Summary: Likelihood-free methods are often required for inference in systems biology. While approximate Bayesian computation (ABC) provides a theoretical solution, its practical application has often been challenging due to its high computational demands. To scale likelihood-free inference to computationally demanding stochastic models, we developed pyABC: a distributed and scalable ABC-Sequential Monte Carlo (ABC-SMC) framework. It implements a scalable, runtime-minimizing parallelization strategy for multi-core and distributed environments scaling to thousands of cores. The framework is accessible to non-expert users and also enables advanced users to experiment with and to custom implement many options of ABC-SMC schemes, such as acceptance threshold schedules, transition kernels and distance functions without alteration of pyABC's source code. pyABC includes a web interface to visualize ongoing and finished ABC-SMC runs and exposes an API for data querying and post-processing. Availability and Implementation: pyABC is written in Python 3 and is released under a 3-clause BSD license. The source code is hosted on https://github.com/icb-dcm/pyabc and the documentation on http://pyabc.readthedocs.io. It can be installed from the Python Package Index (PyPI). Supplementary information: Supplementary data are available at Bioinformatics online.

Current algorithmic approaches for piecewise affine motion estimation are based on alternating motion segmentation and estimation. We propose a new method to estimate piecewise affine motion fields directly without intermediate segmentation. To this end, we reformulate the problem by imposing piecewise constancy of the parameter field, and derive a specific proximal splitting optimization scheme. A key component of our framework is an efficient one-dimensional piecewise-affine estimator for vector-valued signals. The first advantage of our approach over segmentation-based methods is its absence of initialization. The second advantage is its lower computational cost which is independent of the complexity of the motion field. In addition to these features, we demonstrate competitive accuracy with other piecewise-parametric methods on standard evaluation benchmarks. Our new regularization scheme also outperforms the more standard use of total variation and total generalized variation.

We develop a fast algorithm for segmenting 3D images from linear measurements based on the Potts model (or piecewise constant Mumford-Shah model). To that end, we first derive suitable space discretizations of the 3D Potts model, which are capable of dealing with 3D images defined on non-cubic grids. Our discretization allows us to utilize a specific splitting approach, which results in decoupled subproblems of moderate size. The crucial point in the 3D setup is that the number of independent subproblems is so large that we can reasonably exploit the parallel processing capabilities of the graphics processing units (GPUs). Our GPU implementation is up to 18 times faster than the sequential CPU version. This allows to process even large volumes in acceptable runtimes. As a further contribution, we extend the algorithm in order to deal with non-negativity constraints. We demonstrate the efficiency of our method for combined image deconvolution and segmentation on simulated data and on real 3D wide field fluorescence microscopy data.