Implementation of the Legendre Transform for track segment reconstruction in drift tube chambers

In this study, we apply the geometrical properties of the Legendre transform in order 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 a collection of circles, each of which corresponds to a drift tube and defines the trajectory of the charged particle. The particle track candidate is reconstructed as the common tangent line to the drift circles. We tested the method both on an ideal case and on a case of high noise conditions using Monte Carlo generated tracks.