# Generating Straight Outlines of 2D Point Sets and Holes using Dominant Directions or Orthogonal Projections

### Melanie Pohl, Dirk Feldmann

#### Abstract

Representing the shape of finite point sets in 2D by simple polygons becomes a challenge if the resulting outline needs to be non-convex and straight with only few, distinct edges and angles. Such outlines are usually sought in order to border point sets that originate from man-made objects, e.g., for the purpose of building reconstruction from LIDAR data. Algorithms for computing hulls of point sets obtained from such structures usually yield polygons having too many edges and angles and may thus not capture the actual shape very well. Furthermore, many existing approaches cannot handle empty domains within the boundaries of a point set (holes). In this paper, we present methods that create straight, non-convex outlines of finite 2D point sets and of possibly contained holes. The resulting polygons feature fewer vertices and angles than hulls and can thus faithfully represent objects of angular shapes.

#### References

- Asaeedi, S., Didehvar, F., and Mohades, A. (2013). Alpha Convex Hull, a Generalization of Convex Hull. The Computing Research Repository (CoRR), abs/1309.7829.
- Bendels, G. H., Schnabel, R., and Klein, R. (2006). Detecting Holes in Point Set Surfaces. Proceedings of The 14th International Conference in Central Europe on Computer Graphics, Visualization and Computer Vision, 14.
- de Berg, M., Cheong, O., van Krevald, M., and Overmars, M. (2008). Computation Geometry. Springer, 3rd edition.
- Douglas, D. and Peucker, T. (1973). Algorithms for the Reduction of the Number of Points Required to Represent a Digitized Line or Its Caricature. The Canadian Cartographer, 10(2):112 - 122.
- Duckham, M., Kulik, L., Worboys, M., and Galton, A. (2008). Efficient Generation of Simple Polygons for Characterizing the Shape of a Set of Points in the Plane. Pattern Recognition, 41(10):3224-3236.
- Edelsbrunner, H., Kirkpatrick, D., and Seidel, R. (1983). On the Shape of a Set of Points in the Plane. IEEE Transactions on Information Theory, 29(4):551 - 559.
- Galton, A. and Duckham, M. (2006). What is the Region Occupied by a Set of Points? In Proceedings of the 4th International Conference on Geographic Information Science, GIScience'06, pages 81-98, Berlin, Heidelberg. Springer-Verlag.
- Jarvis, R. A. (1973). On the Identification of the Convex Hull of a Finite Set of Points in the Plane. Information Processing Letters, 2(1):18 - 21.
- Moreira, A. and Santos, M. Y. (2007). Concave hull: A k-nearest Neighbours Approach for the Computation of the Region Occupied by a Set of Points. Proceedings of the 2nd International Conference on Computer Graphics Theory and Applications (GRAPP), pages 61 - 68.
- Ramer, U. (1972). An Iterative Procedure for the Polygonal Approximation of Plane Curves. Computer Graphics and Image Processing, 1(3):244 - 256.
- Vosselman, G. (1999). Building Reconstruction Using Planar Faces In Very High Density Height Data. In International Archives of Photogrammetry, Remote Sensing and Spatial Information Sciences, pages 87-92.
- Wang, J. and Oliveira, M. M. (2007). Filling Holes on Locally Smooth Surfaces Reconstructed from Point Clouds. Image and Vision Computing, 25(1):103 - 113.
- Wang, O., Lodha, S. K., and Helmbold, D. P. (2006). A Bayesian Approach to Building Footprint Extraction from Aerial LIDAR Data. In Proceedings of the Third International Symposium on 3D Data Processing, Visualization, and Transmission (3DPVT'06), 3DPVT 7806, pages 192-199, Washington, DC, USA. IEEE Computer Society.
- Wu, X. and Chen, W. (2014). A Scattered Point Set Hole-filling Method Based on Boundary Extension and Convergence. In 11th World Congress on Intelligent Control and Automation, pages 5329 - 5334. IEEE.

#### Paper Citation

#### in Harvard Style

Pohl M. and Feldmann D. (2016). **Generating Straight Outlines of 2D Point Sets and Holes using Dominant Directions or Orthogonal Projections** . In *Proceedings of the 11th Joint Conference on Computer Vision, Imaging and Computer Graphics Theory and Applications - Volume 1: GRAPP, (VISIGRAPP 2016)* ISBN 978-989-758-175-5, pages 59-71. DOI: 10.5220/0005720300570069

#### in Bibtex Style

@conference{grapp16,

author={Melanie Pohl and Dirk Feldmann},

title={Generating Straight Outlines of 2D Point Sets and Holes using Dominant Directions or Orthogonal Projections},

booktitle={Proceedings of the 11th Joint Conference on Computer Vision, Imaging and Computer Graphics Theory and Applications - Volume 1: GRAPP, (VISIGRAPP 2016)},

year={2016},

pages={59-71},

publisher={SciTePress},

organization={INSTICC},

doi={10.5220/0005720300570069},

isbn={978-989-758-175-5},

}

#### in EndNote Style

TY - CONF

JO - Proceedings of the 11th Joint Conference on Computer Vision, Imaging and Computer Graphics Theory and Applications - Volume 1: GRAPP, (VISIGRAPP 2016)

TI - Generating Straight Outlines of 2D Point Sets and Holes using Dominant Directions or Orthogonal Projections

SN - 978-989-758-175-5

AU - Pohl M.

AU - Feldmann D.

PY - 2016

SP - 59

EP - 71

DO - 10.5220/0005720300570069