# Augmented Postprocessing of the FTLS Vectorization Algorithm - Approaching to the Globally Optimal Vectorization of the Sorted Point Clouds

### Ales Jelinek, Ludek Zalud

#### Abstract

Vectorization is a widely used technique in many areas, mainly in robotics and image processing. Applications in these domains frequently require both speed (for real-time operation) and accuracy (for maximal information gain). This paper proposes an optimization for the high speed vectorization methods, which leads to nearly optimal results. The FTLS algorithm uses the total least squares method for fitting the lines into the point cloud and the presented augmentation for the refinement of the results, is based on a modified NelderMead method. As shown on several experiments, this approach leads to better utilization of the information contained in the point cloud. As a result, the quality of approximation grows steadily with the number of points being vectorized, which was not achieved before. Performance costs are still comparable to the original algorithm, so the real-time operation is not endangered.

#### References

- Douglas, D. H. and Peucker, T. K. (1973). Algorithms for the reduction of the number of points required to represent a digitized line or its caricature. Cartographica: The International Journal for Geographic Information and Geovisualization, 10(2):112-122.
- Fischler, M. A. and Bolles, R. C. (1981). Random sample consensus: a paradigm for model fitting with applications to image analysis and automated cartography. Communications of the ACM, 24(6):381-395.
- Heinz, I., Hartl, F., and Frohlich, C. (2001). Semiautomatic 3D CAD model generation of as-built conditions of real environments using a visual laser radar. In Proceedings 10th IEEE International Workshop on Robot and Human Interactive Communication. ROMAN 2001 (Cat. No.01TH8591), pages 400-406. IEEE.
- Hough, P. V. C. (1962). Method and Means for Recognizing Complex Patterns.
- Jelinek, A., Zalud, L., and Jilek, T. (2016). Fast total least squares vectorization. Journal of Real-Time Image Processing.
- Kandal, P. and Karschti, S. (2014). Method for simplified storage of data representing forms.
- Kocmanova, P., Zalud, L., and Chromy, A. (2013). 3D proximity laser scanner calibration. In 2013 18th International Conference on Methods & Models in Automation & Robotics (MMAR), pages 742-747. IEEE.
- Lagarias, J. C., Reeds, J. a., Wright, M. H., and Wright, P. E. (1998). Convergence Properties of the Nelder-Mead Simplex Method in Low Dimensions. SIAM Journal on Optimization, 9(1):112-147.
- Le Floc'h, F. (2012). Issues of Nelder-Mead Simplex Optimisation with Constraints. SSRN Electronic Journal, pages 1-7.
- Liu, Z., Zhang, B., Li, P., Guo, H., and Han, J. (2011). Automatic registration between remote sensing image and vector data based on line features. In 2011 19th International Conference on Geoinformatics, number 2008, pages 1-5. IEEE.
- Mathibela, B., Posner, I., and Newman, P. (2013). A roadwork scene signature based on the opponent colour model. In 2013 IEEE/RSJ International Conference on Intelligent Robots and Systems, pages 4394-4400. IEEE.
- Mirmehdi, M., Palmer, P. L., and Kittler, J. (1997). Robust line segment extraction using genetic algorithms. In Image Processing and Its Applications, 1997., Sixth International Conference on, volume 1, pages 141 - 145 vol.1. IEEE.
- Nelder, J. A. and Mead, R. (1965). A simplex method for function minimization. The Computer Journal, 7(4):308-313.
- Nguyen, V., Gächter, S., Martinelli, A., Tomatis, N., and Siegwart, R. (2007). A comparison of line extraction algorithms using 2D range data for indoor mobile robotics. Autonomous Robots, 23(2):97-111.
- Norouzi, M., Yaghobi, M., Siboni, M., and Jadaliha, M. (2009). Recursive line extraction algorithm from 2d laser scanner applied to navigation a mobile robot. In 2008 IEEE International Conference on Robotics and Biomimetics, pages 2127-2132. IEEE.
- Reumann, K. and Witkam, A. P. M. (1974). Optimizing Curve Segmentation in Computer Graphics. In Proceedings of International Computing Symposium, pages 467-472, Amsterdam. North-Holland Publishing Company.
- Shi, W. and Cheung, C. (2006). Performance Evaluation of Line Simplification Algorithms for Vector Generalization. The Cartographic Journal, 43(1):27-44.
- Werner, M., Schauer, L., and Scharf, A. (2014). Reliable trajectory classification using Wi-Fi signal strength in indoor scenarios. In 2014 IEEE/ION Position, Location and Navigation Symposium - PLANS 2014, pages 663-670. IEEE.
- Xiangyun Hu, Yijing Li, Jie Shan, Jianqing Zhang, and Yongjun Zhang (2014). Road Centerline Extraction in Complex Urban Scenes From LiDAR Data Based on Multiple Features. IEEE Transactions on Geoscience and Remote Sensing, 52(11):7448-7456.
- Xu, C., Frechet, S., Laurendeau, D., and Miralles, F. (2015). Out-of-Core Surface Reconstruction from Large Point Sets for Infrastructure Inspection. In 2015 12th Conference on Computer and Robot Vision, pages 313- 319. IEEE.
- Zalud, L., Kocmanova, P., Burian, F., Jilek, T., Kalvoda, P., and Kopecny, L. (2015). Calibration and Evaluation of Parameters in A 3D Proximity Rotating Scanner. Elektronika ir Elektrotechnika, 21(1):3-12.
- Zalud, L., Kopecny, L., and Burian, F. (2008). Orpheus Reconnissance Robots. In 2008 IEEE International Workshop on Safety, Security and Rescue Robotics, number October, pages 31-34. IEEE.

#### Paper Citation

#### in Harvard Style

Jelinek A. and Zalud L. (2016). **Augmented Postprocessing of the FTLS Vectorization Algorithm - Approaching to the Globally Optimal Vectorization of the Sorted Point Clouds** . In *Proceedings of the 13th International Conference on Informatics in Control, Automation and Robotics - Volume 2: ICINCO,* ISBN 978-989-758-198-4, pages 216-223. DOI: 10.5220/0005962902160223

#### in Bibtex Style

@conference{icinco16,

author={Ales Jelinek and Ludek Zalud},

title={Augmented Postprocessing of the FTLS Vectorization Algorithm - Approaching to the Globally Optimal Vectorization of the Sorted Point Clouds},

booktitle={Proceedings of the 13th International Conference on Informatics in Control, Automation and Robotics - Volume 2: ICINCO,},

year={2016},

pages={216-223},

publisher={SciTePress},

organization={INSTICC},

doi={10.5220/0005962902160223},

isbn={978-989-758-198-4},

}

#### in EndNote Style

TY - CONF

JO - Proceedings of the 13th International Conference on Informatics in Control, Automation and Robotics - Volume 2: ICINCO,

TI - Augmented Postprocessing of the FTLS Vectorization Algorithm - Approaching to the Globally Optimal Vectorization of the Sorted Point Clouds

SN - 978-989-758-198-4

AU - Jelinek A.

AU - Zalud L.

PY - 2016

SP - 216

EP - 223

DO - 10.5220/0005962902160223