Vessel tree reconstruction in volumetric data is a necessary prerequisite in various medical imaging applications. Specifically, when considering the application of automated lung nodule detection in thoracic computed tomography (CT) scans, vessel trees can be used to resolve local ambiguities based on global considerations and so improve the performance of nodule detection algorithms. In this study, a novel approach to vessel tree reconstruction and its application to nodule detection in thoracic CT scans was developed by using correlation-based enhancement filters and a fuzzy shape representation of the data. The proposed correlation-based enhancement filters depend on first-order partial derivatives and so are less sensitive to noise compared with Hessian-based filters. Additionally, multiple sets of eigenvalues are used so that a distinction between nodules and vessel junctions becomes possible. The proposed fuzzy shape representation is based on regulated morphological operations that are less sensitive to noise. Consequently, the vessel tree reconstruction algorithm can accommodate vessel bifurcation and discontinuities. A quantitative performance evaluation of the enhancement filters and of the vessel tree reconstruction algorithm was performed. Moreover, the proposed vessel tree reconstruction algorithm reduced the number of false positives generated by an existing nodule detection algorithm by 38%.