This work describes a new framework for automatic extraction of 2D branching structures images obtained from 3D shapes, such as neurons and retinopathy images. The majority of methods for neuronal cell shape analysis that are based on the 2D contours of cells fall short of properly characterizing such cells because crossings among neuronal processes constrain the access of contour following algorithms to the innermost regions of the cell. The framework presented in this article addresses, possibly for the first time, the problem of determining the continuity along crossings, therefore granting to the contour following algorithm full access to all processes of the neuronal cell under analysis. First, the raw image is preprocessed so as to obtain an 8-connected, one-pixel wide skeleton as well as a set of seed pixels for each subtree and all the branching/ crossing regions. Then, for each seed pixel, the algorithm labels all valid neighbors, until a branching/crossing region is reached, when a decision about the proper continuation is taken based on the tangent continuity. The algorithm has shown robustness for images with parallel segments and low densities of branching/crossing densities. The problem of too high densities of branching/crossing regions can be addressed by using a suitable data structure. Successful experimental results using real data (neural cell images) are presented.