Optimization-based road curve fitting

Various advanced driver assistance systems (ADAS) are under development that intend to provide improved road safety. These systems require precise road models. In particular, accurate curvature is important for some ADAS applications such as curve over speed and lane departure warning. Existing road models often employ spline functions that are fit by least squares to roadway position data. The curvature calculated for such spline curves may not accurately reflect the curvature of the underlying roadway. This article addresses this problem in an unified framework, using optimization with `1-norm regularization. In this approach, known roadway characteristics can be enforced optimally with respect to a cost function which finds the best tradeoff between the match to the available data and the number of changes in curvature. Experimental results with show that the proposed method chooses a sparse set of curvature switching points (i.e., piecewise constant curvature) and achieves a high accuracy fit to the roadway dataset.