, Tomas Pajdla, Margaret Regan.)
    SIAM Journal on Applied Algebra and Geometry, 2023.
  12. Trifocal Relative Pose From Lines at Points
    (With Ricardo Fabbri , Hongyi Fan , Margaret Regan, David da Costa de Pinho, Elias Tsigaridas, Charles Wampler, Jonathan Hauenstein, Benjamin Kimia, Anton Leykin, Tomas Pajdla.) TPAMI, 2023. Conference version: Proceedings of CVPR 2020.
  13. Signatures of algebraic curves via numerical algebraic geometry (With Michael Ruddy.)
    Journal of Symbolic Computation, 2023. Conference version: Proceedings of ISSAC 2020.
  14. Polyhedral homotopies in Cox coordinates (With Simon Telen, Elise Walker, Thomas Yahl.)
    Journal of Algebra and Its Applications, 2023.
  15. An Atlas for the Pinhole Camera (With Sameer Agarwal, Max Lieblich, Rekha Thomas.)
    Foundations of Computational Mathematics, 2022.
  16. Certification for polynomial systems via square subsystems
    (With Nickolas Hein and Frank Sottile.) Journal of Symbolic Computation, 2022.
    Extended abstact presented at MEGA 2019.
  17. PL1P---Point-line minimal problems under partial visibility in three views
    (With Kathlén Kohn, Anton Leykin, Tomas Pajdla.)
    Accepted to IJCV. Conference Version: ECCV 2020.
  18. PLMP - Point-Line Minimal Problems in Complete Multi-View Visibility
    (With Kathlén Kohn, Anton Leykin, Tomas Pajdla.) To appear in TPAMI, 2023.
    Conference version: Proceedings of ICCV 2019, Won best student paper!
  19. Monodromy solver: sequential and parallel (With Nathan Bliss, Anton Leykin, Jeff Sommars.)
    Proceedings of ISSAC 2018.
  20. Solving polynomial systems via homotopy continuation and monodromy (With Cvetelina Hill, Anders Jensen, Kisun Lee, Anton Leykin, Jeff Sommars.)
    IMA Journal of Numerical Analysis, 2018.
  21. Polynomial automata: Zeroness and applications (With Micheal Benedikt, Aditya Sharad, James Worrell.) Proceedings of LICS 2017.
  22. Robust graph ideals (With Adam Boocher, Bryan Brown, Laura Lyman, Takumi Murayama, Amy Nesky, Karl Schaefer.) Annals of Combinatorics, 2015.

Expository Publications

  1. Polynomial systems, homotopy continuation, and applications. (With Margaret Regan.)
    Notices of the American Mathematical Society, 2022
  2. Nonlinear Algebra and Applications (With Paul Breiding, Türkü Özlüm Çelik, Alexander Heaton, Aida Maraj, Anna-Laura Sattelberger, Lorenzo Venturello, Oğuzhan Yürük.)
    Numerical Algebra, Control, and Optimization, 2021.