A variational approach to vesicle membrane reconstruction from fluorescence imaging

Biological applications like vesicle membrane analysis involve the precise segmentation of 3D structures in noisy volumetric data, obtained by techniques like magnetic resonance imaging (MRI) or laser scanning microscopy (LSM). Dealing with such data is a challenging task and requires robust and accurate segmentation methods. In this article, we propose a novel energy model for 3D segmentation fusing various cues like regional intensity subdivision, edge alignment and orientation information. The uniqueness of the approach consists in the definition of a new anisotropic regularizer, which accounts for the unbalanced slicing of the measured volume data, and the generalization of an efficient numerical scheme for solving the arising minimization problem, based on linearization and fixed-point iteration. We show how the proposed energy model can be optimized globally by making use of recent continuous convex relaxation techniques. The accuracy and robustness of the presented approach are demonstrated by evaluating it on multiple real data sets and comparing it to alternative segmentation methods based on level sets. Although the proposed model is designed with focus on the particular application at hand, it is general enough to be applied to a variety of different segmentation tasks.

► In this work we address the problem of 3D segmentation.
► We unify image cues like regional statistics, edge attraction and orientation.
► We propose a convex anisotropic regularizer.
► We derive an efficient numerical optimization scheme.