Color Separation for Image Segmentation

Image segmentation is a fundamental problem in computer vision that has drawn intensive research attention during the past few decades, resulting in a variety of segmentation algorithms. Segmentation is often formulated as a Markov random field (MRF) and the solution corresponding to the maximum a posteriori probability (MAP) is found using energy minimiza- tion framework. Many standard segmentation techniques rely on foreground and background appearance models given a priori. In this case the corresponding energy can be efficiently op- timized globally. If the appearance models are not known, the energy becomes NP-hard, and many methods resort to iterative schemes that jointly optimize appearance and segmentation. Such algorithms can only guarantee local minimum. Here we propose a new energy term explicitly measuring L1 distance between the object and background appearance models that can be globally maximized in one graph cut. Our method directly tries to minimize the appearance overlap between the segments. We show that in many applications including interactive segmentation, shape matching, segmentation from stereo pairs and saliency segmentation our simple term makes NP-hard segmentation functionals unnecessary and renders good segmentation performance both qualitatively and quantitatively

Optimization for Image Segmentation

Image segmentation, i.e., assigning each pixel a discrete label, is an essential task in computer vision with lots of applications. Major techniques for segmentation include for example Markov Random Field (MRF), Kernel Clustering (KC), and nowadays popular Convolutional Neural Networks (CNN). In this work, we focus on optimization for image segmentation. Techniques like MRF, KC, and CNN optimize MRF energies, KC criteria, or CNN losses respectively, and their corresponding optimization is very different. We are interested in the synergy and the complementary benefits of MRF, KC, and CNN for interactive segmentation and semantic segmentation. Our first contribution is pseudo-bound optimization for binary MRF energies that are high-order or non-submodular. Secondly, we propose Kernel Cut, a novel formulation for segmentation, which combines MRF regularization with Kernel Clustering. We show why to combine KC with MRF and how to optimize the joint objective. In the third part, we discuss how deep CNN segmentation can benefit from non-deep (i.e., shallow) methods like MRF and KC. In particular, we propose regularized losses for weakly-supervised CNN segmentation, in which we can integrate MRF energy or KC criteria as part of the losses. Minimization of regularized losses is a principled approach to semi-supervised learning, in general. Our regularized loss method is very simple and allows different kinds of regularization losses for CNN segmentation. We also study the optimization of regularized losses beyond gradient descent. Our regularized losses approach achieves state-of-the-art accuracy in semantic segmentation with near full supervision quality

Advances in Graph-Cut Optimization: Multi-Surface Models, Label Costs, and Hierarchical Costs

Computer vision is full of problems that are elegantly expressed in terms of mathematical optimization, or energy minimization. This is particularly true of low-level inference problems such as cleaning up noisy signals, clustering and classifying data, or estimating 3D points from images. Energies let us state each problem as a clear, precise objective function. Minimizing the correct energy would, hypothetically, yield a good solution to the corresponding problem. Unfortunately, even for low-level problems we are confronted by energies that are computationally hard—often NP-hard—to minimize. As a consequence, a rather large portion of computer vision research is dedicated to proposing better energies and better algorithms for energies. This dissertation presents work along the same line, specifically new energies and algorithms based on graph cuts. We present three distinct contributions. First we consider biomedical segmentation where the object of interest comprises multiple distinct regions of uncertain shape (e.g. blood vessels, airways, bone tissue). We show that this common yet difficult scenario can be modeled as an energy over multiple interacting surfaces, and can be globally optimized by a single graph cut. Second, we introduce multi-label energies with label costs and provide algorithms to minimize them. We show how label costs are useful for clustering and robust estimation problems in vision. Third, we characterize a class of energies with hierarchical costs and propose a novel hierarchical fusion algorithm with improved approximation guarantees. Hierarchical costs are natural for modeling an array of difficult problems, e.g. segmentation with hierarchical context, simultaneous estimation of motions and homographies, or detecting hierarchies of patterns

Maximum Persistency via Iterative Relaxed Inference with Graphical Models

We consider the NP-hard problem of MAP-inference for undirected discrete graphical models. We propose a polynomial time and practically efficient algorithm for finding a part of its optimal solution. Specifically, our algorithm marks some labels of the considered graphical model either as (i) optimal, meaning that they belong to all optimal solutions of the inference problem; (ii) non-optimal if they provably do not belong to any solution. With access to an exact solver of a linear programming relaxation to the MAP-inference problem, our algorithm marks the maximal possible (in a specified sense) number of labels. We also present a version of the algorithm, which has access to a suboptimal dual solver only and still can ensure the (non-)optimality for the marked labels, although the overall number of the marked labels may decrease. We propose an efficient implementation, which runs in time comparable to a single run of a suboptimal dual solver. Our method is well-scalable and shows state-of-the-art results on computational benchmarks from machine learning and computer vision.Comment: Reworked version, submitted to PAM

A Comparative Study of Modern Inference Techniques for Structured Discrete Energy Minimization Problems

International audienceSzeliski et al. published an influential study in 2006 on energy minimization methods for Markov Random Fields (MRF). This study provided valuable insights in choosing the best optimization technique for certain classes of problems. While these insights remain generally useful today, the phenomenal success of random field models means that the kinds of inference problems that have to be solved changed significantly. Specifically , the models today often include higher order interactions, flexible connectivity structures, large label-spaces of different car-dinalities, or learned energy tables. To reflect these changes, we provide a modernized and enlarged study. We present an empirical comparison of more than 27 state-of-the-art optimization techniques on a corpus of 2,453 energy minimization instances from diverse applications in computer vision. To ensure reproducibility, we evaluate all methods in the OpenGM 2 framework and report extensive results regarding runtime and solution quality. Key insights from our study agree with the results of Szeliski et al. for the types of models they studied. However, on new and challenging types of models our findings disagree and suggest that polyhedral methods and integer programming solvers are competitive in terms of runtime and solution quality over a large range of model types

A learning framework for higher-order consistency models in multi-class pixel labeling problems

Recently, higher-order Markov random field (MRF) models have been successfully applied to problems in computer vision, especially scene understanding problems. One successful higher-order MRF model for scene understanding is the consistency model [Kohli and Kumar, 2010; Kohli et al., 2009] and earlier work by Ladicky et al. [2009, 2013] which contain higher-order potentials composed of lower linear envelope functions. In semantic image segmentation problems, which seek to identify the pixels of images with pre-defined labels of objects and backgrounds, this model encourages consistent label assignments over segmented regions of images. However, solving this MRF problem exactly is generally NP-hard; instead, efficient approximate inference algorithms are used. Furthermore, the lower linear envelope functions involve a number of parameters to learn. But, the typical cross-validation used for pairwise MRF models is not a practical method for estimating such a large number of parameters. Nevertheless, few works have proposed efficient learning methods to deal with the large number of parameters in these consistency models. In this thesis, we propose a unified inference and learning framework for the consistency model. We investigate various issues and present solutions for inference and learning with this higher-order MRF model as follows. First, we derive two variants of the consistency model for multi-class pixel labeling tasks. Our model defines an energy function scoring any given label assignments over an image. In order to perform Maximum a posteriori (MAP) inference in this model, we minimize the energy function using move-making algorithms in which the higher-order problems are transformed into tractable pairwise problems. Then, we employ a max-margin framework for learning optimal parameters. This learning framework provides a generalized approach for searching the large parameter space. Second, we propose a novel use of the Gaussian mixture model (GMM) for encoding consistency constraints over a large set of pixels. Here, we use various oversegmentation methods to define coherent regions for the consistency potentials. In general, Mean shift (MS) produces locally coherent regions, and GMM provides globally coherent regions, which do not need to be contiguous. Our model exploits both local and global information together and improves the labeling accuracy on real data sets. Accordingly, we use multiple higher-order terms associated with each over-segmentation method. Our learning framework allows us to deal with the large number of parameters involved with multiple higher-order terms. Next, we explore a dual decomposition (DD) method for our multi-class consistency model. The dual decomposition MRF (DD-MRF) is an alternative method for optimizing the energy function. In dual decomposition, a complex MRF problem is decomposed into many easy subproblems and we optimize the relaxed dual problem using a projected subgradient method. At convergence, we expect a global optimum in the dual space because it is a concave maximization problem. To optimize our higher-order DD-MRF exactly, we propose an exact minimization algorithm for solving the higher-order subproblems. Moreover, the minimization algorithm is much more efficient than graph-cuts. The dual decomposition approach also solves the max-margin learning problem by minimizing the dual losses derived from DD-MRF. Here, our minimization algorithm allows us to optimize the DD learning exactly and efficiently, which in most cases finds better parameters than the previous learning approach. Last, we focus on improving labeling accuracies of our higher-order model by combining mid-level features, which we call region features. The region features help customize the general envelope functions for individual segmented regions. By assigning specified weights to the envelope functions, we can choose subsets of highly likely labels for each segmented region. We train multiple classifiers with region features and aggregate them to increase prediction performance of possible labels for each region. Importantly, introducing these region features does not change the previous inference and learning algorithms

Early Vision Optimization: Parametric Models, Parallelization and Curvature

Early vision is the process occurring before any semantic interpretation of an image takes place. Motion estimation, object segmentation and detection are all parts of early vision, but recognition is not. Many of these tasks are formulated as optimization problems and one of the key factors for the success of recent methods is that they seek to compute globally optimal solutions. This thesis is concerned with improving the efficiency and extending the applicability of the current state of the art. This is achieved by introducing new methods of computing solutions to image segmentation and other problems of early vision. The first part studies parametric problems where model parameters are estimated in addition to an image segmentation. For a small number of parameters these problems can still be solved optimally. In the second part the focus is shifted toward curvature regularization, i.e. when the commonly used length and area regularization is replaced by curvature in two and three dimensions. These problems can be discretized over a mesh and special attention is given to the mesh geometry. Specifically, hexagonal meshes are compared to square ones and a method for generating adaptive methods is introduced and evaluated. The framework is then extended to curvature regularization of surfaces. Thirdly, fast methods for finding minimal graph cuts and solving related problems on modern parallel hardware are developed and extensively evaluated. Finally, the thesis is concluded with two applications to early vision problems: heart segmentation and image registration

Structured Prediction Problem Archive

Structured prediction problems are one of the fundamental tools in machinelearning. In order to facilitate algorithm development for their numericalsolution, we collect in one place a large number of datasets in easy to readformats for a diverse set of problem classes. We provide archival links todatasets, description of the considered problems and problem formats, and ashort summary of problem characteristics including size, number of instancesetc. For reference we also give a non-exhaustive selection of algorithmsproposed in the literature for their solution. We hope that this centralrepository will make benchmarking and comparison to established works easier.We welcome submission of interesting new datasets and algorithms for inclusionin our archive.<br

Doctor of Philosophy

dissertationInteractive editing and manipulation of digital media is a fundamental component in digital content creation. One media in particular, digital imagery, has seen a recent increase in popularity of its large or even massive image formats. Unfortunately, current systems and techniques are rarely concerned with scalability or usability with these large images. Moreover, processing massive (or even large) imagery is assumed to be an off-line, automatic process, although many problems associated with these datasets require human intervention for high quality results. This dissertation details how to design interactive image techniques that scale. In particular, massive imagery is typically constructed as a seamless mosaic of many smaller images. The focus of this work is the creation of new technologies to enable user interaction in the formation of these large mosaics. While an interactive system for all stages of the mosaic creation pipeline is a long-term research goal, this dissertation concentrates on the last phase of the mosaic creation pipeline - the composition of registered images into a seamless composite. The work detailed in this dissertation provides the technologies to fully realize interactive editing in mosaic composition on image collections ranging from the very small to massive in scale