An improved reconstruction method for atom probe tomography is presented. In this approach, the curvature of the field emitter is variable, in contrast to the conventional reconstruction technique. The information about the tip shape at different stages of the reconstruction is directly extracted from the local density of events on the detector. To this end, the detector and the tip surface are split into different segments. According to the density distribution of events observed on the detector, the size of the corresponding segment on the tip surface is calculated, yielding an emitter profile which is not necessarily spherical. The new approach is demonstrated for emitter structures with radial symmetry that contain a spherical precipitate with a substantially lower or higher evaporation field compared to the surrounding matrix. A comparison to the conventional point projection approach is made.