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## Graph Cut based Inference with Co-occurrence Statistics

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Citations: | 100 - 13 self |

### Citations

3787 | Normalized cuts and image segmentation.
- Shi, Malik
- 2000
(Show Context)
Citation Context ...ensitive Conditional Random Field CRF [19]. The majority of mid-level inference schemes [25,20] do not consider pixels directly, rather they assume that the image has been segmented into super-pixels =-=[5,8,28]-=-. A labelling problem is then defined over the set of regions. A significant disadvantage of such approaches is that mistakes in the initial over-segmentation, in which regions span multiple object cl... |

3483 | Conditional random fields: Probabilistic models for segmenting and labeling sequence datasets
- Lafferty, McCallum, et al.
- 2001
(Show Context)
Citation Context ...on, and texton response are used to learn a classifier which provides costs for a single pixel taking a particular label. These costs are combined in a contrast sensitive Conditional Random Field CRF =-=[19]-=-. The majority of mid-level inference schemes [25,20] do not consider pixels directly, rather they assume that the image has been segmented into super-pixels [5,8,28]. A labelling problem is then defi... |

2395 | Mean shift: A robust approach toward feature space analysis
- Comaniciu, Meer
- 2002
(Show Context)
Citation Context ...ensitive Conditional Random Field CRF [19]. The majority of mid-level inference schemes [25,20] do not consider pixels directly, rather they assume that the image has been segmented into super-pixels =-=[5,8,28]-=-. A labelling problem is then defined over the set of regions. A significant disadvantage of such approaches is that mistakes in the initial over-segmentation, in which regions span multiple object cl... |

2120 | R.: Fast approximate energy minimization via graph cuts
- Boykov, Veksler, et al.
(Show Context)
Citation Context ...th the size of a fully connected graph. It grows with complexity O(|V| 2 ) rather than O(|V|) with the size of the graph, violating constraint (iii). Providing the pairwise potentials are semi-metric =-=[3]-=-, it does satisfy the parsimony condition (iv). To minimise these difficulties, previous approaches defined variables over segments rather than pixels. Such segment based methods work under the assump... |

940 | Efficient graph-based image segmentation
- Felzenszwalb, Huttenlocher
- 2004
(Show Context)
Citation Context ...ensitive Conditional Random Field CRF [19]. The majority of mid-level inference schemes [25,20] do not consider pixels directly, rather they assume that the image has been segmented into super-pixels =-=[5,8,28]-=-. A labelling problem is then defined over the set of regions. A significant disadvantage of such approaches is that mistakes in the initial over-segmentation, in which regions span multiple object cl... |

685 |
Learning with Kernels: Support Vector
- Schölkopf, Smola
- 2002
(Show Context)
Citation Context ...he potentials are defined over a clique of size at most 2. Unary potentials are defined over a clique of size one, and typically based upon classifier responses (such as ada-boost [29] or kernel SVMs =-=[27]-=-), while pairwise potentials are defined over cliques of size two and model the correlation between pairs of random variables. 2.1 Incorporating Co-occurrence Potentials To model object class co-occur... |

488 | Convergent tree-reweighted message passing for energy minimization
- Kolmogorov
(Show Context)
Citation Context ...proximately solved as an LP-relaxation [16]. This LP-formulation can be transformed using a Lagrangian relaxation into a pairwise energy, allowing algorithms, such as Belief Propagation [33] or TRW-S =-=[14]-=-, that can minimise arbitrary pairwise energies to be applied [16]. However, reparameterisation methods such as these perform badly on densely connected graphs [15,26]. In this section we show that un... |

426 | A.: textonBoost: Joint appearance, shape and context modeling for multi-class object recognition and segmentation.
- Shotton, Winn, et al.
- 2006
(Show Context)
Citation Context ... the labelling compared to just using a pairwise model. 1 Introduction Class based image segmentation is a highly active area of computer vision research as is shown by a spate of recent publications =-=[11,22,29,31,34]-=-. In this problem, every pixel of the image is assigned a choice of object class label, such as grass, person, or dining table. Formulating this problem as a likelihood, in order to perform inference,... |

415 | C.: A comparative study of energy minimization methods for Markov random fields with smoothness-based priors.
- Szeliski, Zabih, et al.
- 2008
(Show Context)
Citation Context .... (iii) Efficiency: Inference should be tractable, i.e. the use of co-occurrence should not be the bottle-neck preventing inference. As the memory requirements of any conventional inference algorithm =-=[30]-=- is typically O(|V|) for vision problems, the memory requirements of a formulation incorporating co-occurrence potentials should also be O(|V|). (iv) Parsimony: The cost should follow the principle of... |

317 | Context-based vision system for place and object recognition. In:
- Torralba, Murphy, et al.
- 2003
(Show Context)
Citation Context ... the labelling compared to just using a pairwise model. 1 Introduction Class based image segmentation is a highly active area of computer vision research as is shown by a spate of recent publications =-=[11,22,29,31,34]-=-. In this problem, every pixel of the image is assigned a choice of object class label, such as grass, person, or dining table. Formulating this problem as a likelihood, in order to perform inference,... |

315 | Using multiple segmentations to discover objects and their extent in image collections
- Russell, Efros, et al.
- 2006
(Show Context)
Citation Context ...fier which provides costs for a single pixel taking a particular label. These costs are combined in a contrast sensitive Conditional Random Field CRF [19]. The majority of mid-level inference schemes =-=[25,20]-=- do not consider pixels directly, rather they assume that the image has been segmented into super-pixels [5,8,28]. A labelling problem is then defined over the set of regions. A significant disadvanta... |

259 | Robust higher order potentials for enforcing label consistency. In: CVPR
- Kohli, Ladicky, et al.
- 2008
(Show Context)
Citation Context ...et Kohli, and Philip H.S. Torr L successively. The transformation function Tα(xi, ti) for an α-expansion move transforms the label of a random variable xi as: Tα(xi, ti) = { xi if ti = 0 α if ti = 1. =-=(13)-=- To derive a graph-construction that approximates the true cost of an α-expansion move we rewrite C(L) as: C(L) = ∑ kB, (14) B⊆L where the coefficients kB are calculated recursively as: kB = C(B) − ∑ ... |

241 | On the optimality of solutions of the max-product belief-propagation algorithm in arbitrary graphs. Information Theory,
- Weiss, Freeman
- 2001
(Show Context)
Citation Context ...program and approximately solved as an LP-relaxation [16]. This LP-formulation can be transformed using a Lagrangian relaxation into a pairwise energy, allowing algorithms, such as Belief Propagation =-=[33]-=- or TRW-S [14], that can minimise arbitrary pairwise energies to be applied [16]. However, reparameterisation methods such as these perform badly on densely connected graphs [15,26]. In this section w... |

174 | Decomposing a scene into geometric and semantically consistent regions.
- Gould, Fulton, et al.
- 2009
(Show Context)
Citation Context ... of regions. A significant disadvantage of such approaches is that mistakes in the initial over-segmentation, in which regions span multiple object classes, cannot be recovered from. To overcome this =-=[10]-=- proposed a method of reshaping super-pixels to recover from the errors, while the work [17] proposed a novel hierarchical framework which allowed for the integration of multiple region-based CRFs wit... |

172 | Associative hierarchical crfs for object class image segmentation.
- Ladicky, Russell, et al.
- 2009
(Show Context)
Citation Context ...ver-segmentation, in which regions span multiple object classes, cannot be recovered from. To overcome this [10] proposed a method of reshaping super-pixels to recover from the errors, while the work =-=[17]-=- proposed a novel hierarchical framework which allowed for the integration of multiple region-based CRFs with a low-level pixel based CRF, and the elimination of inconsistent regions. These approaches... |

131 | Learning spatial context: using stuff to find things
- Heitz, Koller
- 2008
(Show Context)
Citation Context ... the labelling compared to just using a pairwise model. 1 Introduction Class based image segmentation is a highly active area of computer vision research as is shown by a spate of recent publications =-=[11,22,29,31,34]-=-. In this problem, every pixel of the image is assigned a choice of object class label, such as grass, person, or dining table. Formulating this problem as a likelihood, in order to perform inference,... |

112 | S.: Objects in context. In:
- Rabinovich, Vedaldi, et al.
- 2007
(Show Context)
Citation Context |

110 | Fast approximate energy minimization with label costs.
- Delong, Osokin, et al.
- 2012
(Show Context)
Citation Context ...s in the labelling. The relationship between previous approaches and the desiderata can be seen in figure 2.6 Lubor Ladicky, Chris Russell, Pushmeet Kohli, and Philip H.S. Torr Two efficient schemes =-=[7,12]-=- have been proposed for the minimisation of the number of classes or objects present in a scene. While neither of them directly models class based co-occurrence relationships, their optimisation appro... |

109 | Object categorization using cooccurrence, location and appearance. In: CVPR
- Galleguillos, Rabinovich, et al.
- 2008
(Show Context)
Citation Context ...e pixel. As no cost function K(·) was proposed, it is open to debate if it satisfied (ii) or (iv). Method Global energy (i) Invariance (ii) Efficiency (iii) Parsimony (iv) Unary [31] ✗ ✗ ✓ ✗ Pairwise =-=[22,9,32]-=- ✓ ✗ ✗ ✓ Csurka [6] ✗ — ✓ — Our approach ✓ ✓ ✓ ✓ Fig. 2. A comparison of the capabilities of existing image co-occurrence formulations against our new approach. See section 2.2 for details. Rabinovich... |

95 | Exploiting hierarchical context on a large database of object categories.
- Choi, Lim, et al.
- 2010
(Show Context)
Citation Context ...ng in an image, cooccurrence potentials can also be used to impose an MDL 1 prior that encourages a parsimonious description of an image using fewer labels. As discussed eloquently in the recent work =-=[4]-=-, the need for a bias towards parsimony becomes increasingly important as the number of classes to be considered increases. Figure 1 illustrates the importance of co-occurrence statistics in image lab... |

67 | 3D LayoutCRF for multi-view object class recognition and segmentation.
- Hoiem, Rother, et al.
- 2007
(Show Context)
Citation Context ...s in the labelling. The relationship between previous approaches and the desiderata can be seen in figure 2.6 Lubor Ladicky, Chris Russell, Pushmeet Kohli, and Philip H.S. Torr Two efficient schemes =-=[7,12]-=- have been proposed for the minimisation of the number of classes or objects present in a scene. While neither of them directly models class based co-occurrence relationships, their optimisation appro... |

65 | Digital tapestry
- Rother, Kumar, et al.
- 2005
(Show Context)
Citation Context ...aph Cut based Inference with Co-occurrence Statistics 9 E(t) is, in general, a higher-order non-submodular energy, and intractable. However, when proposing moves we can use the procedure described in =-=[21,24]-=- and overestimate the cost of moving from the current solution. If k ′ ∏ B ≥ 0 the term kB l∈B δl(t) is supermodular, and can be over estimated by a linear function EB(t) such that EB(A) = k ′ ∏ B l∈B... |

52 | Shape guided object segmentation
- Borenstein, Malik
- 2006
(Show Context)
Citation Context ...s. A good labelling should take account of: low-level cues such as colour or texture [29], that govern the labelling of single pixels; mid-level cues such as region continuity, symmetry [23] or shape =-=[2]-=- that govern the assignment of regions within the image; and high-level statistics that encode inter-object relationships, such as which objects can occur together in a scene. This combination of cues... |

49 | Multiple class segmentation using a unified framework over mean-shift patches
- Yang, Meer, et al.
- 2007
(Show Context)
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40 |
where and how many? combining object detectors and crfs
- What
- 2010
(Show Context)
Citation Context ...ed in [17] and the inference method [26], which currently offers state of the art performance on the MSRC data set [29]. On the VOC data set, the baseline also makes use of the detector potentials of =-=[18]-=-. The costs C(L) were created from the training set as follows: let M be theGraph Cut based Inference with Co-occurrence Statistics 11 number of images, x (m) the ground truth labelling of an image m... |

31 | A submodular-supermodular procedure with applications to discriminative structure learning.
- Narasimhan, Bilmes
- 2005
(Show Context)
Citation Context ...aph Cut based Inference with Co-occurrence Statistics 9 E(t) is, in general, a higher-order non-submodular energy, and intractable. However, when proposing moves we can use the procedure described in =-=[21,24]-=- and overestimate the cost of moving from the current solution. If k ′ ∏ B ≥ 0 the term kB l∈B δl(t) is supermodular, and can be over estimated by a linear function EB(t) such that EB(A) = k ′ ∏ B l∈B... |

29 | An exact primal-dual penalty method approach to warmstarting interior-point methods for linear programming
- Benson, Shanno
- 2005
(Show Context)
Citation Context ... VOC2009 data set the average times were 107s and 388s for inference without respectively with co-occurrence costs. We compared the performance of α-expansion with LP relaxation using solver given in =-=[1]-=- for general co-occurrence potential on the sub-sampled images [16]. Both methods produced similar results in terms of energy, however α-expansion was approximately 42, 000 times faster.12 Lubor Ladi... |

28 | C.: Comparison of energy minimization algorithms for highly connected graphs
- Kolmogorov, Rother
(Show Context)
Citation Context ...as Belief Propagation [33] or TRW-S [14], that can minimise arbitrary pairwise energies to be applied [16]. However, reparameterisation methods such as these perform badly on densely connected graphs =-=[15,26]-=-. In this section we show that under assumption, that C(L) is monotonically increasing with respect to L, the problem can be solved efficiently using αβ-swap and αexpansion moves [3], where the number... |

26 | Combining Appearance Models and Markov Random Fields for Category Level Object Segmentation. In CVPR,
- Larlus, Jurie
- 2008
(Show Context)
Citation Context ...fier which provides costs for a single pixel taking a particular label. These costs are combined in a contrast sensitive Conditional Random Field CRF [19]. The majority of mid-level inference schemes =-=[25,20]-=- do not consider pixels directly, rather they assume that the image has been segmented into super-pixels [5,8,28]. A labelling problem is then defined over the set of regions. A significant disadvanta... |

22 | Random field model for integration of local information and global information. - Toyoda, Hasegawa - 2008 |

21 | A simple high performance approach to semantic segmentation
- Csurka, Perronnin
(Show Context)
Citation Context ...h are common to a scene, it does not necessarily encourage parsimony (iv). A similar approach was seen in the Pascal VOC2008 object segmentation challenge, where the best performing method, by Csurka =-=[6]-=-, worked in two stages. Initially the set of object labels present in the image was estimated, and in the second stage, a label from the estimated label set was assigned to each image pixel. As no cos... |

10 | Exact and approximate inference in associative hierarchical networks using graph cuts
- Russell, Ladicky, et al.
- 2010
(Show Context)
Citation Context ...as Belief Propagation [33] or TRW-S [14], that can minimise arbitrary pairwise energies to be applied [16]. However, reparameterisation methods such as these perform badly on densely connected graphs =-=[15,26]-=-. In this section we show that under assumption, that C(L) is monotonically increasing with respect to L, the problem can be solved efficiently using αβ-swap and αexpansion moves [3], where the number... |

7 | Mid-level cues improve boundary detection
- Ren, Fowlkes, et al.
- 2005
(Show Context)
Citation Context ...gnoring new constant terms the move energy becomes: E ′ (t) = k ′ αδα + ∑ ∑ ρ B l δl(t) = k ′ αδα + ∑ δl(t) ∑ where k ′′ l k B⊆A ′ B l∈B = k ′ αδα + ∑ l∈A l∈A B⊆A\{l} k ′ B∪{l} ρB∪{l} l k ′′ l δl(t), =-=(23)-=- b . Coefficients k ′′ l are non-negative, as ∀B ⊆ A, l ∈ B : k ′ B∪{l} ρB∪{l} l ≥ 0, while coefficient k ′ α is non-negative for all C(L) that are monotonically increasing with respect to L. ∑ = B⊆A\... |

1 |
Geremy Heitz. Learning spatial context: Using stuff to find things
- Koller
(Show Context)
Citation Context |