General adjustment procedure

General description

This distribution contains some the Matlab examples for the general adjustment procedure presented at the 31st annual symposium of the German Association for Pattern Recognition DAGM 2009 in Jena, Germany.

Well known estimation techniques in computational geometry usually deal only with single geometric entities as unknown parameters and do not account for constrained observations within the estimation.

The estimation model implemented here is much more general, as it can handle multiple homogeneous vectors as well as multiple constraints. Furthermore, it allows the consistent handling of arbitrary covariance matrices for the observed and the estimated entities. The major novelty is the proper handling of singular observation covariance matrices made possible by additional constraints within the estimation. These properties are of special interest for instance in the calculus of algebraic projective geometry, where singular covariance matrices arise naturally from the non-minimal parameterizations of the entities.

The package includes three examples for applying the adjustment procedure:

  • estimation of the Fundamental Matrix from image points
  • calculating vanishing points from edge segments
  • estimation of image coordinates of corners of a hip-roof from given edge segments

Software description

The file <black_box.m> contains the general procedure. Please add its directory to your current search paths variable. To run one the provided examples change to the directory and run the corresponding <demo_optim_estim_*.m> file.

To solve your own adjustment problem you have to provide the three procedures specifying the constraints g(l,p)=0, h(p)=0, and c(l)=0 for the observations l and the parameters p together with the Jacobians, and a procedure which performs the update of the observations’ covariance matrix, cf. >help black_box.



The following zip-file contains the software: (Version 1.1 from 2009-09-14)



For the adjustment model and its applications see

  1. Jochen Meidow, Christian Beder and Wolfgang Förstner (2009)    “Reasoning with Uncertain Points, Straight Lines, and Straight Line    Segments in 2D”. ISPRS Journal of Photogrammetry and Remote Sensing,    vol. 64, no. 2, p. 125-139
  2. Jochen Meidow, Wolfgang Förstner and Christian Beder (2009)    “Optimal Parameter Estimation with Homogeneous Entities and Arbitrary    Constraints”. In: Pattern Recognition, Proceedings of the 31st DAGM    Symposium, Jena, Germany, p. 292-301, Springer

Send bugs, comments, or suggestions to

  • Jochen Meidow, meidow(at)  or
  • Wolfgang Förstner, wf(at)