Shape-driven three-dimensional watersnake segmentation of biological membranes in electron tomography

Due to the significant complexity of membrane morphology and the generally poor image quality in electron tomographic volumes, current automatic methods for segmentation of membranes perform poorly. Users must resort to manual tracing of recognized patterns on 2-D slices of the volume, a method that suffers from subjectivity and is very labor intensive, preventing quantitative analyses of tomographic data that require comparative analyses of many volumes. To overcome these limitations, we develop an automatic 3-D segmentation method that fully exploits the prior knowledge about the shape of the membranes as well as the 3-D information provided by the tomograms, and systematically combines this knowledge with the image data to improve segmentation results. The method is based on the watersnake framework. By mathematically reformulating the traditional watershed segmentation as an energy minimization problem, the watersnake inherits the many strengths of the watershed method while overcoming the limitations of the traditional energy-based segmentation methods. In our previous work (H. Nguyen et al., 2003), the original watersnake model was successfully modified by incorporating smoothness into watershed segmentation. In this work, we further extend that model to incorporate into the energy function various constraints representing our prior knowledge about the global shape of the cellular features to be segmented. Segmentation can, therefore, be accomplished via minimization of the energy function subject to the shape prior constraints. Finally, the mathematical framework is further extended from 2-D to 3-D so that segmentation can be carried out in 3-D to take advantage of the additional information provided by the tomograms. We apply this method for the automatic extraction of biological membranes of varying complexities including those of bacterial walls and mitochondrial boundaries.