Globally optimal cell segmentation using shape and intensity information

Studies of cellular structures and processes are of key interest in biomedical research and pathology. Such studies often require segmentation of cell nuclei in microscopy images, for example, for cell counting, analysis of the morphology, or for analysis of other cellular structures in the proximity of nuclei. Since accurate manual segmentation of cell nuclei is tedious, automatic segmentation methods are indispensable to facilitate the analysis. Segmentation of cell microscopy images is particularly challenging due to imaging artifacts like strong image noise and intensity inhomogeneities, but also due to closely clustered or partially overlapping objects and shape variation of cell nuclei. In this thesis, three new cell segmentation methods are introduced. The methods are based on implicitly parameterized shape models and address major challenges in cell segmentation by jointly exploiting shape and intensity information. Model fitting is performed by energy minimization, comprising convex and combinatorial optimization schemes, which yields results close to global optimality. Convexity is a computationally favorable property which permits fast, robust, and reproducible energy minimization, independently of the initialization. The proposed cell segmentation methods are based on three new shape parameterizations. First, a non-linear parameterization for elliptical models is presented, which uses the locations of priorly detected objects. Energy minimization is performed by convex optimization using a sequential approximation scheme. Second, a linear parameterization for elliptical models is proposed. This parameterization has the advantage of directly yielding a convex energy, thus sequential approximation is not required. Third, a linear parameterization for deformable shape models is introduced, which also yields a convex energy but permits coping with more general shapes. To enable joint cell segmentation and cluster splitting, the shape parameterizations are generalized from the single-object to the multi-object case. The corresponding energy is non-convex, yet, we show that it is structurally similar to the min-weight set-cover problem. We develop a novel iterative global energy minimization method which exploits the set-cover structure and provably determines a solution close to global optimality. This is achieved by a new necessary optimality condition, which is iteratively evaluated and refined. In addition, a closed-form solution for non-clustered cell nuclei is derived, which directly determines the corresponding segmentation result and further accelerates the computations. The proposed methods were applied to challenging image data, comprising fluorescence microscopy images of six different cell types and publicly available benchmark datasets, and a quantitative comparison with previous methods was performed. It turned out that the proposed methods generally yield competitive or improved results. Furthermore, the applicability of the methods to H&E-stained pathology images was investigated