The vehicle speed is one of the most important parameters in intelligent transportation system. In this paper

a new algorithm for displacement field estimation is present to get vehicle speed. This method can detect the big displacement vectors between frames. In order to alleviate the over smooth problem between the motion object and non motion object

a discontinuity preserving function

Huber function

is introduced instead of globe smoothness constraint term. We first create an energy function

we can get based on the image gray. The energy function consists of two terms:one is matching error;the other is a smoothness constraint. Minimizing this energy function

we can get the displacement field between frames. Using Euler's equation and partial derivative equation

the displacement field could be calculated. The displacements of corners are computed firstly

and then the displacement vectors are smoothed along the tangential direction of edge. The vehicle speed could be getting through calculating displacement field

time and the distance between camera and vehicle

Experiment shows

using this method result is good.