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»  P3P problem
»  P4P + unknown focal length
»  P4P + focal + radial distortion
»  uP2P + known vertical direction
»  uP3P + focal + radial distortion
»  P2P1L problem
»  P1P2L problem
»  5-pt relative pose problem
»  6-pt focal length problem
»  6-pt calibrated-uncalibrated
»  4-pt 3-views relative pose problem
»  2-pt panorama stitching (1 focal)
»  3-pt panorama stitching (2 focals)
»  3-pt panorama stitching (1 focal+ radial distortion)
»  6-pt generalized camera problem
»  6-pt calibrated radial distortion
»  8-pt uncalibrated radial distortion
»  9-pt different distortion problem
»  P2Π registration problem
»  3-view triangulation
»  9-pt catadioptric
»  Hand-eye
»  Automatic generator
»  Grobener basis solver
 
 
 
Overview
 

Minimal problems in computer vision arise when computing geometrical models from image data.
They often lead to solving systems of algebraic equations.

 
This page provides links to publications, software, data, and evaluation of minimal problems.
 
NEW:
ACCV 2010
Bujnak M., Kukelova Z., Pajdla T., New efficient solution to the absolute pose problem for camera with unknown focal length and radial distortion, ACCV 2010, Queenstown, NZ, November 8-12, 2010. [pdf]
CODE:
4-point absolute pose problem with unknown focal length and radial distortion (P4Pfr)
 

Kukelova Z., Bujnak M., Pajdla T., Closed-form solutions to the minimal absolute pose problems with known vertical direction, ACCV 2010, Queenstown, NZ, November 8-12, 2010. [pdf]
CODE:
2-point absolute pose problem with known vertical direction (up2p)
3-point absolute pose problem with known vertical direction and unknown focal length and radial distortion (up3pfr)

 
SOURCE CODES TO SEVERAL MINIMAL PROBLEMS
4-point absolute pose problem with unknown focal length (P4Pf) (new fast Matlab version)
8-point "uncalibrated" relative pose problem with radial distortion
4-point absolute pose problem with unknown focal length and radial distortion (P4Pfr)
2-point absolute pose problem with known vertical direction (up2p)
3-point absolute pose problem with known vertical direction and unknown focal length and radial distortion (up3pfr)
 
Minimal problems:

3-point absolute pose problem (P3P)
4-point absolute pose problem with unknown focal length (P4Pf) NEW FAST MATLAB SOURCE CODE
4-point absolute pose problem with unknown focal length and radial distortion (P4Pfr)
NEW
2-point absolute pose problem with known vertical direction (up2p) NEW
3-point absolute pose problem with known vertical direction and unknown focal length and radial distortion (up3pfr) NEW
2-point + 1-line absolute pose problem NEW
1-point + 2-line absolute pose problem NEW
5-point relative pose problem
6-point relative pose problem with unknown focal length
6-point relative pose problem for one calibrated and one up to focal length calibrated camera
6-point generalized camera problem
4-point 3-view calibrated realtive pose problem
2-point panorama stitching problem with one unknown focal lenth
3-point panorama stitching problem with two different unknown focal lenths
3-point panorama stitching problem with one unknown focal lenth and radial distortion
6-point relative pose problem with radial distortion
8-point "uncalibrated" relative pose problem with radial distortion NEW SOURCE CODE
9-point "uncalibrated" relative pose problem with different radial distortions
6 3D points to 3+ planes registration NEW
3-view triangulation
9-point catadioptric problem


 
 
Tomas Pajdla, Zuzana Kukelova, Martin Bujnak. Maintained by Zuzana Kukelova, 28 January 2011