Abstract—In the last few years, several new algorithms based on graph cuts have been developed to solve energy minimization problems in computer vision. Each of these techniques constructs a graph such that the minimum cut on the graph also minimizes the energy. Yet, because these graph constructions are complex and highly specific to a particular energy function, graph cuts have seen limited application to date. In this paper, we give a characterization of the energy functions that can be minimized by graph cuts. Our results are restricted to functions of binary variables. However, our work generalizes many previous constructions and is easily applicable to vision problems that involve large numbers of labels, such as stereo, motion, image restoration, and scene reconstruction. We give a precise characterization of what energy functions can be minimized using graph cuts, among the energy functions that can be written as a sum of terms containing three or fewer binary variables. We also provide a general-purpose construction to minimize such an energy function. Finally, we give a necessary condition for any energy function of binary variables to be minimized by graph cuts. Researchers who are considering the use of graph cuts to optimize a particular energy function can use our results to determine if this is possible and then follow our construction to create the appropriate graph. A software implementation is freely available.

: The aim of this work is to track specific anatomical structures in temporal sequences of echocardiographic images. Ultrasound images are available in two broad data types: raw or video data. Different stochastic processes using different kind of information are compared on the basis of these two data types. We explain the selection of a particular model w.r.t. the type of data, and describe the relevant properties that must be taken into account to obtain the best possible results. The models are expressed within a Markov random field framework and we also discuss parameter estimation and energy minimization for the different models. Key-words: Segmentation, Markov Random Field, Stochastic Process, Medical Image, Ultrasound. (R'esum'e : tsvp) Unite de recherche INRIA Rocquencourt Domaine de Voluceau, Rocquencourt, BP 105, 78153 LE CHESNAY Cedex (France) Telephone : (33 1) 39 63 55 11 -- Telecopie : (33 1) 39 63 53 Segmentation d'images 'echocardiographiques par champs de Markov R...