Markov random fields with higher order potentials have emerged as a powerful model for several problems in computer vision. In order to facilitate their use, we propose a new representation for higher order potentials as upper and lower envelopes of linear functions. Our representation concisely models several commonly used higher order potentials, thereby providing a unified framework for minimizing the corresponding Gibbs energy functions. We exploit this framework by converting lower envelope potentials to standard pairwise functions with the addition of a small number of auxiliary variables. This allows us to minimize energy functions with lower envelope potentials using conventional algorithms such as BP, TRW and α-expansion. Furthermore, we show how the minimization of energy functions with upper envelope potentials leads to a difficult minmax problem. We address this difficulty by proposing a new message passing algorithm that solves a linear programming relaxation of the problem. Although this is primarily a theoretical paper, we demonstrate the efficacy of our approach on the binary (fg/bg) segmentation problem. 1.

This paper makes two contributions to the area of single-word based word alignment for bilingual sentence pairs. Firstly, it integrates the – seemingly rather different – works of (Bodrumlu et al., 2009) and the standard probabilistic ones into a single framework. Secondly, we present two algorithms to optimize the arising task. The first is an iterative scheme similar to Viterbi training, able to handle large tasks. The second is based on the inexact solution of an integer program. While it can handle only small corpora, it allows more insight into the quality of the model and the performance of the iterative scheme. Finally, we present an alternative way to handle prior dictionary knowledge and discuss connections to computing IBM-3 Viterbi alignments. 1

We propose a novel and fast interactive image segmentation algorithm for use on mobile phones. Instead of using global optimization, our algorithm begins with an initial over-segmentation using the mean shift algorithm and follows this by discriminative clustering and local neighborhood classification. This procedure obtains better quality results than previous methods that use graph cuts on oversegmented regions or region merging based on maximal similarity, yet its running time is smaller by an order of magnitude. Wecompare andanalyze thestrengths and limitations ofthethreeapproaches andhaveimplementedouralgorithm as part of an interactive object cut out application running on a mobile phone.

There is a growing interest in building probabilistic models with high order potentials (HOPs), or interactions, among discrete variables. Message passing inference in such models generally takes time exponential in the size of the interaction, but in some cases maximum a posteriori (MAP) inference can be carried out efficiently. We build upon such results, introducing two new classes, including composite HOPs that allow us to flexibly combine tractable HOPs using simple logical switching rules. We present efficient message update algorithms for the new HOPs, and we improve upon the efficiency of message updates for a general class of existing HOPs. Importantly, we present both new and existing HOPs in a common representation; performing inference with any combination of these HOPs requires no change of representations or new derivations. 1

Abstract. We present a technique to handle computer vision problems inducing models with very high order terms- in fact terms of maximal order. Here we consider terms where the cost function depends only on the number of variables that are assigned a certain label, but where the dependence is arbitrary. Applications include image segmentation with a histogram-based data term [28] and the recently introduced marginal probability fields [31]. The presented technique makes use of linear and integer linear programming. We include a set of customized cuts to strengthen the formulations. 1