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.

In this paper we describe a new technique for general purpose interactive segmentation of N-dimensional images. The user marks certain pixels as “object” or “background” to provide hard constraints for segmentation. Additional soft constraints incorporate both boundary and region information. Graph cuts are used to find the globally optimal segmentation of the N-dimensional image. The obtained solution gives the best balance of boundary and region properties among all segmentations satisfying the constraints. The topology of our segmentation is unrestricted and both “object” and “background” segments may consist of sev-eral isolatedparts. Some experimental results are presented in the context ofphotohideo editing and medical image seg-mentation. We also demonstrate an interesting Gestalt example. A fast implementation of our segmentation method is possible via a new mar-$ow algorithm in [2].

... alternative to pure automatic segmentation in many applications. While automatic segmentation can be very challenging, a small amount of user input can often resolve ambiguous decisions on the part of the algorithm. In this work, we devise a graph cut algorithm for interactive segmentation which incorporates shape priors. While traditional graph cut approaches to interactive segmentation are often quite successful, they may fail in cases where there are diffuse edges, or multiple similar objects in close proximity to one another. Incorporation of shape priors within this framework mitigates these problems. Positive results on both medical and natural images are demonstrated.

The recently introduced random walker segmentation algorithm of [14] has been shown to have desirable theoretical properties and to perform well on a wide variety of images in practice. However, this algorithm requires user-specified labels and produces a segmentation where each segment is connected to a labeled pixel. We show that incorporation of a nonparametric probability density model allows for an extended random walkers algorithm that can locate disconnected objects and does not require user-specified labels. Finally, we show that this formulation leads to a deep connection with the popular graph cuts method of [8, 24]. 1

Interactive, efficient, methods of foreground extraction and alpha-matting are of increasing practical importance for digital image editing. Although several new approaches to this problem have recently been developed, many challenges remain. We propose a new technique based on random walks that has the following advantages: First, by leveraging a recent technique from manifold learning theory, we effectively use RGB values to set boundaries for the random walker, even in fuzzy or low-contrast images. Second, the algorithm is straightforward to implement, requires specification of only a single free parameter (set the same for all images), and performs the segmentation and alpha-matting in a single step. Third, the user may locally fine tune the results by interactively manipulating the foreground/background maps. Finally, the algorithm has an inherit parallelism that leads to a particularly efficient implementation via the graphics processing unit (GPU). Our method processes a 1024 × 1024 image at the interactive speed of 0.5 seconds and, most importantly, produces highquality results. We show that our algorithm can generate good segmentation and matting results at an interactive rate with minimal user interaction.

Efficient segmentation of globally optimal surfaces representing object boundaries in volumetric data sets is important and challenging in many medical image analysis applications. We have developed an optimal surface detection method capable of simultaneously detecting multiple interacting surfaces, in which the optimality is controlled by the cost functions designed for individual surfaces and by several geometric constraints defining the surface smoothness and interrelations. The method solves the surface segmentation problem by transforming it into computing a minimum s-t cut in a derived arc-weighted directed graph. The proposed algorithm has a low-order polynomial time complexity and is computationally efficient. It has been extensively validated on more than 300 computer-synthetic volumetric images, 72 CT-scanned data sets of different-sized plexiglas tubes, and tens of medical images spanning various imaging modalities. In all cases, the approach yielded highly accurate results. Our approach can be readily extended to higher-dimensional image segmentation.

Interactive object extraction is an important part in any image editing software. We present a two step segmentation algorithm that first obtains a binary segmentation and then applies matting on the border regions to obtain a smooth alpha channel. The proposed segmentation algorithm is based on the minimization of the Geodesic Active Contour energy. A fast Total Variation minimization algorithm is used to find the globally optimal solution. We show how user interaction can be incorporated and outline an efficient way to exploit color information. A novel matting approach, based on energy minimization, is presented. Experimental evaluations are discussed, and the algorithm is compared to state of the art object extraction algorithms. The GPU based binaries are available online.

Abstract. Fully automatic, completely reliable segmentation in medical images is an unrealistic expectation with today’s technology. However, many automatic segmentation algorithms may achieve a near-correct solution, incorrect only in a small region. For these situations, an interactive editing tool is required, ideally in 3D, that is usually left to a manual correction. We formulate the editing task as an energy minimization problem that may be solved with a modified version of either graph cuts or the random walker 3D segmentation algorithms. Both algorithms employ a seeded user interface, that may be used in this scenario for a user to seed erroneous voxels as belonging to the foreground or the background. In our formulation, it is unnecessary for the user to specify both foreground and background seeds. 1

Existing parallel MRI methods are limited by a fundamental trade-off in that suppressing noise introduces aliasing artifacts. Bayesian methods with an appropriately chosen image prior offer a promising alternative; however, previous methods with spatial priors assume that intensities vary smoothly over the entire image, resulting in blurred edges. Here we introduce an edge-preserving prior (EPP) that instead assumes that intensities are piecewise smooth, and propose a new approach to efficiently compute its Bayesian estimate. The estimation task is formulated as an optimization problem that requires a nonconvex objective function to be minimized in a space with thousands of dimensions. As a result, traditional continuous minimization methods cannot be applied. This optimization task is closely related to some problems in the field of computer vision for which discrete optimization methods have been developed in the last few years. We adapt these algorithms, which are based on graph cuts, to address our optimization problem. The results of several parallel imaging experiments on brain and torso regions performed under challenging conditions with high acceleration factors are shown and compared with the results of conventional sensitivity encoding (SENSE) methods. An empirical analysis indicates that the proposed method visually improves overall quality compared to conventional methods.

Abstract. Tracking is usually interpreted as finding an object in single consecutive frames. Regularization is done by enforcing temporal smoothness of appearance, shape and motion. We propose a tracker, by interpreting the task of tracking as segmentation of a volume in 3D. Inherently temporal and spatial regularization is unified in a single regularization term. Segmentation is done by a variational approach using anisotropic weighted Total Variation (TV) regularization. The proposed convex energy is solved globally optimal by a fast primal-dual algorithm. Any image feature can be used in the segmentation cue of the proposed Mumford-Shah like data term. As a proof of concept we show experiments using a simple color-based appearance model. As demonstrated in the experiments, our tracking approach is able to handle large variations in shape and size, as well as partial and complete occlusions. 1