Liquid Argon Time Projection Chamber (LAr TPC) detectors offer charged particle imaging capability with remarkable spatial resolution. Precise event reconstruction procedures are critical in order to fully exploit the potential of this technology. In this paper we present a new, general approach to 3D reconstruction for the LAr TPC with a practical application to the track reconstruction. The efficiency of the method is evaluated on a sample of simulated tracks. We present also the application of the method to the analysis of stopping particle tracks collected during the ICARUS T600 detector operation with the CNGS neutrino beam. © 2013 M. Antonello et al.