## Graph cut based image segmentation with connectivity priors (2008)

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Citations: | 52 - 4 self |

### BibTeX

@TECHREPORT{Vicente08graphcut,

author = {Sara Vicente and Vladimir Kolmogorov and Carsten Rother},

title = {Graph cut based image segmentation with connectivity priors},

institution = {},

year = {2008}

}

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### Abstract

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. For some of these versions we propose two optimization algorithms: (i) a practical heuristic technique which we call DijkstraGC, and (ii) a slow method based on problem decomposition which provides a lower bound on the problem. We use the second technique to verify that for some practical examples DijkstraGC is able to find the global minimum. 1.

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Citation Context ...we developed a second (slow) technique based on dual decomposition, which provides a lower bound on the problem. Related work Connectivity is automatically enforced in the classical “snakes” approach =-=[11]-=-, since the segmentation is represented by a simple closed contour. Han et al. [9] proposed a topology preserving level set method which allows to specify more general topologies. A disadvantage of bo... |

2757 | Normalized cuts and image segmentation
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Citation Context ...the issue of choosing a good vector field for color images remains. Other interesting approaches include the method in [21] which imposes a prior on the curvature of the boundary, spectral techniques =-=[22]-=- and the random walker algorithm [6]; results in [24] indicate that this method is slightly more robust towards the shrinking bias. Our approach In this paper we propose a very different way to solve ... |

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Citation Context ...ll help us to verify that for some instances DijkstraGC gives an optimal solution. 3.1. DijkstraGC: Merging Dijkstra and graph cuts The idea of our first method is motivated by the Dijkstra algorithm =-=[1]-=-. Recall that the latter technique computes shortest distances d(p) in a directed graph with nonnegative weights from a specified “source” node s to all other nodes p. Similar to the Dijkstra method, ... |

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Citation Context ...verify that for some practical examples DijkstraGC is able to find the global minimum. 1. Introduction The task of interactive image segmentation has attracted a significant attention in recent years =-=[10, 3, 18, 6, 24, 21]-=-. The ultimate goal is to extract an object with as few user interactions as possible. It is widely accepted that some prior on segmentations is needed for achieving this goal. Different priors have a... |

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Citation Context ...verify that for some practical examples DijkstraGC is able to find the global minimum. 1. Introduction The task of interactive image segmentation has attracted a significant attention in recent years =-=[10, 3, 18, 6, 24, 21]-=-. The ultimate goal is to extract an object with as few user interactions as possible. It is widely accepted that some prior on segmentations is needed for achieving this goal. Different priors have a... |

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Citation Context ...chieving this goal. Different priors have a preference towards different types of shapes, as we discuss next. Graph cut A very popular approach, which we also use in this paper, is based on graph cut =-=[7, 3, 18]-=-. It minimizes an energy function consisting of a data term (computed using color likelihoods of foreground and background) and a spatial coherency term. The latter term is the length of the boundary ... |

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Citation Context ... [27] who decomposed the problem into a convex combination of trees and proposed message passing techniques for optimizing vector θ. These techniques do not necessarily find the best lower bound (see =-=[14]-=- or review article [28]). Schlesinger and Giginyak [19, 20] and Komodakis et al. [17] proposed to use subgradient techniques [23, 2] for MRF optimization, which guarantee to converge to a vector θ yie... |

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Citation Context ...verify that for some practical examples DijkstraGC is able to find the global minimum. 1. Introduction The task of interactive image segmentation has attracted a significant attention in recent years =-=[10, 3, 18, 6, 24, 21]-=-. The ultimate goal is to extract an object with as few user interactions as possible. It is widely accepted that some prior on segmentations is needed for achieving this goal. Different priors have a... |

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Citation Context ...e problem into a convex combination of trees and proposed message passing techniques for optimizing vector θ. These techniques do not necessarily find the best lower bound (see [14] or review article =-=[28]-=-). Schlesinger and Giginyak [19, 20] and Komodakis et al. [17] proposed to use subgradient techniques [23, 2] for MRF optimization, which guarantee to converge to a vector θ yielding the best possible... |

107 | Flux Maximizing Geometric Flows
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Citation Context ...d regularization, and it indicates that some form of coherency is crucial. Alternative segmentation models One approach to overcome the shrinking bias is to add flux of some vector field to the model =-=[10, 25, 12, 15]-=-. It has been shown to be effective for segmenting thin objects such as blood vessels in grayscale images [25]. The vector field was taken as the image gradient, which corresponds to the assumption th... |

90 | A topology preserving level set method for geometric deformable models
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Citation Context ...a lower bound on the problem. Related work Connectivity is automatically enforced in the classical “snakes” approach [11], since the segmentation is represented by a simple closed contour. Han et al. =-=[9]-=- proposed a topology preserving level set method which allows to specify more general topologies. A disadvantage of both techniques is that the objective is optimized via gradient descent, which can e... |

86 | L.: Fast extraction of minimal paths in 3D images and applications to virtual endoscopy
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Citation Context ...which we call DijkstraGC. On an abstract level it merges the Dijkstra algorithm and graph cut. Note that Dijkstra-like methods have already been used for extracting thin objects such as blood vessels =-=[5]-=-, although without an explicit segmentation. (A fast marching technique was used in [5], which can be viewed as a continuous analogue of the Dijkstra algorithm for discrete graphs.) The key feature of... |

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Citation Context ...age passing techniques for optimizing vector θ. These techniques do not necessarily find the best lower bound (see [14] or review article [28]). Schlesinger and Giginyak [19, 20] and Komodakis et al. =-=[17]-=- proposed to use subgradient techniques [23, 2] for MRF optimization, which guarantee to converge to a vector θ yielding the best possible lower bound. Solving P1 via problem decomposition We now appl... |

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Citation Context ... graph from a set of nodes “behind” node s to a set of nodes “behind” node t. (This is motivated by the 2 Instead of restricting function E 0 to be submodular, one could use the roof duality approach =-=[8]-=- to get a lower bound on E 0 (x | θ). For submodular functions this lower bound coincides with the global minimum, therefore the best lower bound on the original function can only become better. We ha... |

65 | A seeded image segmentation framework unifying graph cuts and random walker which yields a new algorithm, in: ICCV
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53 | Efficiently solving dynamic markov random fields using graph cuts
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Citation Context ...certain selection rule DijkstraGC becomes equivalent to the algorithm in Fig. 4. Flow and search tree recycling We used the maxflow algorithm in [4], and reused flows and search trees as described in =-=[13]-=-. In DijkstraGC we often need to fix/unfix nodes in different parts of the graph in a rather chaotic order. We believe that this significantly reduces the effectiveness of flow and search tree recycli... |

50 | BOYKOV Y.: What metrics can be approximated by geo-cuts, or global optimization of length/area and flux
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Citation Context ...d regularization, and it indicates that some form of coherency is crucial. Alternative segmentation models One approach to overcome the shrinking bias is to add flux of some vector field to the model =-=[10, 25, 12, 15]-=-. It has been shown to be effective for segmenting thin objects such as blood vessels in grayscale images [25]. The vector field was taken as the image gradient, which corresponds to the assumption th... |

40 | Applications of parametric maxflow in computer vision
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Citation Context ...overcome in the level set framework [12], but at the expense of losing global optimality. One possible method to integrate flux into segmentation is to optimize the ratio of flux over boundary length =-=[10, 16]-=-. Thus, we are looking for the boundary with the highest average contrast. Arguably, this model has no bias towards any particular shape [10, 16]. However, the issue of choosing a good vector field fo... |

14 |
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Citation Context ...d regularization, and it indicates that some form of coherency is crucial. Alternative segmentation models One approach to overcome the shrinking bias is to add flux of some vector field to the model =-=[10, 25, 12, 15]-=-. It has been shown to be effective for segmenting thin objects such as blood vessels in grayscale images [25]. The vector field was taken as the image gradient, which corresponds to the assumption th... |

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Citation Context ...ion of trees and proposed message passing techniques for optimizing vector θ. These techniques do not necessarily find the best lower bound (see [14] or review article [28]). Schlesinger and Giginyak =-=[19, 20]-=- and Komodakis et al. [17] proposed to use subgradient techniques [23, 2] for MRF optimization, which guarantee to converge to a vector θ yielding the best possible lower bound. Solving P1 via problem... |

12 | Topology cuts: a novel min-cut/maxflow algorithm for topology preserving segmentation
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Citation Context ...ows to specify more general topologies. A disadvantage of both techniques is that the objective is optimized via gradient descent, which can easily get stuck in a local minimum. Recently, Zeng et al. =-=[29]-=- followed a similar approach with a discrete graph-based formulation. After posing the problem the authors of [29] proved an NP-hardness result and proposed to modify the maxflow algorithm in [4] so t... |

4 |
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