Curvilinear networks are prevalent in nature and span many different scales, ranging from micron-scale neural structures in the brain to petameter-scale dark-matter arbors binding massive galaxy clusters. Reliably reconstructing them in an automated fashion is of great value in many different scientific domains. However, it remains an open Computer Vision problem. In this thesis we focus on automatically delineating curvilinear tree structures in images of the same object of interest taken at different time instants. Unlike virtually all of the existing methods approaching the task of tree structures delineation we process all the images at once. This is useful in the more ambiguous regions and allows to reason for the tree structure that fits best to all the acquired data. We propose two methods that utilize this principle of temporal consistency to achieve results of higher quality compared to single time instant methods. The first, simpler method starts by building an overcomplete graph representation of the final solution in all time instants while simultaneously obtaining correspondences between image features across time. We then define an objective function with a temporal consistency prior and reconstruct the structures in all images at once by solving a mathematical optimization. The role of the prior is to encourage solutions where for two consecutive time instants corresponding candidate edges are either both retained or both rejected from the final solution. The second multiple time instant method uses the same overcomplete graph principle but handles the temporal consistency in a more robust way. Instead of focusing on the very local consistency of single edges of the overcomplete graph we propose a method for describing topological relationships. This favors solutions whose connectivity is consistent over time. We show that by making the temporal consistency more global we achieve additional robustness to errors in the initial features matching step, which is shared by both the approaches. In the end, this yields superior performance. Furthermore, an added benefit of both our approaches is the ability to automatically detect places where significant changes have occurred over time, which is challenging when considering large amounts of data. We also propose a simple single time instant method for delineating tree structures. It computes a Minimum Spanning Arborescence of an initial overcomplete graph and proceeds to optimally prune spurious branches. This yields results of lower but still competitive quality compared to the mathematical optimization based methods, while keeping low computational complexity. Our methods can applied to both 2D and 3D data. We demonstrate their performance in 3D on microscopy volumes of mouse brain and rat brain. We also test them in 2D on time-lapse images of a growing runner bean and aerial images of a road network.