Fraunhofer Institute of Optronics, System Technologies and Image Exploitation IOSB

Algebraic Reasoning

Algebraic Reasoning

The construction of 3D models of man-made structures (especially buildings) can profit from the detection of geometric relations such as orthogonality or parallelism. In point clouds for instance, planar point groups are often extracted and the resulting planes and polygons are the base of the subsequent reasoning process to obtain watertight building reconstructions.

The detected constraints are typically formulated as sets of multivariate polynomials. For the enforcement of constraints within an adjustment process, a set of independent und consistent constraints has to be determined. Gröbner bases are in many cases the tool of choice to identify such sets exactly. To evaluate the approach, we utilized a fusion of the “Abenberg” data sets acquired by airborne laser scanning which is publicly available via

A detail description of the workflow can be found in the cited publication below. For comparison and reproducibility, we provide three data sets which exemplify the approach. The data sets cover

  • the cut point clouds,
  • the unconstrained building reconstructions, and
  • the constrained, i.e. adjusted, building reconstructions,

and comprise files in Polygon File format (PLY) and Wavefront OBJ format.







J. Meidow, H. Hammer (2016) Algebraic Reasoning for the Enhancement of Data-driven Building Reconstructions. Submitted to the ISPRS Journal of Photogrammetry and Remote Sensing.