Capacity Scaling for Graph Cuts in Vision

ÐMany tasks in computer vision involve assigning a label (such as disparity) to every pixel. A common constraint is that the labels should vary smoothly almost everywhere while preserving sharp discontinuities that may exist, e.g., at object boundaries. These tasks are naturally stated in terms of energy minimization. In this paper, we consider a wide class of energies with various smoothness constraints. Global minimization of these energy functions is NP-hard even in the simplest discontinuity-preserving case. Therefore, our focus is on efficient approximation algorithms. We present two algorithms based on graph cuts that efficiently find a local minimum with respect to two types of large moves, namely expansion moves and swap moves. These moves can simultaneously change the labels of arbitrarily large sets of pixels. In contrast, many standard algorithms (including simulated annealing) use small moves where only one pixel changes its label at a time. Our expansion algorithm finds a labeling within a known factor of the global minimum, while our swap algorithm handles more general energy functions. Both of these algorithms allow important cases of discontinuity preserving energies. We experimentally demonstrate the effectiveness of our approach for image restoration, stereo and motion. On real data with ground truth, we achieve 98 percent accuracy.

2015 IEEE International Conference on Computer Vision (ICCV), 2015

Formulations of the image decomposition problem [7] as a multicut problem (MP) w.r.t. a superpixel graph have received considerable attention. In contrast, instances of the MP w.r.t. a pixel grid graph have received little attention, firstly, because the MP is NP-hard and instances w.r.t. a pixel grid graph are hard to solve in practice, and, secondly, due to the lack of long-range terms in the objective function of the MP. We propose a generalization of the MP with longrange terms (LMP). We design and implement two efficient algorithms (primal feasible heuristics) for the MP and LMP which allow us to study instances of both problems w.r.t. the pixel grid graphs of the images in the BSDS-500 benchmark [7]. The decompositions we obtain do not differ significantly from the state of the art at the time of writing, suggesting that the LMP is a competitive formulation of the image decomposition problem. To demonstrate the generality of the LMP formulation, we apply it also to the mesh decomposition problem posed by the Princeton benchmark [15], obtaining state-of-the-art decompositions.

Image Processing & Communications, 2014

When applied to the segmentation of 3D medical images, graph-cut segmentation algorithms require an extreme amount of memory and time resources in order to represent the image graph and to perform the necessary processing on the graph. These requirements actually exclude the graph-cut based approaches from their practical application. Hence, there is a need to develop the dedicated graph size reduction methods. In this paper, several techniques for the graph size reduction are proposed. These apply the idea of superpixels. In particular, two methods for superpixel creation are introduced. The results of applying the proposed methods to the segmentation of CT datasets using min-cut/max-flow algorithm are presented, compared and discussed.

IEEE Transactions on Pattern Analysis and Machine Intelligence, 2000

A new framework is presented for both understanding and developing graph-cut based combinatorial algorithms suitable for the approximate optimization of a very wide class of MRFs that are frequently encountered in computer vision. The proposed framework utilizes tools from the duality theory of linear programming in order to provide an alternative and more general view of state-of-the-art techniques like the α-expansion algorithm, which is included merely as a special case. Moreover, contrary to αexpansion, the derived algorithms generate solutions with guaranteed optimality properties for a much wider class of problems, e.g. even for MRFs with non-metric potentials. In addition, they are capable of providing per-instance suboptimality bounds in all occasions, including discrete Markov Random Fields with an arbitrary potential function. These bounds prove to be very tight in practice (i.e. very close to 1), which means that the resulting solutions are almost optimal. Our algorithms' effectiveness is demonstrated by presenting experimental results on a variety of low level vision tasks, such as stereo matching, image restoration, image completion and optical flow estimation, as well as on synthetic problems.

Journal of Real-Time Image Processing, 2013

Rapid advances in image acquisition and storage technology underline the need for algorithms that are capable of solving large scale image processing and computer-vision problems. The minimum cut problem plays an important role in processing many of these imaging problems such as, image and video segmentation, stereo vision, multi-view reconstruction and surface fitting. While several min-cut/max-flow algorithms can be found in the literature, their performance in practice has been studied primarily outside the scope of computer vision. We present here the results of a comprehensive computational study, in terms of execution times and memory utilization, of the four leading published algorithms, which optimally solve the s-t cut and maximum flow problems: (i) Goldberg's and Tarjan's Push-Relabel; (ii) Hochbaum's pseudoflow; (iii) Boykov's and Kolmogorov's augmenting paths; and (iv) Goldberg's partial augment-relabel. Our results demonstrate that while the augmenting paths algorithm is more suited for small problem instances or for problems with short paths from s to t, the pseudoflow algorithm, is more suited for large general problem instances and utilizes less memory than the other algorithms on all problem instances investigated.

2006

Abstract. Image segmentation using graph cuts have become very popular in the last years. These methods are computationally expensive, even with hard constraints (seed pixels). We present a solution that runs in time proportional to the number of pixels. Our method computes an ordered region growing from a set of seeds inside the object, where the propagation order of each pixel is proportional to the cost of an optimum path in the image graph from the seed set to that pixel.

Computing Research Repository - CORR, 2010

Maximum flow (and minimum cut) algorithms have had a strong impact on computer vision. In particular, graph cuts algorithms provide a mechanism for the discrete optimization of an energy functional which has been used in a variety of applications such as image segmentation, stereo, image stitching and texture synthesis. Algorithms based on the classical formulation of max-flow defined on a graph are known to exhibit grid (metrication) bias in the solution. Therefore, a recent trend has been to instead employ a spatially continuous maximum flow (or the dual min-cut problem) in these same applications to produce solutions with no grid bias. However, known fast continuous max-flow algorithms have no stopping criteria or have not been proved to converge. In this work, we revisit the continuous max-flow problem and show that the analogous discrete formulation is different from the classical max-flow problem. We then apply an appropriate combinatorial optimization technique to this combin...

Computer Vision and Image Understanding, 2008

Topology is an important prior in many image segmentation tasks. In this paper, we design and implement a novel graph-based min-cut/max-flow algorithm that incorporates topology priors as global constraints. We show that the optimization of the energy function we consider here is NP-hard. However, our algorithm is guaranteed to find an approximate solution that conforms to the initialization, which is a desirable property in many applications since the globally optimum solution does not consider any initialization information. The key innovation of our algorithm is the organization of the search for maximum flow in a way that allows consideration of topology constraints. In order to achieve this, we introduce a label attribute for each node to explicitly handle the topology constraints, and we use a distance map to keep track of those nodes that are closest to the boundary. We employ the bucket priority queue data structure that records nodes of equal distance and we efficiently extract the node with minimal distance value. Our methodology of embedding distance functions in a graph-based algorithm is general and can also account for other geometric priors. Experimental results show that our algorithm can efficiently handle segmentation cases that are challenging for graph-cut algorithms. Furthermore, our algorithm is a natural choice for problems with rich topology priors such as object tracking.

Image Processing, 2005. ICIP 2005. …, 2005

Fundamental to any graph cut segmentation methods is the assignment of edge weights. The existing solutions typically use gaussian, exponential or rectangular cost functions with a parameter chosen in an ad-hoc fashion. We demonstrate the importance of the shape of the cost function in images of convoluted shaped objects. Our asymptotical analysis and empirical results show that the gaussian cost function outperforms the rectangular and exponential cost functions. For the gaussian cost function we construct a theoretical framework to determine the optimal value of its parameter based on the image data and shape complexity.

2008

In the last decade, graph-cut optimization has been popular for a variety of pixel labeling problems. Typically graph-cut methods are used to incorporate a smoothness prior on a labeling. Recently several methods incorporated ordering constraints on labels for the application of object segmentation. An example of an ordering constraint is prohibiting a pixel with a "car wheel" label to be above a pixel with a "car roof" label. We observe that the commonly used graph-cut based α-expansion is more likely to get stuck in a local minimum when ordering constraints are used. For certain models with ordering constraints, we develop new graph-cut moves which we call order-preserving moves. Order-preserving moves act on all labels, unlike αexpansion. Although the global minimum is still not guaranteed, optimization with order-preserving moves performs significantly better than α-expansion. We evaluate orderpreserving moves for the geometric class scene labeling (introduced by Hoiem et al.) where the goal is to assign each pixel a label such as "sky", "ground", etc., so ordering constraints arise naturally. In addition, we use orderpreserving moves for certain simple shape priors in graphcut segmentation, which is a novel contribution in itself.