Jochen Meidow and Christian Beder and Wolfgang Förstner, "Reasoning with uncertain points, straight lines, and straight line segments in 2D", ISPRS Journal of Photogrammetry and Remote Sensing. Vol. 64(2), pp. 125-139. 2009.

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Decisions based on basic geometric entities can only be optimal, if their uncertainty is propagated trough the entire reasoning chain. This concerns the construction of new entities from given ones, the testing of geometric relations between geometric entities, and the parameter estimation of geometric entities based on spatial relations which have been found to hold. Basic feature extraction procedures often provide measures of uncertainty. These uncertainties should be incorporated into the representation of geometric entities permitting statistical testing, eliminates the necessity of specifying non-interpretable thresholds and
enables statistically optimal parameter estimation. Using the calculus of homogeneous coordinates the power of algebraic projective geometry can be exploited in these steps of image analysis. This review collects, discusses and evaluates the various representations of uncertain geometric entities in 2D together with their conversions. The representations are extended to achieve a consistent set of representations allowing geometric reasoning. The statistical testing of geometric relations is presented. Furthermore, a generic estimation procedure is provided for multiple uncertain geometric entities based on possibly correlated observed geometric entities and geometric constraints.

@article{Meidow2009Reasoning,
  author = {Meidow, Jochen and Beder, Christian and F\"orstner, Wolfgang},
  title = {Reasoning with uncertain points, straight lines, and straight line segments in 2D},
  journal = {ISPRS Journal of Photogrammetry and Remote Sensing},
  year = {2009},
  volume = {64},
  number = {2},
  pages = {125--139},
  doi = {10.1016/j.isprsjprs.2008.09.013}
}

Jochen Meidow and Wolfgang Förstner and Christian Beder, "Optimal Parameter Estimation with Homogeneous Entities and Arbitrary Constraints", In Pattern Recognition (Symposium of DAGM). Denzler, J. and Notni, G. (Eds.) Jena, Germany, pp. 292-301. Springer. 2009.

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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 proposed in this paper 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 validity of the proposed adjustment model will be demonstrated by the estimation of a fundamental matrix from synthetic data and compared to heteroscedastic regression [?], which is considered as state-ofthe- art estimator for this task. As the latter is unable to simultaneously estimate multiple entities, we will also demonstrate the usefulness and the feasibility of our approach by the constrained estimation of three vanishing points from observed uncertain image line segments.

@inproceedings{Meidow2009Optimal,
  author = {Meidow, Jochen and F\"orstner, Wolfgang and Beder, Christian},
  editor = {Denzler, J. and Notni, G.},
  title = {Optimal Parameter Estimation with Homogeneous Entities and Arbitrary Constraints},
  booktitle = {Pattern Recognition (Symposium of DAGM)},
  publisher = {Springer},
  year = {2009},
  pages = {292--301},
  doi = {10.1007/978-3-642-03798-6_30}
}

Jochen Meidow and Hanns-Florian Schuster, "Voxel-based Quality Evaluation of Photogrammetic Buildingacquisitions" 2005.

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Automatic quality evaluation of photogrammetric building acquisitions is important to realize deficiencies of acquisition approaches, tocompare different acquisitions approaches and to check the keeping of contractual specifications. For the decision-makers a procedure will be suggested taking a few, good interpretable quality measures into account. Therefore, useful quality measures have to be identifiedby the formulation of criteria. These quantities can be derived from the comparison of a test data set and a reference data set capturing the same scene. The acquired topology is usually uncertain as for instance two adjacent buildings may be acquired as one building ortwo buildings. Thus a screening of the registered area is suggested to compute the quantities. The approach is independent of the used acquisition method. For the application of large data sets the corresponding data structures will be explained. In experimental tests thebuildings registered by two commercial acquisition systems will be compared by the quality measures determined in 2D and 3D.

@inproceedings{Meidow2005Voxel,
  author = {Meidow, Jochen and Schuster, Hanns-Florian},
  title = {Voxel-based Quality Evaluation of Photogrammetic Buildingacquisitions},
  year = {2005}
}

Jochen Meidow, "Calibration of Stationary Cameras by Observing Objects of Equal Heights on a Ground Plane", In Proc. 20th ISPRS Congress, Istanbul, Turkey. Istanbul, Turkey, pp. 1067-1072. 2004.

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With the increasing number of cameras the need for plug-and-play calibration procedures arises to realize a subsequent automatic geometric evaluation of observed scenes. An easy calibration procedure is proposed for a non-zooming stationary camera observing objects of initially equal and known heights above a ground plane. The image coordinates of the corresponding foot and head points of these objects serve as observations. For the interior and exterior orientation of the camera a minimal parametrization is introduced with the height of the camera above the ground plane, its pitch and roll angle and the principal distance. With the idea of corresponding foot and head trajectories being homologue, the situation can be reformulated with a virtual second camera observing the scene. Therefore a plane induced homography can be established for the observation model. This special planar homology can be parametrisied with the unknown calibration quantities. Initially the calibration is estimated by observing foot and head points of objects with known heights. In the subsequent evaluation phase the height and positions of unknown objects can be determined. With the same procedure the calibration can be checked and updated if needed. The approach is evaluated with a real scene.

@inproceedings{Meidow2004Calibration,
  author = {Meidow, Jochen},
  title = {Calibration of Stationary Cameras by Observing Objects of Equal Heights on a Ground Plane},
  booktitle = {Proc. 20th ISPRS Congress, Istanbul, Turkey},
  year = {2004},
  pages = {1067--1072}
}