Skip to content
minimal problems with points, lines, and their incidences
Branch: master
Clone or download
Latest commit c4932be Oct 30, 2019
Type Name Latest commit message Commit time
Failed to load latest commit information.
CODE create NEDGES global Oct 30, 2019
supplementary.pdf revive IVA, HZ references Apr 6, 2019

PLMP -- point-line minimal problems

This repository hosts code for checking minimality and computing algebraic degrees of relative pose estimation problems in computer vision involving complete correspondences of points, lines, and their incidence relations across some number of views. It was used to classify all PLMPs in complete multi-view visibility.

To get started, read through and execute the Macaulay2-based examples described in this supplemental document (See caveats.)

Files in CODE/

  • Suplementary material exposition:
    • supplementary.pdf
  • Examples with detailed commentary:
    • example-jacobian_1.m2
    • example-2111_1-numerical.m2
    • example-2111_1-unrolled.m2
    • example-2111_1.m2
  • Numerical degree computations:
    • degree-5cameras.m2
    • degree-4cameras.m2
  • Symbolic minimality check and degree computations:
    • dim-5cameras.m2
    • dim-6cameras.m2
    • dim-degree-F4-3cameras.m2
    • dim-degree-F4-4cameras.m2
    • dim-degree-F4-2cameras.m2
  • Methods and functions used by the scripts above:
    • numerical-problem-builder.m2
    • partial-view-builder.m2
    • problem-builder.m2
    • tester.m2
    • common.m2
    • partial-line-builder.m2
    • problem-builder-core.m2
    • problem-builder-matrices.m2
    • vision-toolbox.m2


  • Certain computations may take a long time (couple of hours) and may exceed the RAM capacity (one example employing F4 consumed ~16Gb).
  • At the moment the numerical degree computations need a version of Macaulay2 at this branch of this fork.
You can’t perform that action at this time.