Active Surfaces for Selective Object Segmentation in 3D

Segmentation is a fundamental problem in image processing. In biomedical applications, for example cell analysis, it is important to recognize cells with certain shape characteristics. Although recent advances in microscopy and in experimental methods have made the culturing and imaging of cells in 3D environments possible, there is a great need for advanced image processing methods capable of handling such data. In this paper we present an energy minimization based method designed to segment individual objects in 3D satisfying certain size and shape properties. We introduce novel energy functionals designed to penalize shapes unfit to given priors. The three dimensional Euler elastica is also introduced as a new smoothness term, which causes the least possible interference with other terms. Solving the corresponding Euler-Lagrange equations, we demonstrate the selective segmentation capabilities of such priors.