# Line-based Registration of Photogrammetric Point Clouds with 3D City Models by Means of Mixed Integer Linear Programming

### Steffen Goebbels, Regina Pohle-Fröhlich

#### Abstract

This paper describes a method to align photogrammetric point clouds with CityGML 3D city models. Amongst others, we use photogrammetric point clouds that are generated from videos taken from the driver’s perspective of a car. Clouds are computed with the Structure-from-Motion algorithm. We detect wall planes to rotate these clouds so that walls become vertical. This allows us to find buildings’ footprints by accumulating points that are orthogonally projected to the ground. Thus, the main alignment step can be performed in 2D. To this end, we match detected footprints with corresponding footprints of CityGML models in a x-y-plane based on line segments. These line segments are detected using a probabilistic Hough transform. Then we apply a Mixed Integer Linear Program to find a maximum number of matching line segment pairs. Using a Linear Program, we optimize a rigid affine transformation to align the lines of these pairs. Finally, we use height information along CityGML terrain intersection lines to estimate scaling and translation in z-direction. By combining the results, we obtain an affine mapping that aligns the point cloud with the city model. Linear Programming is not widely applied to registration problems; however the technique presented is a fast alternative to Iterative Closest Point algorithms that align photogrammetric point clouds with clouds sampled from city models.

Download#### Paper Citation

#### in Harvard Style

Goebbels S. and Pohle-Fröhlich R. (2018). **Line-based Registration of Photogrammetric Point Clouds with 3D City Models by Means of Mixed Integer Linear Programming**.In *Proceedings of the 13th International Joint Conference on Computer Vision, Imaging and Computer Graphics Theory and Applications - Volume 4: VISAPP,* ISBN 978-989-758-290-5, pages 299-306. DOI: 10.5220/0006533002990306

#### in Bibtex Style

@conference{visapp18,

author={Steffen Goebbels and Regina Pohle-Fröhlich},

title={Line-based Registration of Photogrammetric Point Clouds with 3D City Models by Means of Mixed Integer Linear Programming},

booktitle={Proceedings of the 13th International Joint Conference on Computer Vision, Imaging and Computer Graphics Theory and Applications - Volume 4: VISAPP,},

year={2018},

pages={299-306},

publisher={SciTePress},

organization={INSTICC},

doi={10.5220/0006533002990306},

isbn={978-989-758-290-5},

}

#### in EndNote Style

TY - CONF

JO - Proceedings of the 13th International Joint Conference on Computer Vision, Imaging and Computer Graphics Theory and Applications - Volume 4: VISAPP,

TI - Line-based Registration of Photogrammetric Point Clouds with 3D City Models by Means of Mixed Integer Linear Programming

SN - 978-989-758-290-5

AU - Goebbels S.

AU - Pohle-Fröhlich R.

PY - 2018

SP - 299

EP - 306

DO - 10.5220/0006533002990306