## An efficient algorithm for Co-segmentation

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Citations: | 28 - 2 self |

### BibTeX

@MISC{Hochbaum_anefficient,

author = {Dorit S. Hochbaum and Vikas Singh},

title = {An efficient algorithm for Co-segmentation},

year = {}

}

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### Abstract

This paper is focused on the Co-segmentation problem [1] – where the objective is to segment a similar object from a pair of images. The background in the two images may be arbitrary; therefore, simultaneous segmentation of both images must be performed with a requirement that the appearance of the two sets of foreground pixels in the respective images are consistent. Existing approaches [1, 2] cast this problem as a Markov Random Field (MRF) based segmentation of the image pair with a regularized difference of the two histograms – assuming a Gaussian prior on the foreground appearance [1] or by calculating the sum of squared differences [2]. Both are interesting formulations but lead to difficult optimization problems, due to the presence of the second (histogram difference) term. The model proposed here bypasses measurement of the histogram differences in a direct fashion; we show that this enables obtaining efficient solutions to the underlying optimization model. Our new algorithm is similar to the existing methods in spirit, but differs substantially in that it can be solved to optimality in polynomial time using a maximum flow procedure on an appropriately constructed graph. We discuss our ideas and present promising experimental results. 1.

### Citations

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Citation Context ...milarity in (3) as a bias term. 3.1. MRF segmentation We formulate the task of segmenting both images as a binary labeling of Markov Random Field (MRF) on the graphs corresponding to the input images =-=[17, 18]-=-. That is, in each image I, we find the assignment of values to every pixel, as either foreground or background label. This is represented by a binary variable xj assigned to each pixel j and is equal... |

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Citation Context ...ation problem of) co-segmentation. The identification of similar objects in more than one image is a fundamental problem in computer vision and has relied on user annotation or construction of models =-=[8, 9]-=-. A number of recent techniques [1, 10, 11, 12], however, have preferred an unsupervised (or semi-supervised) approach to the problem and obtained good overall performance. Cosegmentation belongs to t... |

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Citation Context ...ation problem of) co-segmentation. The identification of similar objects in more than one image is a fundamental problem in computer vision and has relied on user annotation or construction of models =-=[8, 9]-=-. A number of recent techniques [1, 10, 11, 12], however, have preferred an unsupervised (or semi-supervised) approach to the problem and obtained good overall performance. Cosegmentation belongs to t... |

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Citation Context ...em was partly motivated in [1] by the need for computing meaningful similarity measures between images of the same subject but with different (and unrelated) backdrops in image retrieval applications =-=[3]-=-. A related goal was to facilitate segmentation of an object (or a region of interest) by providing minimal additional information (such as just one additional image). The Figure 1. A similar object i... |

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Citation Context ... identification of similar objects in more than one image is a fundamental problem in computer vision and has relied on user annotation or construction of models [8, 9]. A number of recent techniques =-=[1, 10, 11, 12]-=-, however, have preferred an unsupervised (or semi-supervised) approach to the problem and obtained good overall performance. Cosegmentation belongs to this second category. The key idea adopted in [1... |

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Citation Context ...al histogram buckets. We note that treating |F1| = |F2| as normalization constants for a and b resp., this is also similar to Hellinger affinity (see [15], pg. 24), frequently used in computer vision =-=[16]-=-. 3. Problem Statement Maximizing similarity of histograms as in (3), by itself is not sufficient to obtain meaningful segmentations. This is because Co-segmentation must take the spatial homogeneity ... |

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Citation Context ...at the dependence of the results on some user tunable parameters. In the experiments described here, we used histograms derived from the image intensity values and Gabor filter based texture features =-=[20]-=-. Our method is transparent of the underlying appearance model (i.e., parameterization of its distribution), and other texture representations [21] can be used easily, if desired. For comparisons with... |

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Citation Context ... identification of similar objects in more than one image is a fundamental problem in computer vision and has relied on user annotation or construction of models [8, 9]. A number of recent techniques =-=[1, 10, 11, 12]-=-, however, have preferred an unsupervised (or semi-supervised) approach to the problem and obtained good overall performance. Cosegmentation belongs to this second category. The key idea adopted in [1... |

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Citation Context ...nsity values and Gabor filter based texture features [20]. Our method is transparent of the underlying appearance model (i.e., parameterization of its distribution), and other texture representations =-=[21]-=- can be used easily, if desired. For comparisons with existing techniques, we used an implementation of the algorithm in [1]: we start with a segmentation of the two images using graph cuts, and then ... |

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Citation Context ..., Berkeley Vikas Singh www.biostat.wisc.edu/∼vsingh Biostatistics & Medical Informatics, and Computer Sciences Univ. of Wisconsin–Madison Abstract This paper is focused on the Co-segmentation problem =-=[1]-=- – where the objective is to segment a similar object from a pair of images. The background in the two images may be arbitrary; therefore, simultaneous segmentation of both images must be performed wi... |

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Citation Context ... identification of similar objects in more than one image is a fundamental problem in computer vision and has relied on user annotation or construction of models [8, 9]. A number of recent techniques =-=[1, 10, 11, 12]-=-, however, have preferred an unsupervised (or semi-supervised) approach to the problem and obtained good overall performance. Cosegmentation belongs to this second category. The key idea adopted in [1... |

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Citation Context ... of pixel pairs (one from each image) with identical histogram buckets. We note that treating |F1| = |F2| as normalization constants for a and b resp., this is also similar to Hellinger affinity (see =-=[15]-=-, pg. 24), frequently used in computer vision [16]. 3. Problem Statement Maximizing similarity of histograms as in (3), by itself is not sufficient to obtain meaningful segmentations. This is because ... |

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Citation Context ... replacing the second term with the squared difference of the two histograms. This approach no longer requires the histograms to be Gaussian, and leads to a quadratic pseudoboolean optimization model =-=[14]-=-. The authors prove that their formulation yields half-integral solutions (i.e., {0, 1 2 , 1}) to the optimization problem. However, the problem still remains hard (and cannot be solved optimally), an... |

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Citation Context ...n our experiments, λ = 0.001 worked well). We note, however, that it is easy to make this procedure rigorous if desired. This involves parameterizing λ, solving a single parametric max-flow procedure =-=[22, 23]-=-, and finding the correlation coefficient of the two foreground regions for each breakpoint. Number of histogram buckets. The number of histogram buckets should be chosen such that the corresponding s... |

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Citation Context ...milarity in (3) as a bias term. 3.1. MRF segmentation We formulate the task of segmenting both images as a binary labeling of Markov Random Field (MRF) on the graphs corresponding to the input images =-=[17, 18]-=-. That is, in each image I, we find the assignment of values to every pixel, as either foreground or background label. This is represented by a binary variable xj assigned to each pixel j and is equal... |

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Citation Context ... of other concurrent foreground extraction tasks using multiple images [4], images acquired with/without camera flash [5], image sequences [6], and for identifying individuals using image collections =-=[7]-=-. Later in the paper, we discuss how the idea may be applied for pathology identification problems in biomedical images. The purpose of this paper, however, is to investigate efficient means of solvin... |

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Citation Context ...tive to [1, 13]. However, the technique [4] was focused on the empirical performance, and less effort was devoted toward better means of optimizing the co-segmentation cost function in [1]. Recently, =-=[2]-=- proposes addressing some of these difficulties by replacing the second term with the squared difference of the two histograms. This approach no longer requires the histograms to be Gaussian, and lead... |

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Citation Context ...n our experiments, λ = 0.001 worked well). We note, however, that it is easy to make this procedure rigorous if desired. This involves parameterizing λ, solving a single parametric max-flow procedure =-=[22, 23]-=-, and finding the correlation coefficient of the two foreground regions for each breakpoint. Number of histogram buckets. The number of histogram buckets should be chosen such that the corresponding s... |

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Citation Context ... as large as possible (that is 1) and yij to be as small as possible (that is 0). It is not difficult to verify that: Property 3.1 The model of the (Co-seg) problem is defined on monotone constraints =-=[19]-=- and with a totally unimodular constraint matrix. Due to Property 3.1, we can make use of a construction of an s, t graph G, where the solution to the s, t-cut problem will provide an optimal solution... |

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Citation Context ...the authors in [4] extended many of these ideas further by incorporating local context, i.e., patterns characterizing the local color and edge configurations. This led to improved results relative to =-=[1, 13]-=-. However, the technique [4] was focused on the empirical performance, and less effort was devoted toward better means of optimizing the co-segmentation cost function in [1]. Recently, [2] proposes ad... |

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Citation Context ...foreground (of row 2 images) is shown in row 3. idea has been utilized in a number of other concurrent foreground extraction tasks using multiple images [4], images acquired with/without camera flash =-=[5]-=-, image sequences [6], and for identifying individuals using image collections [7]. Later in the paper, we discuss how the idea may be applied for pathology identification problems in biomedical image... |

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Citation Context ...n two images in rows 1-2. The histogram of the foreground (of row 2 images) is shown in row 3. idea has been utilized in a number of other concurrent foreground extraction tasks using multiple images =-=[4]-=-, images acquired with/without camera flash [5], image sequences [6], and for identifying individuals using image collections [7]. Later in the paper, we discuss how the idea may be applied for pathol... |

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Citation Context ...images) is shown in row 3. idea has been utilized in a number of other concurrent foreground extraction tasks using multiple images [4], images acquired with/without camera flash [5], image sequences =-=[6]-=-, and for identifying individuals using image collections [7]. Later in the paper, we discuss how the idea may be applied for pathology identification problems in biomedical images. The purpose of thi... |