A Gradient Descent Approximation for Graph Cuts

2008

Graph cut is a popular technique for interactive image segmentation. However, it has certain shortcomings. In particular, graph cut has problems with segmenting thin elongated objects due to the "shrinking bias". To overcome this problem, we propose to impose an additional connectivity prior, which is a very natural assumption about objects. We formulate several versions of the connectivity constraint and show that the corresponding optimization problems are all NP-hard.

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.

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.

Medical image computing and computer-assisted intervention : MICCAI ... International Conference on Medical Image Computing and Computer-Assisted Intervention, 2011

Though graph cut based segmentation is a widely-used technique, it is known that segmentation of a thin, elongated structure is challenging due to the "shrinking problem". On the other hand, many segmentation targets in medical image analysis have such thin structures. Therefore, the conventional graph cut method is not suitable to be applied to them. In this study, we developed a graph cut segmentation method with novel Riemannian metrics. The Riemannian metrics are determined from the given "initial contour," so that any level-set surface of the distance transformation of the contour has the same surface area in the Riemannian space. This will ensure that any shape similar to the initial contour will not be affected by the shrinking problem. The method was evaluated with clinical CT datasets and showed a fair result in segmenting vertebral bones.

2012

ABSTRACT We present a general graph-cut segmentation framework GGC, in which the delineated objects returned by the algorithms optimize the energy functions associated with the lp norm, 1≤ p≤∞. Two classes of well known algorithms belong to GGC: the standard graph cut GC (such as the min-cut/max-flow algorithm) and the relative fuzzy connectedness algorithms RFC (including iterative RFC, IRFC).

International Journal for Research in Applied Science and Engineering Technology

In image processing, segmentation is the process of partitioning digital image into multiple sets of pixels, according to some homogeneity standard. The goal of segmentation is to simplify or change the representation of an image into something that is more meaningful and easier to analyze. Segmentation by computing a minimal cut in a graph is a new and quite general approach for segmenting images. This approach guarantees global solutions, which always find best solution. Graph cut has emerged as a preferred method to solve a class of energy minimization problems such as Image Segmentation. In this paper we used graph cut method to solve image segmentation problem and we got successful results in image segmentation. In this project we proposed a new approach by using optimized normalized cut with combination with K-means algorithm to do the segmentation of static image. In this method we used efficient computational technique based on eigen values and eigen vectors to get optimized segmented image.

2007 IEEE 11th International Conference on Computer Vision, 2007

Capacity scaling is a hierarchical approach to graph representation that can improve theoretical complexity and practical efficiency of max-flow/min-cut algorithms. Introduced by Edmonds, Karp, and Dinic [7, 6] in 1972, capacity scaling is well known in the combinatorial optimization community. Surprisingly, this major performance improving technique is overlooked in computer vision where graph cut methods typically solve energy minimization problems on huge N-D grids and algorithms' efficiency is a widely studied issue [3, 12, 16, 10]. Unlike some earlier hierarchical methods addressing efficiency of graph cuts in imaging, e.g. [16], capacity scaling preserves global optimality of the solution. This is the main motivation for our work studying capacity scaling in the context of vision. We show that capacity scaling significantly reduces non-polynomial theoretical time complexity of the max-flow algorithm in [3] to weakly polynomial O(m 2 n 2 log(U)) where U is the largest edge weight. While [3] is the fastest method for many applications in vision, capacity scaling gives several folds speed-ups for problems with large number of local minima. The effect is particularly strong in 3D applications with denser neighborhoods.

An image can be considered as a group of nodes as vertices and edges as links. Various techniques are formed based upon this assumption and energy minimization. Graph cut is one of the promising techniques for image segmentation. Boykov and Kolmogorov use mincut/ maxflow graph principal for image segmentation. We have discussed some other techniques such as grab cut which is user interactive and very effective technique. In last the current problems were also highlighted.

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.

Procedings of the British Machine Vision Conference 2008, 2008

The graph cut based approach has become very popular for interactive segmentation of the object of interest from the background. One of the most important and yet largely unsolved issues in the graph cut segmentation framework is parameter selection. Parameters are usually fixed beforehand by the developer of the algorithm. There is no single setting of parameters, however, that will result in the best possible segmentation for any general image. Usually each image has its own optimal set of parameters. If segmentation of an image is not as desired under the current setting of parameters, the user can always perform more interaction until the desired results are achieved. However, significant interaction may be required if parameter settings are far from optimal. In this paper, we develop an algorithm for automatic parameter selection. We design a measure of segmentation quality based on different features of segmentation that are combined using AdaBoost. Then we run the graph cut segmentation algorithm for different parameter values and choose the segmentation of highest quality according to our learnt measure. We develop a new way to normalize feature weights for the AdaBoost based classifier which is particularly suitable for our framework. Experimental results show a success rate of 95.6% for parameter selection.