A discriminative view of MRF pre-processing algorithms

While Markov Random Fields (MRFs) are widely used in computer vision, they present a quite challenging inference problem. MRF inference can be accelerated by pre-processing techniques like Dead End Elimination (DEE) or QPBO-based approaches which compute the optimal labeling of a subset of variables. These techniques are guaranteed to never wrongly label a variable but they often leave a large number of variables unlabeled. We address this shortcoming by interpreting pre-processing as a classification problem, which allows us to trade off false positives (i.e., giving a variable an incorrect label) versus false negatives (i.e., failing to label a variable). We describe an efficient discriminative rule that finds optimal solutions for a subset of variables. Our technique provides both per-instance and worst-case guarantees concerning the quality of the solution. Empirical studies were conducted over several benchmark datasets. We obtain a speedup factor of 2 to 12 over expansion moves without preprocessing, and on difficult non-submodular energy functions produce slightly lower energy.Comment: ICCV 201

Block Stability for MAP Inference

To understand the empirical success of approximate MAP inference, recent work (Lang et al., 2018) has shown that some popular approximation algorithms perform very well when the input instance is stable. The simplest stability condition assumes that the MAP solution does not change at all when some of the pairwise potentials are (adversarially) perturbed. Unfortunately, this strong condition does not seem to be satisfied in practice. In this paper, we introduce a significantly more relaxed condition that only requires blocks (portions) of an input instance to be stable. Under this block stability condition, we prove that the pairwise LP relaxation is persistent on the stable blocks. We complement our theoretical results with an empirical evaluation of real-world MAP inference instances from computer vision. We design an algorithm to find stable blocks, and find that these real instances have large stable regions. Our work gives a theoretical explanation for the widespread empirical phenomenon of persistency for this LP relaxation

Towards Accurate and Efficient Cell Tracking During Fly Wing Development

Understanding the development, organization, and function of tissues is a central goal in developmental biology. With modern time-lapse microscopy, it is now possible to image entire tissues during development and thereby localize subcellular proteins. A particularly productive area of research is the study of single layer epithelial tissues, which can be simply described as a 2D manifold. For example, the apical band of cell adhesions in epithelial cell layers actually forms a 2D manifold within the tissue and provides a 2D outline of each cell. The Drosophila melanogaster wing has become an important model system, because its 2D cell organization has the potential to reveal mechanisms that create the final fly wing shape. Other examples include structures that naturally localize at the surface of the tissue, such as the ciliary components of planarians. Data from these time-lapse movies typically consists of mosaics of overlapping 3D stacks. This is necessary because the surface of interest exceeds the field of view of todays microscopes. To quantify cellular tissue dynamics, these mosaics need to be processed in three main steps: (a) Extracting, correcting, and stitching individ- ual stacks into a single, seamless 2D projection per time point, (b) obtaining cell characteristics that occur at individual time points, and (c) determine cell dynamics over time. It is therefore necessary that the applied methods are capable of handling large amounts of data efficiently, while still producing accurate results. This task is made especially difficult by the low signal to noise ratios that are typical in live-cell imaging. In this PhD thesis, I develop algorithms that cover all three processing tasks men- tioned above and apply them in the analysis of polarity and tissue dynamics in large epithelial cell layers, namely the Drosophila wing and the planarian epithelium. First, I introduce an efficient pipeline that preprocesses raw image mosaics. This pipeline accurately extracts the stained surface of interest from each raw image stack and projects it onto a single 2D plane. It then corrects uneven illumination, aligns all mosaic planes, and adjusts brightness and contrast before finally stitching the processed images together. This preprocessing does not only significantly reduce the data quantity, but also simplifies downstream data analyses. Here, I apply this pipeline to datasets of the developing fly wing as well as a planarian epithelium. I additionally address the problem of determining cell polarities in chemically fixed samples of planarians. Here, I introduce a method that automatically estimates cell polarities by computing the orientation of rootlets in motile cilia. With this technique one can for the first time routinely measure and visualize how tissue polarities are established and maintained in entire planarian epithelia. Finally, I analyze cell migration patterns in the entire developing wing tissue in Drosophila. At each time point, cells are segmented using a progressive merging ap- proach with merging criteria that take typical cell shape characteristics into account. The method enforces biologically relevant constraints to improve the quality of the resulting segmentations. For cases where a full cell tracking is desired, I introduce a pipeline using a tracking-by-assignment approach. This allows me to link cells over time while considering critical events such as cell divisions or cell death. This work presents a very accurate large-scale cell tracking pipeline and opens up many avenues for further study including several in-vivo perturbation experiments as well as biophysical modeling. The methods introduced in this thesis are examples for computational pipelines that catalyze biological insights by enabling the quantification of tissue scale phenomena and dynamics. I provide not only detailed descriptions of the methods, but also show how they perform on concrete biological research projects

Discrete graphical models -- an optimization perspective

This monograph is about discrete energy minimization for discrete graphical models. It considers graphical models, or, more precisely, maximum a posteriori inference for graphical models, purely as a combinatorial optimization problem. Modeling, applications, probabilistic interpretations and many other aspects are either ignored here or find their place in examples and remarks only. It covers the integer linear programming formulation of the problem as well as its linear programming, Lagrange and Lagrange decomposition-based relaxations. In particular, it provides a detailed analysis of the polynomially solvable acyclic and submodular problems, along with the corresponding exact optimization methods. Major approximate methods, such as message passing and graph cut techniques are also described and analyzed comprehensively. The monograph can be useful for undergraduate and graduate students studying optimization or graphical models, as well as for experts in optimization who want to have a look into graphical models. To make the monograph suitable for both categories of readers we explicitly separate the mathematical optimization background chapters from those specific to graphical models.Comment: 270 page