Estimation of Road Centerline Curvature From Raw GPS Data

Peter Lipar, Mitja Lakner, Tomaž Maher, Marijan Žura


Development and wide use of route guidance systems lead to the need for suitable digital maps that can be used for some advanced applications. Sufficient accuracy of road geometry with emphasis on road centerline positions and curvature is crucial. In this paper is presented a method for finding road centerline curvature from raw GPS data. The approach consists of a few processing steps. First it is necessary to fit raw data of each road section using B-splines, and generate equidistant vertices of polyline of the fitted curve. Then follows the appliance of stereographic projection of chosen polyline segments onto the unit sphere. Using the least square method, the plane that best fits the points on the unit sphere is found and the circle that is the intersection of the plane and the unit sphere. Stereographic projection of this circle back to the equatorial plane gives the corresponding circular arc and curvature. The method is also applicable in higher dimensions. The 3D case is numerically presented and results show that the proposed procedure is efficient and yields accurate results.


digital curve; road centerline GPS; segmentation; circular arc; B-splines; stereographic projection

Full Text:



Barai, S. K. 2003. Data Mining Applications in Transportation Engineering, Transport 18(5): 216–223.

Bartels, R.; Beatty, J.; Barsky, B. 1987. An Introduction to Splines for Use in Computer Graphics and Geometric Modeling. Los Altos: Morgan Kaufmann, 476 p. ISBN 0934613273.

Cafiso, S.; Di Graziano, A.; Di Silvestro, G.; La Cava, G.; Persaud, B. 2010. Development of Comprehensive Accident Models for Two-Lane Rural Highways Using Exposure, Geometry, Consistency and Context Variables, Accident Analysis and Prevention 42(4): 1072–1079. doi:10.1016/j.aap.2009.12.015

Coeurjolly, D.; Gérard, J.; Reveillès, J. P.; Tougne, L. 2001. An Elementary Algorithm for Digital Arc Segmentation, Electronic Notes in Theoretical Computer Science 46: 355–370. doi:10.1016/S1571-0661(04)80997-6

Dell’Acqua, G.; Russo, F. 2010. Speed Factors on Low-Volume Roads for Horizontal Curves and Tangents, The Baltic Journal of Road and Bridge Engineering 5(2): 89–97. doi:10.3846/bjrbe.2010.13

Discetti, P. 2010. Experimetal Analysis on Hairpin Curves, The Baltic Journal of Road and Bridge Engineering 5(3): 148–155. doi:10.3846/bjrbe.2010.21

Estrozi, L. F.; Campos, A. G.; Rios, L. G.; Cesar, R. M. 1999. Comparing Curvature Estimation Technique, in Proc. of the 4th Simpósio Brasileiro de Automação Inteligente (SBAI), São Paulo, Brazil, 58–63.

Fairney, D. P.; Fairney, P. T. 1994. On the Accuracy of Point Curvature Estimators in a Discrete Environment, Image and Vision Computing 12(5): 259–265. doi:10.1016/0262-8856(94)90031-0

Farin, G. 1997. Curves and Surfaces for Computer Aided Geometric Design: a Practical Guide. San Diego: Academic Press. 429 p. ISBN 0122490541.

Gontran, H.; Gilliéron, P. Y.; Skaloud, J. 2005. Precise Road Geometry for Integrated Transport Safety Systems, in The 2nd Conference STRC 05, EPFL. Laboratoire de Topométrie.

Horng, J.-H.; Li, J. T. 2001. A Dynamic Programming Approach for Fitting Digital Planar Curves with Line Segments and Circular Arcs, Pattern Recognition Letters 22(2): 183–197. doi:10.1016/S0167-8655(00)00104-5

Ichoku, C.; Deffontaines, B.; Chorowicz, J. 1996. Segmentation of Digital Plane Curves: a Dynamic Focusing Approach, Pattern Recognition Letters 17(7): 741–750. doi:10.1016/0167-8655(96)00015-3

Imran, M.; Hasan, Y.; Patterson, D. 2006. GPS-GIS Based Procedure for Tracking Vehicle Path on Horizontal Alignments, Computer-Aided Civil and Infrastructure Engineering 21(5): 383–394. doi:10.1111/j.1467-8667.2006.00444.x

Laurent, P. J.; Méhauté, A. L.; Schumaker, L. L. 1991. Curves and Surfaces. Boston: Academic Press. 514 p. ISBN 0124386601.

Lewiner, T.; Gomes, J. D.; Jr.; Lopes, H.; Craizer, M. 2004. Arc-Length Based Curvature Estimator, in Proc. of the 17th Brazilian Symposium on Computer Graphics and Image. October 17–20, 2004. IEEE Press, 250–257. doi:10.1109/SIBGRA.2004.1352968

Mokhtarian, F.; Mackworth, A. 1992. A Theory of Multiscale, Curvature-Based Shape Representation for Planar Curves, IEEE Transactions on Pattern Analysis and Machine Intelligence 14(8): 789–805. doi:10.1109/34.149591

Pei, S. C.; Horng, J. H. 1996. Optimum Approximation of Digital Planar Curves Using Circular Arcs, Pattern Recognition 29(3): 383–388. doi:10.1016/0031-3203(95)00104-2

Pei, S. C.; Horng, J. H. 1995. Fitting Digital Curve Using Circular Arcs, Pattern Recognition 28(1): 107–116.

Perez, J. C.; Vidal, E. 1994. Optimum Polygonal Approximation of Digitized Curves, Pattern Recognition Letters 15(8): 743–750. doi:10.1016/0167-8655(94)90002-7

Pellegrino, O. 2009. An Analysis of the Effect of Roadway Design on Driver’s Workload, The Baltic Journal of Road and Bridge Engineering 4(2): 45–53. doi:10.3846/1822-427X.2009.4.45-53

Perco, P. 2008. Influence of the General Character of Horizontal Alignment on Operating Speed of Two-Lane Rural Roads, Transportation Research Record 2075: 16–23. doi: 10.3141/2075-03

Pikaz, A.; Averbuch, A. 1996. On Automatic Threshold Selection for Polygonal Approximations of Digital Curves, Pattern Recognition 29(11): 1835–1845. doi:10.1016/0031-3203(96)00037-4

Ray, B. K.; Ray, K. S. 1994. A Non-Parametric Sequential Method for Polygonal Approximation of Digital Curves, Pattern Recognition Letters 15(2): 161–167. doi:10.1016/0167-8655(94)90045-0

Ray, B. K.; Ray, K. S. 1993. Determination of Optimal Polygon from Digital Curves Using L1 Norm, Pattern Recognition 26(4): 505–509. doi:10.1016/0031-3203(93)90106-7

Rosin, P. L.; West, G. A. W. 1989. Segmentation of Edges into Lines and Arcs, Image and Vision Computing 7(2): 109–114. doi:10.1016/0262-8856(89)90004-8

Schroedl, S.; Wagstaff, K.; Rogers, S.; Langley, P.; Wilson, C. 2004. Mining GPS Traces for Map Refinement, Data Mining and Knowledge Discovery 9(1): 59–87. doi:10.1023/B:DAMI.0000026904.74892.89

Šliupas, T. 2009. The Impact of Road Parameters and the Surrounding Area on Traffic Accidents, Transport 24(1): 42–47. doi:10.3846/1648-4142.2009.24.42-47

Vorobjovas, V. 2011. Assurance of the Function of Low-Volume Roads for the Improvement of Driving Conditions, The Baltic Journal of Road and Bridge Engineering 6(1): 67–75. doi:10.3846/bjrbe.2011.09

Worring, M.; Smeulders, A. W. M. 1993. Digital Curvature Estimation, CVGIP: Image Understanding 58(3): 366–382. doi:10.1006/ciun.1993.1048

Yang, S. N.; Du, W. C. 1996. Numerical Methods for Approximating Digitized Curves by Piecewise Circular Arcs, Journal of Computational and Applied Mathematics 66(1–2): 557–569. doi:10.1016/0377-0427(95)00191-3

Zuriaga, A. M. P.; Garcia, A. G.; Torregrosa F. J. C.; D’Attoma, P. 2010. Modeling Operating Speed and Deceleration on Two-Lane Rural Roads with Global Positioning System Data, Transportation Research Record 2171: 11–20. doi: 10.3141/2171-02

DOI: 10.3846/bjrbe.2011.21


  • There are currently no refbacks.

Copyright (c) 2011 Vilnius Gediminas Technical University (VGTU) Press Technika