In this paper, a Next Best View (NBV) approach with a profiling stage and a novel utility function for 3D reconstruction using an Unmanned Aerial Vehicle (UAV) is proposed. The proposed approach performs an initial scan in order to build a rough model of the structure that is later used to improve coverage completeness and reduce flight time. Then, a more thorough NBV process is initiated, utilizing the rough model in order to create a dense 3D reconstruction of the structure of interest. The proposed approach exploits the reflectional symmetry feature if it exists in the initial scan of the structure. The proposed NBV approach is implemented with a novel utility function, which consists of four main components: information theory, model density, traveled distance, and predictive measures based on symmetries in the structure. This system outperforms classic information gain approaches with a higher density, entropy reduction and coverage completeness. Simulated and real experiments were conducted and the results show the effectiveness and applicability of the proposed approach.