Mathematical formulation and preliminary testing of a spline approximation algorithm for the extraction of road alignments

This paper presents a methodology that allows the identification of the road alignments (curves, straights and clothoids) and their corresponding values of curvature based on a list of points with UTM coordinates obtained from field data. The procedure reconstructs the geometry of a road using a cubic spline that gives the road's singular points, geographically referenced, with the curvature values for each element. The methodology allows the user to select different parameters depending on the road type analyzed. It was applied in almost 1500 km of road with satisfactory results. The results of applying the methodology on a recently built road (whose alignments according to its project are known) are shown. A comparison of the project alignments with the alignments obtained according to the proposed method gives good results with small errors relative values, with maximum values of less than 4%.

[1]  P. M. Prenter.  Splines and variational methods , 1975 .

[2]  S. Cafiso A. Di Graziano,et al.  Automated in-vehicle data collection and treatment for existing roadway alignment , 2008 .

[3]  A note on the discrete approximation of discontinuous curves and surfaces , 2007 .

[4]  Kai-Wei Chiang,et al.  Direct Sensor Orientation of a Land-Based Mobile Mapping System , 2011, Sensors.

[5]  A. Gruen,et al.  Semi-Automatic Linear Feature Extraction by Dynamic Programming and LSB-Snakes , 1997 .

[6]  David Ben-Arieh,et al.  Geometric Modeling of Highways Using Global Positioning System Data and B -Spline Approximation , 2004 .

[7]  Maria Castro,et al.  Sight distance analysis of highways using GIS tools , 2011 .

[8]  Francisco Aparicio,et al.  Measurement uncertainty determination and curve-fitting algorithms for development of accurate digital maps for advanced driver assistance systems , 2009 .

[9]  Kay Fitzpatrick,et al.  Evaluating the Effects of Freeway Design Elements on Safety , 2010 .

[10]  V. Gikas,et al.  Determining Rail Track Axis Geometry Using Satellite and Terrestrial Geodetic Data , 2008 .

[11]  N. Sneeuw.  Global spherical harmonic analysis by least‐squares and numerical quadrature methods in historical perspective , 1994 .

[12]  Guizhen Yu,et al.  Highway Curve Speed Precaution System Based on VII , 2011 .

[13]  Xiaohua Tong,et al.  Estimating Geometric Parameters of Highways and Railways Using Least-Squares Adjustment , 2010 .

[14]  Orazio Pellegrino,et al.  An Analysis of the Effect of Roadway Design on Driver’s Workload , 2009 .

[15]  Grazia La Cava,et al.  Safety Performance Indicators for Local Rural Roads: Comprehensive Procedure from Low-Cost Data Survey to Accident Prediction Model , 2008 .

[16]  Basil Psarianos,et al.  PRECISE ESTIMATION OF ROAD HORIZONTAL AND VERTICAL GEOMETRIC FEATURES USING MOBILE MAPPING TECHNIQUES , 2009 .

[17]  Stephen Wolfram,et al.  Mathematica: a system for doing mathematics by computer (2nd ed.) , 1991 .

[18]  Yasser Hassan,et al.  GPS–GIS‐Based Procedure for Tracking Vehicle Path on Horizontal Alignments , 2006, Comput. Aided Civ. Infrastructure Eng..

[19]  José Alberto Gonçalves,et al.  Sensor Integration in a Low Cost Land Mobile Mapping System , 2012, Sensors.

[20]  Said M. Easa,et al.  PREDICTION OF OPERATING SPEED ON THREE-DIMENSIONAL HIGHWAY ALIGNMENTS , 2001 .

[21]  L. Schumaker.  Spline Functions: Basic Theory , 1981 .

[22]  A. Kouibia,et al.  Approximation by discrete variational splines , 2000 .

[23]  Maria Castro,et al.  Geometric modelling of highways using global positioning system (GPS) data and spline approximation , 2006 .

[24]  Alfredo Garcia,et al.  Modeling Operating Speed and Deceleration on Two-Lane Rural Roads with Global Positioning System Data , 2010 .

[25]  M. Fogli,et al.  Probabilistic assessment of roadway departure risk in a curve , 2011 .

[26]  Glen Koorey.  Road Data Aggregation and Sectioning Considerations for Crash Analysis , 2009 .

[27]  Vassilis Gikas,et al.  A Novel Geodetic Engineering Method for Accurate and Automated Road/Railway Centerline Geometry Extraction Based on the Bearing Diagram and Fractal Behavior , 2012, IEEE Transactions on Intelligent Transportation Systems.

[28]  Alexander Drakopoulos,et al.  USE OF VEHICLE-COLLECTED DATA TO CALCULATE EXISTING ROADWAY GEOMETRY , 2000 .

[29]  Richard M. Murray,et al.  Model-based estimation of off-highway road geometry using single-axis LADAR and inertial sensing , 2006, Proceedings 2006 IEEE International Conference on Robotics and Automation, 2006. ICRA 2006..