Electric rail vehicles use current collection system which consists of overhead contact line and a current collector (pantograph) mounted on the roof of a vehicle. A pantograph is equipped with contact strips, which slide along the contact wire, ensuring steady electric contact. Contact strips are made of carbon layer, fixed to an aluminum carrier. The carbon layer wears down due to friction. Using overly worn contact strips increases the rate of contact wire wear and, significantly, the risk of contact line damage. Therefore, thickness of carbon strips has to be inspected periodically. In previous work a 3D-scanning system has been proposed for recording data of contact strips when vehicles pass an inspection point on a railway line. However, the system has to be complemented with data analysis algorithm to estimate the thickness of the carbon layer. Data processing has to be performed quickly and automatically to prevent faulty pantographs from being used. The main difficulty of wear analysis is caused by diverse altitude and tilt of scanned contact strips. To determine the smallest thickness of carbon layer, the carbon surface data have to be normalized with respect to an aluminum carrier. The location and shape of the aluminum carrier can be extracted from the registered data. Due to the fact that the profile of the carrier is highly distorted, a robust Whittaker approximation algorithm has been proposed in order to deal with the noise and the missing data.