Electron Cryo-microscopy is an advanced imaging technique that is able to produce volumetric images of proteins that are large or hard to crystallize. De novo modeling is a process that aims at deriving the structure of the protein using the images produced by Electron Cryo-microscopy. At the medium resolutions (5 to 10Å), the location and orientation of the secondary structure elements can be computationally identified on the images. However, there is no registration between the detected secondary structure elements and the protein sequence, and therefore it is challenging to derive the atomic structure from such volume data. The skeleton of the volume image is used to interpret the connections between the secondary structure elements in order to reduce the search space of the registration problem. Unfortunately, not all features of the image can be captured using a single segmentation. Moreover, the skeleton is sensitive to the threshold used which leads to gaps in the skeleton. In this paper, we present a threshold-independent approach to overcome the problem of gaps in the skeletons. The approach uses a novel representation of the image where the image is modeled as a graph and a set of volume trees. A test containing thirteen synthesized images and two authentic images showed that our approach could improve the existent skeletons. The percent of improvement achieved were 117% and 40% for Gorgon and MapEM, respectively.