timduff35 / PLMP

minimal problems with points, lines, and their incidences

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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).
  • The numerical degree computations require a recent version of Macaulay2.


minimal problems with points, lines, and their incidences


Language:Macaulay2 99.3%Language:Scilab 0.7%