Implementation of the Legendre transform for the muon track segment reconstruction in the ATLAS MDT chambers

In this study, the geometrical properties of the Legendre transform are used to implement a segment reconstruction algorithm for drift tube chambers used in high energy physics experiments. The output signal of a drift tube chamber consists of co-centric circles in each drift tube that define the possible points of the charged particle trajectory. The particle track is reconstructed as the common tangent line to the drift circles. The method is tested on an ideal case and on a case of high noisy conditions using Monte Carlo generated tracks.