## Joint optimization of segmentation and appearance models (2009)

Citations: | 24 - 3 self |

### BibTeX

@TECHREPORT{Vicente09jointoptimization,

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

title = {Joint optimization of segmentation and appearance models},

institution = {},

year = {2009}

}

### OpenURL

### Abstract

Many interactive image segmentation approaches use an objective function which includes appearance models as an unknown variable. Since the resulting optimization problem is NP-hard the segmentation and appearance are typically optimized separately, in an EM-style fashion. One contribution of this paper is to express the objective function purely in terms of the unknown segmentation, using higher-order cliques. This formulation reveals an interesting bias of the model towards balanced segmentations. Furthermore, it enables us to develop a new dual decomposition optimization procedure, which provides additionally a lower bound. Hence, we are able to improve on existing optimizers, and verify that for a considerable number of real world examples we even achieve global optimality. This is important since we are able, for the first time, to analyze the deficiencies of the model. Another contribution is to establish a property of a particular dual decomposition approach which involves convex functions depending on foreground area. As a consequence, we show that the optimal decomposition for our problem can be computed efficiently via a parametric maxflow algorithm. 1.

### Citations

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Citation Context ... Also we perform parametric maxflow iterations in the inner loop of the procedure in section 4.1 rather than in the outer loop; the latter could be faster. Finally, the maxflow algorithm that we used =-=[6]-=- does not appear to handle well nodes with high degree. 5These were the images where EM achieves the global optimum.error rate is 10.5% for dual decomposition, while for EM it is 8.1%. The dual decom... |

779 | A.: Grabcut: Interactive foreground extraction using iterated graph cuts
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Citation Context ..., with additional user guidance. The ultimate goal is to minimize the user interaction and to maximize the quality of the segmentation. Therefore, it is very common to exploit appearance models, e.g. =-=[5, 15, 11, 14]-=-, to distinguish better the foreground from the background segment. An appearance model is a statistical model for the color, texture, etc. of the pixels of the segment. The usage of appearance models... |

754 | P.: Interactive graph cuts for optimal boundary and region segmentation of objects in N-D images
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Citation Context ..., with additional user guidance. The ultimate goal is to minimize the user interaction and to maximize the quality of the segmentation. Therefore, it is very common to exploit appearance models, e.g. =-=[5, 15, 11, 14]-=-, to distinguish better the foreground from the background segment. An appearance model is a statistical model for the color, texture, etc. of the pixels of the segment. The usage of appearance models... |

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Citation Context ...otes the dot product between two vectors. In other words, we added unary terms to one subproblem and subtracted them from the other one. This is a standard use of the DD approach for MRF optimization =-=[19, 16, 17, 9, 20]-=-. Taking the minimum of each term in (9) over x gives a lower bound on E(x): Φ(y) = min[E x 1 (x)−〈y, x〉] } {{ } Φ1 (y) + min x [E 2 (x)+〈y, x〉] } {{ } Φ 2 (y) ≤ min E(x) (10) x Note that both minima ... |

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Citation Context ...otes the dot product between two vectors. In other words, we added unary terms to one subproblem and subtracted them from the other one. This is a standard use of the DD approach for MRF optimization =-=[19, 16, 17, 9, 20]-=-. Taking the minimum of each term in (9) over x gives a lower bound on E(x): Φ(y) = min[E x 1 (x)−〈y, x〉] } {{ } Φ1 (y) + min x [E 2 (x)+〈y, x〉] } {{ } Φ 2 (y) ≤ min E(x) (10) x Note that both minima ... |

43 | Applications of parametric maxflow in computer vision
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Citation Context ...points of λ. Accordingly, function minx[E1 (x) − λ〈1, x〉] is a piecewise-linear concave function. All solutions and breakpoints can be computed efficiently by a divide-and-conquer algorithm (see e.g. =-=[8]-=- for a review). The second function can also be handled efficiently. It is not difficult to show that if E2 (x) =h( ∑ p∈V xp) then minx[E2 (x)+λ〈1, x〉] is a piecewise-linear concave function with brea... |

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Citation Context ...nd segmentation system. • The appearance is fixed, based on the user input. For instance [5, 14] used color model from user-labeled pixels. • The appearance is optimized jointly with the segmentation =-=[15, 10, 1]-=-, allowing to choose from a set of models the one that best fits the segments. This paper considers the most challenging third option. The advantage is that in the absence of apriori information (firs... |

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Citation Context ..., with additional user guidance. The ultimate goal is to minimize the user interaction and to maximize the quality of the segmentation. Therefore, it is very common to exploit appearance models, e.g. =-=[5, 15, 11, 14]-=-, to distinguish better the foreground from the background segment. An appearance model is a statistical model for the color, texture, etc. of the pixels of the segment. The usage of appearance models... |

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Citation Context ...nd segmentation system. • The appearance is fixed, based on the user input. For instance [5, 14] used color model from user-labeled pixels. • The appearance is optimized jointly with the segmentation =-=[15, 10, 1]-=-, allowing to choose from a set of models the one that best fits the segments. This paper considers the most challenging third option. The advantage is that in the absence of apriori information (firs... |

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