Multi-Target Tracking with Probabilistic Graphical Models

Thanks to revolutionary developments in microscopy techniques such as robotic high-throughput setups or light sheet microscopy, vast amounts of data can be acquired at unprecedented temporal and spatial resolution. The mass of data naturally prohibits manual analysis, though, and life scientists thus have to rely more and more on automated cell tracking methods. However, automated cell tracking involves intricacies that are not commonly found in traditional tracking applications. For instance, cells may undergo mitosis, which results in variable numbers of tracking targets across successive frames. These difficulties have been addressed by tracking-by-assignment models in the past, which dissect the task into two stages, detection and tracking. However, as with every two-stage framework, the approach hinges on the quality of the first stage, and errors propagate partially irrevocably from the detection to the tracking phase. The research in this thesis thus focuses on methods to advance tracking-by-assignment models in order to avoid these errors by exploiting synergy effects between the two (previously) separate stages. We propose two approaches, both in terms of probabilistic graphical models, which allow for information exchange between the detection and the tracking step to different degrees. The first algorithm, termed Conservation tracking, models both possible over- and undersegmentation errors and implements global consistency constraints in order to reidentify target identities even across occlusion or erroneous detections. Wrong detections from the first step can hence be corrected in the second stage. The second method goes one step further and optimizes the two stages completely jointly in one holistic model. In this way, the detection and tracking step can maximally benefit from each other and reach the overall most likely interpretation of the data. Both algorithms yield notable results which are state-of-the-art. In spite of the distinguished results achieved with these methods, automated cell tracking methods are still error-prone and manual proof-reading is often unavoidable for life scientists. To avoid the time-consuming manual identification of errors on very large datasets, most ambiguous predictions ought to be detected automatically so that these can be corrected by a human expert with minimal effort. In response, we propose two easy-to-use methods to sample multiple solutions from a tracking-by-assignment graphical model and derive uncertainty measures from the variations across the samples. We showcase the usefulness for guided proof-reading on the cell tracking model proposed in this work. Finally, the successful application of structured output learning algorithms to cell tracking in previous work inspired us to advance the state-of-the-art by an algorithm called Coulomb Structured Support Vector Machine (CSSVM). The CSSVM improves the expected generalization error for unseen test data by the training of multiple concurrent graphical models. Through the novel diversity encouraging term, motivated from experimental design, the ensemble of graphical models is learned to yield diverse predictions for test data. The best prediction amongst these models may then be selected by an oracle or with respect to a more complex loss. Experimental evaluation shows significantly better results than using only one model and achieves state-of-the-art performance on challenging computer vision tasks

Validation of Composite Systems by Discrepancy Propagation

Assessing the validity of a real-world system with respect to given quality criteria is a common yet costly task in industrial applications due to the vast number of required real-world tests. Validating such systems by means of simulation offers a promising and less expensive alternative, but requires an assessment of the simulation accuracy and therefore end-to-end measurements. Additionally, covariate shifts between simulations and actual usage can cause difficulties for estimating the reliability of such systems. In this work, we present a validation method that propagates bounds on distributional discrepancy measures through a composite system, thereby allowing us to derive an upper bound on the failure probability of the real system from potentially inaccurate simulations. Each propagation step entails an optimization problem, where -- for measures such as maximum mean discrepancy (MMD) -- we develop tight convex relaxations based on semidefinite programs. We demonstrate that our propagation method yields valid and useful bounds for composite systems exhibiting a variety of realistic effects. In particular, we show that the proposed method can successfully account for data shifts within the experimental design as well as model inaccuracies within the used simulation.Comment: 20 pages incl. 10 pages appendi

Probabilistic Recurrent State-Space Models

State-space models (SSMs) are a highly expressive model class for learning patterns in time series data and for system identification. Deterministic versions of SSMs (e.g. LSTMs) proved extremely successful in modeling complex time series data. Fully probabilistic SSMs, however, are often found hard to train, even for smaller problems. To overcome this limitation, we propose a novel model formulation and a scalable training algorithm based on doubly stochastic variational inference and Gaussian processes. In contrast to existing work, the proposed variational approximation allows one to fully capture the latent state temporal correlations. These correlations are the key to robust training. The effectiveness of the proposed PR-SSM is evaluated on a set of real-world benchmark datasets in comparison to state-of-the-art probabilistic model learning methods. Scalability and robustness are demonstrated on a high dimensional problem

ilastik: interactive machine learning for (bio)image analysis

We present ilastik, an easy-to-use interactive tool that brings machine-learning-based (bio)image analysis to end users without substantial computational expertise. It contains pre-defined workflows for image segmentation, object classification, counting and tracking. Users adapt the workflows to the problem at hand by interactively providing sparse training annotations for a nonlinear classifier. ilastik can process data in up to five dimensions (3D, time and number of channels). Its computational back end runs operations on-demand wherever possible, allowing for interactive prediction on data larger than RAM. Once the classifiers are trained, ilastik workflows can be applied to new data from the command line without further user interaction. We describe all ilastik workflows in detail, including three case studies and a discussion on the expected performance

Proof-reading guidance in cell tracking by sampling from tracking-by-assignment models

Automated cell tracking methods are still error-prone. On very large data sets, uncertainty measures are thus needed to guide the expert to the most ambiguous events so these can be corrected with minimal effort. We present two easy-to-use methods to sample multiple proposal solutions from a tracking-by-assignment graphical model and experimentally evaluate the benefits of the uncertainty measures derived. Ex-pert time for proof-reading is reduced greatly compared to random selection of predicted events. Index Terms — Cell tracking, uncertainty, machine learn-ing, probabilistic graphical model