In current biomedical research 3D time-lapse microscopy allows to investigate developmental processes, such as the growth of whole organisms, on the cellular level. Embryos of zebrafish Danio rerio or fruit fly Drosophila, for example, can be recorded in vivo in 3D space. Processes such as cell division and cell migration can be observed, that lead to the formation and growth of tissue, and finally, to the development of the whole organism. Analyzing cell motion and the emerging motion patterns is crucial for the understanding of developmental processes and their underlying mechanisms. Typically, experiments in genomics, proteomics and metabolomics aim at comparing wild-type organisms to genetically manipulated organisms, usually referred to as mutants. The goal is to link observable changes in the manipulated organisms (changes in the phenotype) to the underlying genetic manipulation (manipulation of the genotype) to infer the function of certain genes. Generally, a quantitative and unbiased comparison is desired to discover differences and verify their statistical significance. Such experiments usually generate huge amounts of data, consisting of time sequences of 3D volumetric images. Since manual evaluation is neither feasible nor desired, techniques for automated image analysis have become indispensable. This thesis presents approaches that enable motion pattern analysis in complex biomedical applications based on 2D and 3D time-lapse microscopy. They allow precise physical measurements for quantitative analysis and robust comparisons of motion patterns, which is essential for evaluating experiments in biomedical research and specifically in developmental biology. Two methods that are based on a trajectory representation of motion provide the main contributions of this thesis. Trajectories yield a rich motion representation, including long-term motion information, that is independent of object appearance, which is very important in microscopy when comparing images that are affected by different imaging settings. In chapter 2 we propose a general method to detect motion anomalies in 3D+time data. The setting of anomaly detection fits well to the usual biomedical tasks where wild-type patterns define a normal model and significant deviations, i.e. anomalies, are to be detected in mutants. We detect anomalies by placing spatiotemporally deformed instances of a prototype pattern to reconstruct a test pattern. In the test pattern, we regard poorly reconstructed patterns showing strong deviations from the elastically registered prototype patterns as anomalies. To define accepted variations a prototype model is learned from multiple training sequences. We propose a new method for elastic registration of 3D+time trajectory patterns, together with a new efficient and robust supertrajectory representation and a modified hashing approach to efficiently produce transformation hypotheses. The method performs well in detecting subtle anomalies on a new motion anomaly dataset of juggling patterns, and we demonstrated the applicability to biological motion patterns in zebrafish development. The second trajectory-based method allows to detect specific motion patterns in 3D+time data using spatiotemporal geometrical models. In particular, we developed a model to detect cell intercalation which is an essential pattern in developmental biology. Cell intercalations occur when cells enter the space between adjacent cells and play an important role in tissue formation. The approach builds on single cell motion trajectories and specifies the motion pattern to be detected by spatiotemporal transition functions of a geometrical model. The method is robust to noisy and incomplete measurements and handles the variability within the class of 3D intercalations. We applied our method to biological data from zebrafish development and performed a quantitative comparison of cell intercalations and their motion statistics between wild-type and mutant embryos. Two contour-based approaches form the second part of this thesis. Instead of trajectories, sequences of evolving contours are used to represent motion patterns. We propose a new robust, effective, and surprisingly simple approach for the segmentation of cells in phase contrast microscopy. Phase contrast microscopy generates strong intensity gradients along interfaces of media with different physical densities. They allow to obtain clear boundary responses even for perfectly transparent samples. However, classical edge-based image segmentation fails due to the complex intensity profile consisting of a bright-to-dark and a dark-to-bright transition at the boundary and other artifacts from phase contrast microscopy. Our algorithm exploits the properties of positive phase contrast microscopy where the true cell borders always appear as a dark-to-bright transition in outwards direction. The segmentation mask is effectively found by a fast min-cut approach. In contrast to classical min-cut our graph contains directed edges with asymmetric edge weights. This modification to classical min-cut allows to choose optimization parameters from a wider range without affecting segmentation performance and surpasses segmentation quality with symmetric edge weights. We outperformed the top ranked methods from the ISBI Cell Tracking Challenge (CTC) 2014 on the phase contrast dataset, and reached second place in the ISBI CTC 2015. We were able to directly apply our approach for cell segmentation on phase contrast images to produce cell contour input data for our second contour-based method. It investigates migrating cells and their motion patterns. We developed a method to detect symmetry-breaking events, which enabled automatic browsing of large amounts of data for these cellular events of interest. To investigate motion patterns along the cell contour, we implemented a method to compute protrusion/retraction maps that visualize the contour velocities in a 2D map in polar contour coordinates over time. We applied the approach to the analysis of spontaneous and electric field-controlled front-rear polarization of human keratinocytes. Our approach enabled the quantification of several experimental conditions and led to the extraction of biologically relevant results. In conclusion, this thesis contains several contributions to tackle the task of motion pattern analysis and quantitative comparison in biomedical applications from 3D+time data. The presented approaches build on trajectory- and contour-based representations and yielded robust methods that have been successfully applied in real biomedical applications and published in the field of computer vision, as well as in the field of biology and at the intersection of image analysis, imaging and biomedical applications. It seems reasonable to focus future research into the direction of deep learning as it is currently the most exciting and promising field for advances. However, many open questions and challenges have to be addressed to solve the tasks considered in this thesis using deep learning. For the near future, using a mixture of conventional and deep learning methods seems to be the most promising approach.